{"data":[{"id":"10.5281/zenodo.23611353","type":"dois","attributes":{"doi":"10.5281/zenodo.23611353","identifiers":[],"creators":[{"nameType":"Personal","givenName":"Gulrux","familyName":"Akramova","name":"Akramova, Gulrux","nameIdentifiers":[],"affiliation":[]}],"titles":[{"title":"RAQAMLI TEXNOLOGIYALAR VA GADJETLARNING O'SMIRLAR  RUHIYATIGA TA'SIRI"}],"publisher":"Zenodo","container":{},"publicationYear":2025,"subjects":[{"subject":"Kalit so'zlar: Raqamli texnologiyalar, gadjetlar, o'smirlar psixologiyasi, ruhiy  salomatlik, internet, virtual aloqa, ijtimoiy tarmoqlar, axborot xavfsizligi, ota-ona nazorati."}],"contributors":[],"dates":[{"date":"2025-12-24","dateType":"Issued"},{"date":"2025-12-02","dateType":"Accepted"}],"language":"auz","types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":""},"relatedIdentifiers":[{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.23611354","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[{"descriptionType":"Abstract","description":"Annotatsiya: Ushbu maqolada raqamli texnologiyalar va gadjetlarning o‘smirlar ruhiyatiga ta’siri tahlil qilinadi. Bugungi kunda yoshlar orasida smartfon, planshet, kompyuter va internet tarmoqlaridan foydalanish hayotning ajralmas qismiga aylangan. Shu bilan birga, bu texnologik vositalarning ortiqcha ishlatilishi o‘smirlarning psixologik holati, ijtimoiy faolligi, o‘z-o‘zini anglash jarayoni hamda shaxslararo munosabatlariga salbiy ta’sir ko‘rsatishi mumkin. Maqolada raqamli texnologiyalar bilan bog‘liq ijobiy va salbiy omillar, shuningdek, o‘smirlar ruhiy salomatligini saqlashda ota-ona va pedagoglarning roli yoritilgan.. "}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.23611353","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T06:42:55Z","registered":"2026-10-24T06:42:55Z","published":null,"updated":"2026-10-24T06:42:55Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.23611354","type":"dois","attributes":{"doi":"10.5281/zenodo.23611354","identifiers":[{"identifier":"oai:zenodo.org:23611354","identifierType":"oai"}],"creators":[{"nameType":"Personal","givenName":"Gulrux","familyName":"Akramova","name":"Akramova, Gulrux","nameIdentifiers":[],"affiliation":[]}],"titles":[{"title":"RAQAMLI TEXNOLOGIYALAR VA GADJETLARNING O'SMIRLAR  RUHIYATIGA TA'SIRI"}],"publisher":"Zenodo","container":{},"publicationYear":2025,"subjects":[{"subject":"Kalit so'zlar: Raqamli texnologiyalar, gadjetlar, o'smirlar psixologiyasi, ruhiy  salomatlik, internet, virtual aloqa, ijtimoiy tarmoqlar, axborot xavfsizligi, ota-ona nazorati."}],"contributors":[],"dates":[{"date":"2025-12-24","dateType":"Issued"},{"date":"2025-12-02","dateType":"Accepted"}],"language":"auz","types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":""},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.23611353","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[{"descriptionType":"Abstract","description":"Annotatsiya: Ushbu maqolada raqamli texnologiyalar va gadjetlarning o‘smirlar ruhiyatiga ta’siri tahlil qilinadi. Bugungi kunda yoshlar orasida smartfon, planshet, kompyuter va internet tarmoqlaridan foydalanish hayotning ajralmas qismiga aylangan. Shu bilan birga, bu texnologik vositalarning ortiqcha ishlatilishi o‘smirlarning psixologik holati, ijtimoiy faolligi, o‘z-o‘zini anglash jarayoni hamda shaxslararo munosabatlariga salbiy ta’sir ko‘rsatishi mumkin. Maqolada raqamli texnologiyalar bilan bog‘liq ijobiy va salbiy omillar, shuningdek, o‘smirlar ruhiy salomatligini saqlashda ota-ona va pedagoglarning roli yoritilgan.. "}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.23611354","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T06:42:54Z","registered":"2026-10-24T06:42:55Z","published":null,"updated":"2026-10-24T06:42:55Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.23611188","type":"dois","attributes":{"doi":"10.5281/zenodo.23611188","identifiers":[{"identifier":"oai:zenodo.org:23611188","identifierType":"oai"}],"creators":[{"nameType":"Personal","givenName":"Gulrux","familyName":"Akramova","name":"Akramova, Gulrux","nameIdentifiers":[],"affiliation":[]}],"titles":[{"title":"EMOTSIOANL-PSIXOLOGIK BARQARORLIK TUSHUNCHASI VA UNING  SHAKLLANISHI"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"Kalit so'zlar: emotsional barqarorlik, psixologik barqarorlik, hissiy boshqaruv, shaxsiy  rivojlanish, stressga chidamlilik, ijtimoiy moslashuvchanlik, psixologik omillar."}],"contributors":[],"dates":[{"date":"2026-12-24","dateType":"Issued"},{"date":"2025-12-02","dateType":"Available"}],"language":"uz","types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":""},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.23611187","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[{"descriptionType":"Abstract","description":"Annotatsiya: Ushbu maqolada emotsional-psixologik barqarorlik tushunchasi, uning mazmuni va shaxs rivojlanishidagi o‘rni tahlil qilinadi. Maqolada barqaror shaxsiyat shakllanishiga ta’sir qiluvchi psixologik, ijtimoiy va individual omillar ko‘rib chiqiladi. Shuningdek, emotsional- psixologik barqarorlikning pedagogik jarayonlarda va kundalik hayotdagi ahamiyati, uning shakllanishi va rivojlanish bosqichlari haqida ilmiy nazariyalar asosida fikr yuritiladi. Tadqiqot shuni ko‘rsatadiki, emotsional barqarorlik shaxsning stressga chidamliligi, hissiy boshqaruv qobiliyati va ijtimoiy moslashuvchanligini oshiradi."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.23611188","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T06:40:51Z","registered":"2026-10-24T06:40:51Z","published":null,"updated":"2026-10-24T06:40:51Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.23611187","type":"dois","attributes":{"doi":"10.5281/zenodo.23611187","identifiers":[],"creators":[{"nameType":"Personal","givenName":"Gulrux","familyName":"Akramova","name":"Akramova, Gulrux","nameIdentifiers":[],"affiliation":[]}],"titles":[{"title":"EMOTSIOANL-PSIXOLOGIK BARQARORLIK TUSHUNCHASI VA UNING  SHAKLLANISHI"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"Kalit so'zlar: emotsional barqarorlik, psixologik barqarorlik, hissiy boshqaruv, shaxsiy  rivojlanish, stressga chidamlilik, ijtimoiy moslashuvchanlik, psixologik omillar."}],"contributors":[],"dates":[{"date":"2026-12-24","dateType":"Issued"},{"date":"2025-12-02","dateType":"Available"}],"language":"uz","types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":""},"relatedIdentifiers":[{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.23611188","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[{"descriptionType":"Abstract","description":"Annotatsiya: Ushbu maqolada emotsional-psixologik barqarorlik tushunchasi, uning mazmuni va shaxs rivojlanishidagi o‘rni tahlil qilinadi. Maqolada barqaror shaxsiyat shakllanishiga ta’sir qiluvchi psixologik, ijtimoiy va individual omillar ko‘rib chiqiladi. Shuningdek, emotsional- psixologik barqarorlikning pedagogik jarayonlarda va kundalik hayotdagi ahamiyati, uning shakllanishi va rivojlanish bosqichlari haqida ilmiy nazariyalar asosida fikr yuritiladi. Tadqiqot shuni ko‘rsatadiki, emotsional barqarorlik shaxsning stressga chidamliligi, hissiy boshqaruv qobiliyati va ijtimoiy moslashuvchanligini oshiradi."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.23611187","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T06:40:51Z","registered":"2026-10-24T06:40:51Z","published":null,"updated":"2026-10-24T06:40:51Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.6084/m9.figshare.34763439.v1","type":"dois","attributes":{"doi":"10.6084/m9.figshare.34763439.v1","identifiers":[],"creators":[{"givenName":"La","familyName":"Parquer","name":"La Parquer","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"\u003cb\u003eThe Settlement of Canaan\u003c/b\u003e"}],"publisher":"figshare","container":{},"publicationYear":2026,"subjects":[{"classificationCode":"440107","schemeUri":"http://www.abs.gov.au/ausstats/abs@.nsf/0/6BB427AB9696C225CA2574180004463E","subject":"Social and cultural anthropology","subjectScheme":"ANZSRC Fields of Research"}],"contributors":[],"dates":[{"date":"2026-10-24","dateType":"Created"},{"date":"2026-10-24","dateType":"Updated"},{"date":"2026-10-24","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":"Thesis"},"relatedIdentifiers":[{"relationType":"IsIdenticalTo","relatedIdentifier":"10.6084/m9.figshare.34763439","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["375387 Bytes"],"formats":[],"version":"1","rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[{"descriptionType":"Abstract","description":"This paper argues that the people conventionally designated “Canaanites” were not later arrivals to the southern Levant but were, in the fullest material and cultural sense, the indigenous founding population of that region — Semitic-speaking agro-pastoralists whose continuous occupation from the Neolithic through the Roman period constitutes one of the longest and most consequential trajectories of cultural evolution in the ancient world. Drawing on the materialist theoretical framework advanced by Marvin Harris in The Rise of Anthropological Theory (1968), this paper traces the physical archaeological evidence from initial Neolithic settlement through the emergence of Bronze Age urbanism, the development of inter-regional trade networks, the invention of alphabetic writing, the Iron Age reorganisation of society, and the persistence of Canaanite cultural and demographic identity through the Hellenistic and early Roman periods to approximately 100 CE. The argument is advanced that the driving mechanism of Canaanite social evolution was not external conquest or ideational change but the material logic of agricultural surplus, craft specialisation, and the requirements of long-distance exchange — the infrastructural conditions that Harris identifies as the primary determinants of cultural superstructure."}],"geoLocations":[],"fundingReferences":[],"url":"https://figshare.com/articles/thesis/_b_The_Settlement_of_Canaan_b_/34763439/1","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T06:34:38Z","registered":"2026-10-24T06:34:39Z","published":null,"updated":"2026-10-24T06:34:40Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}}}},{"id":"10.6084/m9.figshare.34763439","type":"dois","attributes":{"doi":"10.6084/m9.figshare.34763439","identifiers":[],"creators":[{"givenName":"La","familyName":"Parquer","name":"La Parquer","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"\u003cb\u003eThe Settlement of Canaan\u003c/b\u003e"}],"publisher":"figshare","container":{},"publicationYear":2026,"subjects":[{"classificationCode":"440107","schemeUri":"http://www.abs.gov.au/ausstats/abs@.nsf/0/6BB427AB9696C225CA2574180004463E","subject":"Social and cultural anthropology","subjectScheme":"ANZSRC Fields of Research"}],"contributors":[],"dates":[{"date":"2026-10-24","dateType":"Created"},{"date":"2026-10-24","dateType":"Updated"},{"date":"2026-10-24","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":"Thesis"},"relatedIdentifiers":[],"relatedItems":[],"sizes":["375387 Bytes"],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[{"descriptionType":"Abstract","description":"This paper argues that the people conventionally designated “Canaanites” were not later arrivals to the southern Levant but were, in the fullest material and cultural sense, the indigenous founding population of that region — Semitic-speaking agro-pastoralists whose continuous occupation from the Neolithic through the Roman period constitutes one of the longest and most consequential trajectories of cultural evolution in the ancient world. Drawing on the materialist theoretical framework advanced by Marvin Harris in The Rise of Anthropological Theory (1968), this paper traces the physical archaeological evidence from initial Neolithic settlement through the emergence of Bronze Age urbanism, the development of inter-regional trade networks, the invention of alphabetic writing, the Iron Age reorganisation of society, and the persistence of Canaanite cultural and demographic identity through the Hellenistic and early Roman periods to approximately 100 CE. The argument is advanced that the driving mechanism of Canaanite social evolution was not external conquest or ideational change but the material logic of agricultural surplus, craft specialisation, and the requirements of long-distance exchange — the infrastructural conditions that Harris identifies as the primary determinants of cultural superstructure."}],"geoLocations":[],"fundingReferences":[],"url":"https://figshare.com/articles/thesis/_b_The_Settlement_of_Canaan_b_/34763439","contentUrl":null,"metadataVersion":1,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T06:31:46Z","registered":"2026-10-24T06:34:39Z","published":null,"updated":"2026-10-24T06:34:39Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}}}},{"id":"10.5281/zenodo.23611147","type":"dois","attributes":{"doi":"10.5281/zenodo.23611147","identifiers":[{"identifier":"oai:zenodo.org:23611147","identifierType":"oai"}],"creators":[{"nameType":"Personal","givenName":"Gulrux","familyName":"Akramova","name":"Akramova, Gulrux","nameIdentifiers":[],"affiliation":[]}],"titles":[{"title":"Psixologiya fanida o'smirlarning emotsional psixologik barqarorligini ta'minlash muammosi"}],"publisher":"Zenodo","container":{},"publicationYear":2025,"subjects":[{"subject":"Kalit so'zlar: o'smirlik davri, emotsional barqarorlik, psixologik muvozanat,  stress, shaxs rivojlanishi, psixoprofilaktika, ruhiy salomatlik, moslashuv, ijtimoiy  muhit, psixokorreksiya."}],"contributors":[],"dates":[{"date":"2025-10-24","dateType":"Issued"},{"date":"2025-09-02","dateType":"Available"}],"language":"uz","types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":""},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.23611146","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[{"descriptionType":"Abstract","description":"Annotatsiya: Ushbu maqolada psixologiya fanida o‘smirlarning emotsionalpsixologik barqarorligini ta’minlash muammosi tahlil qilinadi. O‘smirlik davri inson hayotidagi o‘tish davri bo‘lib, bu bosqichda shaxsning hissiy holati, o‘z-o‘zini anglash jarayoni va ijtimoiy moslashuvi faol rivojlanadi. Shu sababli, emotsional beqarorlik, stress, xavotir, o‘zini past baholash kabi holatlar tez-tez uchraydi. Maqolada o‘smirlarning ruhiy barqarorligini shakllantirishda oilaning, maktab psixologi va pedagoglarning roli, shuningdek, psixoprofilaktik va psixokorreksion ishlarning ahamiyati yoritilgan."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.23611147","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T06:32:07Z","registered":"2026-10-24T06:32:07Z","published":null,"updated":"2026-10-24T06:32:07Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.23611146","type":"dois","attributes":{"doi":"10.5281/zenodo.23611146","identifiers":[],"creators":[{"nameType":"Personal","givenName":"Gulrux","familyName":"Akramova","name":"Akramova, Gulrux","nameIdentifiers":[],"affiliation":[]}],"titles":[{"title":"Psixologiya fanida o'smirlarning emotsional psixologik barqarorligini ta'minlash muammosi"}],"publisher":"Zenodo","container":{},"publicationYear":2025,"subjects":[{"subject":"Kalit so'zlar: o'smirlik davri, emotsional barqarorlik, psixologik muvozanat,  stress, shaxs rivojlanishi, psixoprofilaktika, ruhiy salomatlik, moslashuv, ijtimoiy  muhit, psixokorreksiya."}],"contributors":[],"dates":[{"date":"2025-10-24","dateType":"Issued"},{"date":"2025-09-02","dateType":"Available"}],"language":"uz","types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":""},"relatedIdentifiers":[{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.23611147","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[{"descriptionType":"Abstract","description":"Annotatsiya: Ushbu maqolada psixologiya fanida o‘smirlarning emotsionalpsixologik barqarorligini ta’minlash muammosi tahlil qilinadi. O‘smirlik davri inson hayotidagi o‘tish davri bo‘lib, bu bosqichda shaxsning hissiy holati, o‘z-o‘zini anglash jarayoni va ijtimoiy moslashuvi faol rivojlanadi. Shu sababli, emotsional beqarorlik, stress, xavotir, o‘zini past baholash kabi holatlar tez-tez uchraydi. Maqolada o‘smirlarning ruhiy barqarorligini shakllantirishda oilaning, maktab psixologi va pedagoglarning roli, shuningdek, psixoprofilaktik va psixokorreksion ishlarning ahamiyati yoritilgan."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.23611146","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T06:32:07Z","registered":"2026-10-24T06:32:07Z","published":null,"updated":"2026-10-24T06:32:07Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.23610814","type":"dois","attributes":{"doi":"10.5281/zenodo.23610814","identifiers":[{"identifier":"oai:zenodo.org:23610814","identifierType":"oai"}],"creators":[{"nameType":"Personal","affiliation":["GRE Foundry"],"givenName":"Garret R J","familyName":"Krampe","name":"Krampe, Garret R J","nameIdentifiers":[]}],"titles":[{"title":"The Polymath with AI Enhancements: Scientific Discovery, AGI, Superintelligence and Institutional Gatekeeping"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-10-24","dateType":"Issued"}],"language":"en","types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":""},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.23610813","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":"1.0","rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution Non Commercial No Derivatives 4.0 International","rightsIdentifier":"cc-by-nc-nd-4.0"},{"rightsUri":"http://rightsstatements.org/vocab/InC/1.0/","rights":"© 2025-2026 Garret R. J. Krampe (GRE Foundry)"}],"descriptions":[{"descriptionType":"Abstract","description":"The Polymath with AI Enhancements: Scientific Discovery, AGI, Superintelligence and Institutional Gatekeeping\n\nDescription\n\nThis publication presents two companion papers examining the future of scientific discovery in an era of artificial intelligence, the limitations of autonomous AI research, and the institutional structures governing scientific validity.\n\nPaper 1: The Polymath with AI Enhancements: Human-Directed Discovery Versus Artificial General Intelligence and Superintelligence\n\nThis paper investigates whether a human polymath supported by specialised AI assistants may offer a more effective architecture for scientific discovery than autonomous Artificial General Intelligence (AGI) or hypothetical Superintelligence (SI).\n\nIt examines the combinatorial explosion of possible relationships within large knowledge systems, the importance of first-principles reasoning, causal selection, conceptual continuity, relevance filtering, and the distinction between computational correctness and scientific understanding.\n\nThe development of Regulated Trinary Reduction Theory (RTRT) and the MREPY computational framework provides a case study of AI-assisted scientific investigation, including repeated instances of conceptual drift despite successful mathematical and software verification.\n\nThe paper proposes comparative research methods for evaluating scientific productivity, hypothesis quality, computational efficiency, conceptual fidelity, and independently validated discovery.\n\nPaper 2: Beyond Gatekeeping: Scientific Validity, Academic Freedom, and the Polymath–AI Research Architecture\n\nThis companion discussion examines the institutional implications of AI-enhanced independent research.\n\nIt considers the distinction between scientific validity and institutional acceptance, the strengths and limitations of conventional peer review, academic freedom, institutional governance, ideological conformity, and the potential for artificial intelligence to reproduce established assumptions and institutional biases.\n\nThe discussion considers contested academic-freedom disputes, including the Joanna Howe controversy, and proposes more transparent systems of independent verification, adversarial review, reproducibility, and post-publication scientific criticism.\n\nCentral Proposition\n\nScientific discovery is not determined solely by the volume of available information or computational processing capacity. It also requires the ability to identify meaningful relationships, challenge inherited assumptions, preserve conceptual coherence, reject irrelevant possibilities, and distinguish mathematical consistency from physical reality.\n\nHuman-directed, AI-enhanced research may provide an effective alternative or complement to increasingly autonomous scientific AI systems.\n\nTogether, these papers propose that scientific authority should ultimately rest upon transparent reasoning, reproducible evidence, falsifiable predictions, and independent verification rather than institutional endorsement alone.\n\nThe publications are conceptual and methodological research contributions. They do not claim experimental validation of RTRT or establish that any particular human–AI architecture is universally superior.\n\nKeywords\n\nArtificial Intelligence; AGI; Superintelligence; Polymath; Human–AI Collaboration; Scientific Discovery; First Principles; Philosophy of Science; Scientific Method; Conceptual Drift; Computational Complexity; Independent Research; Peer Review; Academic Freedom; Institutional Gatekeeping; Scientific Validation; RTRT; MREPY.\n\nCopyright and Licence\n\nCopyright © 2026 GRE Foundry.\n\nBoth papers are released under Creative Commons Attribution–NonCommercial–NoDerivatives 4.0 International (CC BY-NC-ND 4.0).\n\nNoncommercial sharing of the unmodified works is permitted with appropriate attribution. Distribution of modified versions requires separate permission.\n\nhttps://creativecommons.org/licenses/by-nc-nd/4.0/"}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.23610814","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T06:27:50Z","registered":"2026-10-24T06:27:50Z","published":null,"updated":"2026-10-24T06:27:50Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.23610813","type":"dois","attributes":{"doi":"10.5281/zenodo.23610813","identifiers":[],"creators":[{"nameType":"Personal","affiliation":["GRE Foundry"],"givenName":"Garret R J","familyName":"Krampe","name":"Krampe, Garret R J","nameIdentifiers":[]}],"titles":[{"title":"The Polymath with AI Enhancements: Scientific Discovery, AGI, Superintelligence and Institutional Gatekeeping"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-10-24","dateType":"Issued"}],"language":"en","types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":""},"relatedIdentifiers":[{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.23610814","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":"1.0","rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution Non Commercial No Derivatives 4.0 International","rightsIdentifier":"cc-by-nc-nd-4.0"},{"rightsUri":"http://rightsstatements.org/vocab/InC/1.0/","rights":"© 2025-2026 Garret R. J. Krampe (GRE Foundry)"}],"descriptions":[{"descriptionType":"Abstract","description":"The Polymath with AI Enhancements: Scientific Discovery, AGI, Superintelligence and Institutional Gatekeeping\n\nDescription\n\nThis publication presents two companion papers examining the future of scientific discovery in an era of artificial intelligence, the limitations of autonomous AI research, and the institutional structures governing scientific validity.\n\nPaper 1: The Polymath with AI Enhancements: Human-Directed Discovery Versus Artificial General Intelligence and Superintelligence\n\nThis paper investigates whether a human polymath supported by specialised AI assistants may offer a more effective architecture for scientific discovery than autonomous Artificial General Intelligence (AGI) or hypothetical Superintelligence (SI).\n\nIt examines the combinatorial explosion of possible relationships within large knowledge systems, the importance of first-principles reasoning, causal selection, conceptual continuity, relevance filtering, and the distinction between computational correctness and scientific understanding.\n\nThe development of Regulated Trinary Reduction Theory (RTRT) and the MREPY computational framework provides a case study of AI-assisted scientific investigation, including repeated instances of conceptual drift despite successful mathematical and software verification.\n\nThe paper proposes comparative research methods for evaluating scientific productivity, hypothesis quality, computational efficiency, conceptual fidelity, and independently validated discovery.\n\nPaper 2: Beyond Gatekeeping: Scientific Validity, Academic Freedom, and the Polymath–AI Research Architecture\n\nThis companion discussion examines the institutional implications of AI-enhanced independent research.\n\nIt considers the distinction between scientific validity and institutional acceptance, the strengths and limitations of conventional peer review, academic freedom, institutional governance, ideological conformity, and the potential for artificial intelligence to reproduce established assumptions and institutional biases.\n\nThe discussion considers contested academic-freedom disputes, including the Joanna Howe controversy, and proposes more transparent systems of independent verification, adversarial review, reproducibility, and post-publication scientific criticism.\n\nCentral Proposition\n\nScientific discovery is not determined solely by the volume of available information or computational processing capacity. It also requires the ability to identify meaningful relationships, challenge inherited assumptions, preserve conceptual coherence, reject irrelevant possibilities, and distinguish mathematical consistency from physical reality.\n\nHuman-directed, AI-enhanced research may provide an effective alternative or complement to increasingly autonomous scientific AI systems.\n\nTogether, these papers propose that scientific authority should ultimately rest upon transparent reasoning, reproducible evidence, falsifiable predictions, and independent verification rather than institutional endorsement alone.\n\nThe publications are conceptual and methodological research contributions. They do not claim experimental validation of RTRT or establish that any particular human–AI architecture is universally superior.\n\nKeywords\n\nArtificial Intelligence; AGI; Superintelligence; Polymath; Human–AI Collaboration; Scientific Discovery; First Principles; Philosophy of Science; Scientific Method; Conceptual Drift; Computational Complexity; Independent Research; Peer Review; Academic Freedom; Institutional Gatekeeping; Scientific Validation; RTRT; MREPY.\n\nCopyright and Licence\n\nCopyright © 2026 GRE Foundry.\n\nBoth papers are released under Creative Commons Attribution–NonCommercial–NoDerivatives 4.0 International (CC BY-NC-ND 4.0).\n\nNoncommercial sharing of the unmodified works is permitted with appropriate attribution. Distribution of modified versions requires separate permission.\n\nhttps://creativecommons.org/licenses/by-nc-nd/4.0/"}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.23610813","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T06:27:50Z","registered":"2026-10-24T06:27:50Z","published":null,"updated":"2026-10-24T06:27:50Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.6084/m9.figshare.34763001.v1","type":"dois","attributes":{"doi":"10.6084/m9.figshare.34763001.v1","identifiers":[],"creators":[{"givenName":"ANASTASIA","familyName":"THEOCHARI","name":"ANASTASIA THEOCHARI","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","schemeUri":"https://orcid.org","nameIdentifier":"https://orcid.org/0009-0006-0255-8579"}],"affiliation":[]}],"titles":[{"title":"Human Centred Digital Leadership and the Digital Transformation of Public Organisations Challenges and Prospects for the Greek Public Sector Workforce"}],"publisher":"figshare","container":{},"publicationYear":2026,"subjects":[{"classificationCode":"520403","schemeUri":"http://www.abs.gov.au/ausstats/abs@.nsf/0/6BB427AB9696C225CA2574180004463E","subject":"Learning, motivation and emotion","subjectScheme":"ANZSRC Fields of Research"},{"classificationCode":"520402","schemeUri":"http://www.abs.gov.au/ausstats/abs@.nsf/0/6BB427AB9696C225CA2574180004463E","subject":"Decision making","subjectScheme":"ANZSRC Fields of Research"}],"contributors":[],"dates":[{"date":"2026-10-24","dateType":"Created"},{"date":"2026-10-24","dateType":"Updated"},{"date":"2026-10-24","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":"Thesis"},"relatedIdentifiers":[{"relationType":"IsIdenticalTo","relatedIdentifier":"10.6084/m9.figshare.34763001","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["3948471 Bytes"],"formats":[],"version":"1","rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[{"descriptionType":"Abstract","description":"Digital transformation in public organizations is not merely a technological upgrade, but a process of organizational change that reshapes administrative practices, forms of work, and modes of public value creation. This thesis examines digital transformation from the perspective of employees, focusing on the role of human-centered digital leadership, predispositions toward digital change, willingness to participate, and techno-overload. The purpose of the study was to investigate whether human-centered digital leadership is associated with the willingness of Greek public sector employees to participate in digital transformation initiatives through cognitive and emotional predisposition, and whether techno-overload conditions the strength of these indirect relationships.The study followed a quantitative, explanatory, and cross-sectional research design. Data were collected through a structured online self-report questionnaire from 726 employees in the Greek public sector and were analyzed using IBM SPSS Statistics. The analysis included descriptive statistics, reliability and validity tests, correlations, linear regressions, and a conditional mediation analysis using bootstrap confidence intervals.The findings showed that human-centered digital leadership is positively associated with cognitive predisposition, emotional predisposition, and willingness to participate. In the integrated conditional mediation model, emotional predisposition emerged as the key intervening mechanism linking leadership to willingness to participate, whereas cognitive predisposition did not retain a comparable independent indirect effect when examined simultaneously with emotional predisposition. Techno-overload was not confirmed as a statistically significant moderating condition, and no statistically significant conditional mediation was established. Overall, willingness to participate in digital transformation appears to depend less on the formal acceptance of change and more on whether digital transition acquires positive work-related meaning through human-centered leadership practices."}],"geoLocations":[],"fundingReferences":[{"funderIdentifierType":"ROR","funderName":"Centers for Disease Control and Prevention","funderIdentifier":"https://ror.org/042twtr12","schemeUri":"https://ror.org/","awardTitle":"None","awardNumber":"U2GPS000658"}],"url":"https://figshare.com/articles/thesis/Human_Centred_Digital_Leadership_and_the_Digital_Transformation_of_Public_Organisations_Challenges_and_Prospects_for_the_Greek_Public_Sector_Workforce/34763001/1","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T06:01:37Z","registered":"2026-10-24T06:01:38Z","published":null,"updated":"2026-10-24T06:01:39Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}}}},{"id":"10.6084/m9.figshare.34763001","type":"dois","attributes":{"doi":"10.6084/m9.figshare.34763001","identifiers":[],"creators":[{"givenName":"ANASTASIA","familyName":"THEOCHARI","name":"ANASTASIA THEOCHARI","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","schemeUri":"https://orcid.org","nameIdentifier":"https://orcid.org/0009-0006-0255-8579"}],"affiliation":[]}],"titles":[{"title":"Human Centred Digital Leadership and the Digital Transformation of Public Organisations Challenges and Prospects for the Greek Public Sector Workforce"}],"publisher":"figshare","container":{},"publicationYear":2026,"subjects":[{"classificationCode":"520403","schemeUri":"http://www.abs.gov.au/ausstats/abs@.nsf/0/6BB427AB9696C225CA2574180004463E","subject":"Learning, motivation and emotion","subjectScheme":"ANZSRC Fields of Research"},{"classificationCode":"520402","schemeUri":"http://www.abs.gov.au/ausstats/abs@.nsf/0/6BB427AB9696C225CA2574180004463E","subject":"Decision making","subjectScheme":"ANZSRC Fields of Research"}],"contributors":[],"dates":[{"date":"2026-10-24","dateType":"Created"},{"date":"2026-10-24","dateType":"Updated"},{"date":"2026-10-24","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":"Thesis"},"relatedIdentifiers":[],"relatedItems":[],"sizes":["3948471 Bytes"],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[{"descriptionType":"Abstract","description":"Digital transformation in public organizations is not merely a technological upgrade, but a process of organizational change that reshapes administrative practices, forms of work, and modes of public value creation. This thesis examines digital transformation from the perspective of employees, focusing on the role of human-centered digital leadership, predispositions toward digital change, willingness to participate, and techno-overload. The purpose of the study was to investigate whether human-centered digital leadership is associated with the willingness of Greek public sector employees to participate in digital transformation initiatives through cognitive and emotional predisposition, and whether techno-overload conditions the strength of these indirect relationships.The study followed a quantitative, explanatory, and cross-sectional research design. Data were collected through a structured online self-report questionnaire from 726 employees in the Greek public sector and were analyzed using IBM SPSS Statistics. The analysis included descriptive statistics, reliability and validity tests, correlations, linear regressions, and a conditional mediation analysis using bootstrap confidence intervals.The findings showed that human-centered digital leadership is positively associated with cognitive predisposition, emotional predisposition, and willingness to participate. In the integrated conditional mediation model, emotional predisposition emerged as the key intervening mechanism linking leadership to willingness to participate, whereas cognitive predisposition did not retain a comparable independent indirect effect when examined simultaneously with emotional predisposition. Techno-overload was not confirmed as a statistically significant moderating condition, and no statistically significant conditional mediation was established. Overall, willingness to participate in digital transformation appears to depend less on the formal acceptance of change and more on whether digital transition acquires positive work-related meaning through human-centered leadership practices."}],"geoLocations":[],"fundingReferences":[{"funderIdentifierType":"ROR","funderName":"Centers for Disease Control and Prevention","funderIdentifier":"https://ror.org/042twtr12","schemeUri":"https://ror.org/","awardTitle":"None","awardNumber":"U2GPS000658"}],"url":"https://figshare.com/articles/thesis/Human_Centred_Digital_Leadership_and_the_Digital_Transformation_of_Public_Organisations_Challenges_and_Prospects_for_the_Greek_Public_Sector_Workforce/34763001","contentUrl":null,"metadataVersion":1,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T05:32:01Z","registered":"2026-10-24T06:01:38Z","published":null,"updated":"2026-10-24T06:01:38Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}}}},{"id":"10.5281/zenodo.23610721","type":"dois","attributes":{"doi":"10.5281/zenodo.23610721","identifiers":[],"creators":[{"nameType":"Personal","givenName":"Shokhrukhbek","familyName":"Yuldoshev","name":"Yuldoshev, Shokhrukhbek","nameIdentifiers":[],"affiliation":[]},{"nameType":"Personal","givenName":"D","familyName":"Muhamadiyeva","name":"Muhamadiyeva, D","nameIdentifiers":[],"affiliation":[]},{"nameType":"Personal","givenName":"D","familyName":"Yusupova","name":"Yusupova, D","nameIdentifiers":[],"affiliation":[]},{"nameType":"Personal","givenName":"D","familyName":"Yusupov","name":"Yusupov, D","nameIdentifiers":[],"affiliation":[]}],"titles":[{"title":"CALCULATION BASED ON OPTIMIZATION OF ARITHMETIC OPERATIONS ON Z-NUMBERS"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-04-21","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":""},"relatedIdentifiers":[{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.23610722","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.23610721","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T06:01:17Z","registered":"2026-10-24T06:01:17Z","published":null,"updated":"2026-10-24T06:01:17Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.23610722","type":"dois","attributes":{"doi":"10.5281/zenodo.23610722","identifiers":[{"identifier":"oai:zenodo.org:23610722","identifierType":"oai"}],"creators":[{"nameType":"Personal","givenName":"Shokhrukhbek","familyName":"Yuldoshev","name":"Yuldoshev, Shokhrukhbek","nameIdentifiers":[],"affiliation":[]},{"nameType":"Personal","givenName":"D","familyName":"Muhamadiyeva","name":"Muhamadiyeva, D","nameIdentifiers":[],"affiliation":[]},{"nameType":"Personal","givenName":"D","familyName":"Yusupova","name":"Yusupova, D","nameIdentifiers":[],"affiliation":[]},{"nameType":"Personal","givenName":"D","familyName":"Yusupov","name":"Yusupov, D","nameIdentifiers":[],"affiliation":[]}],"titles":[{"title":"CALCULATION BASED ON OPTIMIZATION OF ARITHMETIC OPERATIONS ON Z-NUMBERS"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-04-21","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":""},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.23610721","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.23610722","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T06:01:17Z","registered":"2026-10-24T06:01:17Z","published":null,"updated":"2026-10-24T06:01:17Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.48620/101961","type":"dois","attributes":{"doi":"10.48620/101961","identifiers":[{"identifier":"urn:nbn:ch:bel-bes-13693","identifierType":"URN"}],"creators":[{"affiliation":["Faculty of Science"],"name":"Li, Shaopeng","nameIdentifiers":[]}],"titles":[{"title":"Remote sensing of land surface albedo and biophysical effects of vegetation dynamics on climate"}],"publisher":"University of Bern","container":{},"publicationYear":2026,"subjects":[{"subject":"Albedo"},{"subject":"Amazon"},{"subject":"Dryland"},{"subject":"Remote Sensing"},{"subject":"land surface energy balance"},{"subject":"land-atmosphere interactions"}],"contributors":[],"dates":[{"date":"2026","dateType":"Issued"},{"date":"2026","dateType":"Accepted"},{"date":"2026-10-23T14:32:34Z","dateType":"Available"}],"language":"en","types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":"dissertation"},"relatedIdentifiers":[],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[],"descriptions":[{"descriptionType":"Abstract","description":"Land surface albedo regulates the surface energy balance by controlling solar radiation reflection and absorption, influencing surface temperature and land–atmosphere interactions. Vegetation greening and browning modify albedo, evapotranspiration, aerodynamic roughness, and energy partitioning, thereby altering exchanges of energy, water, and carbon. These changes produce radiative and non-radiative climate effects across regional to global scales. Understanding these coupled processes is essential for predicting ecosystem responses to environmental change and their climatic consequences."}],"geoLocations":[],"fundingReferences":[],"url":"https://boris-portal.unibe.ch/handle/20.500.12422/255542","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-23T15:00:22Z","registered":"2026-10-23T15:00:57Z","published":null,"updated":"2026-10-24T06:00:19Z"},"relationships":{"client":{"data":{"id":"unibe.boris-portal","type":"clients"}}}},{"id":"10.48620/101800","type":"dois","attributes":{"doi":"10.48620/101800","identifiers":[{"identifier":"urn:nbn:ch:bel-bes-13705","identifierType":"URN"}],"creators":[{"affiliation":["Faculty of Science"],"name":"Masanti, Corina Danja","nameIdentifiers":[]}],"titles":[{"title":"Boosting and transferable representations for grammatical error detection"}],"publisher":"University of Bern","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026","dateType":"Issued"},{"date":"2026","dateType":"Accepted"},{"date":"2026-10-23T14:52:08Z","dateType":"Available"}],"language":"en","types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":"dissertation"},"relatedIdentifiers":[],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[],"descriptions":[{"descriptionType":"Abstract","description":"Automated proofreading aims to support writers by identifying and correcting potential errors in written text. In natural language processing, these tasks are commonly studied within grammatical error detection and correction. Both have benefited substantially from transformer-based language models capable of capturing complex linguistic patterns and adapting to different tasks. Nevertheless, reliably detecting and correcting errors remains difficult under realistic proofreading conditions. Current systems still struggle when annotated data is limited, when errors are subtle and context-dependent, and when models need to be adapted efficiently to new error types, domains, or languages. These challenges are especially relevant beyond standard benchmark settings, where data is often less abundant, error distributions are uneven, and distinguishing between correct and incorrect language use can be difficult to model. This thesis investigates grammatical error detection within the broader setting of automated proofreading, with a focus on realistic proofreading data, difficult error types, and efficient adaptation. It addresses three central challenges. First, annotated data for grammatical error detection and correction is unevenly available across languages, domains, and error categories. While English has received substantial attention, other languages remain less well represented. Second, some error types are particularly difficult to detect because they cannot be identified from the erroneous word form alone. This is especially true for real-word errors, where the incorrect word is itself a valid word in the dictionary but is inappropriate in the given context of the sentence. Third, although modern language models are effective, their repeated adaptation can be computationally expensive, especially when separate models or training runs are required for different error types. The thesis makes three main contributions. It introduces and analyzes a multilingual real-world proofreading data set based on manual corrections by professional proofreaders. This data set provides a realistic basis for studying grammatical error detection in professionally edited texts. Building on this broad analysis, the thesis then focuses on context-dependent real-word errors and develops a boosting-inspired training strategy for their detection. The method uses validation errors to identify cases that remain difficult for the model and selects additional synthetic examples accordingly. These examples are then integrated step by step during training. Finally, the thesis investigates efficient adaptation between error types through post-hoc embedding alignment. Instead of fine-tuning a separate model for each target error type, it examines whether representations from different error types can be aligned so that knowledge learned in one setting can be reused in another. In exhaustive and thorough experimental evaluations, three main findings emerge. First, the real-world proofreading data reveals that the limitations of current automated error detection systems depend strongly on the error type. Second, for context-dependent real-word errors, systematically selected synthetic data improves detection more effectively than untargeted data selection. Third, representation-level alignment enables transfer between error types without repeated model fine-tuning, with the effectiveness of this transfer depending on the relation between the source and target error types."}],"geoLocations":[],"fundingReferences":[],"url":"https://boris-portal.unibe.ch/handle/20.500.12422/255192","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-23T15:00:22Z","registered":"2026-10-23T15:00:54Z","published":null,"updated":"2026-10-24T06:00:18Z"},"relationships":{"client":{"data":{"id":"unibe.boris-portal","type":"clients"}}}},{"id":"10.5281/zenodo.23296718","type":"dois","attributes":{"doi":"10.5281/zenodo.23296718","identifiers":[{"identifier":"oai:zenodo.org:23296718","identifierType":"oai"}],"creators":[{"nameType":"Personal","givenName":"Li","familyName":"Y.Y.N.","name":"Y.Y.N., Li","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0009-0002-6471-139x"}],"affiliation":[]}],"titles":[{"title":"In-Weight Computing"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-10-11","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":""},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.22097583","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[{"descriptionType":"Abstract","description":"1. Overview and Research Positioning\n\n\n\nEarly connectionist formalisms treated connection topology and computational state as fundamentally unified (McCulloch and Pitts, 1943). In contrast, constrained by the physical limitations of early discrete electronics, stored-program computing formalized a foundational separation between computational operators and mutable state at both physical and operational levels (von Neumann, 1945)—a pragmatic engineering compromise that sacrificed endogenous unity to secure manufacturability and deterministic execution. This architectural division remains the default assumption of modern mainstream deep learning: in standard fixed-weight inference, learned parameters are relegated to immutable, read-only operators, while the evolution of all dynamic, mutable state is offloaded entirely to transient activations, recurrent vectors, and external attention key-value caches.\n\nWe investigate a complementary computational organization:  In-Weight Computing. In this setting, selected parameter coordinates serve as addressable, writable state while continuing to participate in the model's computational operators. We formulate a parameter-level framework in which declared readout maps and state-transition relations specify stored contents, functional addresses, and the intended effects of write operations. Geometrically,  the framework connects continuous parameter updates to declared discrete state transitions through constrained subspace projections, providing a testable operational interface between neural representations and symbolic state manipulation. Auditability and rollback are specified through update records and explicit criteria for restoring declared parameter and memory states.\n\nHinton \u0026 Plaut (1987), Ba et al. (2016), and Schlag et al. (2021) successively introduced the concepts of fast weights and fast weight programmers, establishing a viable pathway for storing and manipulating information through dynamic adjustments of connection weights. We share this broad objective and focus on a constrained writable interface: requested changes to stored content, preservation of declared baseline responses, and readout requirements are specified and evaluated together. The distinction lies in these explicit interface requirements and their validation,  rather than in a general opposition to fast-weight update mechanisms.\n\nMathematically, writing is formulated as a constrained inverse problem: construct an update within the selected parameter domain that realizes the requested state change while satisfying specified response-error and Kullback–Leibler (KL) divergence budgets on declared evaluation inputs and output distributions. Response-Jacobian null spaces and near-kernel operators provide local, first-order geometric constructions. Geometric conditions do not, by themselves, guarantee finite-update acceptance. They depend on nonlinear residuals and numerical error; we therefore state geometric conditions separately from empirical acceptance criteria, with explicit coordinates, domains, and tolerances.\n\n2. Current Evidence and Validation Targets\n\nEvidence snapshot: 23 October 2026. Each capability claim is restricted to its recorded model, parameter coordinates, protocol, workload and evaluation scope. Layers I–IV organize the research questions; LC1–LC6 denote validation targets; C-numbered identifiers denote experimental runs. The targets form a claim-dependent partial order rather than a strictly serial ladder. The prospective coverage requirements below guide future evaluations and do not retroactively change earlier experimental decisions.\n\nLC1: local development target met. C35–C37 meet the declared LC1 local development acceptance target with both frozen composite writers. Each final proposal uses prewrite information and requires no online Jacobian construction, singular value decomposition (SVD), postwrite response correction, backtracking or teacher fallback. Offline fitting and calibration remain part of writer preparation. Independent archival and model-level confirmation of those specific local results remains pending; subsequent audits of other experiments do not discharge that requirement.\n\nLC2: open. C140 achieved complete acceptance on its declared 36-state training cohort in each of two rounds. Its frozen writer subsequently passed 42/48 prospectively declared local confirmation states in each C141 round, retaining six response-preservation failures. C142 completed a read-only audit that retained the C141 failure decision. Later training-side comparisons and numerical diagnostics provide additional development evidence, but no successful excluded-input acceptance result has been established.\n\nEvidence provenance. The present update distinguishes original-archive-backed records for C141, C142, C148 and C150 from supplied execution-log evidence for C154–C156. The latter records report completed diagnostics or audits, but their original result ZIPs have not been independently reverified for this update. C157 software has been delivered; its formal GPT-2 execution result is pending. Archive consistency, fresh model replay and capability acceptance are separate evidence levels.\n\nThe earlier development record remains relevant. C63 reported acceptance on 108/108 training states but only 38/48 prospectively declared new states from trained input classes; ten failed response preservation. On a different twelve-state cohort, C136 passed 11/12 and C137 passed 12/12 under the unchanged response budget of 0.002. C138 V2 then encountered 22 preparation failures among 24 requested confirmation states; frozen C137 passed 1/24 overall and one of the two valid preparations. C139 changed those exposed coordinates through a declared projected-preparation construction: all 24 projected preparations passed, and frozen C137 passed 23/24. These development results neither rescue the original C138 coordinates nor constitute independent confirmation.  All 24 projected states subsequently entered C140 training.\n\nThe following selected record separates training qualification, confirmation boundaries and numerical diagnostics.\n\n\n\n\nRun\nRecorded result\nInterpretation and boundary\n\n\nC140: expanded training acceptance\nRaw, frozen C137 and fixed-final C140 proposals passed 26/36, 35/36 and 36/36 respectively in each of two rounds. C140’s maximum response drift was approximately 0.00180817.\nComplete acceptance on the declared training cohort. All 36 states participated in development; the two rounds do not constitute 72 independent states. The tighter 0.00125 training response target was met on 23/36 states and is not a uniform established margin.\n\n\nC141: frozen local confirmation\nOn 48 new local states from the three represented input classes, raw, frozen C137 and frozen C140 proposals passed 32/48, 40/48 and 42/48 respectively in each round. Six C140 response failures remained.\nThe complete local confirmation target was not met. These are seen-class new-state results, not excluded-class generalisation. All exposed confirmation states are ineligible for reuse as unseen evaluation data.\n\n\nC142: read-only confirmation audit\nThe completed archive, tensor and arithmetic audit retained C141_FROZEN_KERNEL_LOCAL_CONFIRMATION_FAILURE.\nConfirms the audited archival consistency and arithmetic within its scope; it does not independently replay GPT-2 or reclassify the parent failure.\n\n\nC148: global and context-routed development\nGlobal continuation and fixed context routing both passed 79/84 exposed training states in each round.\nNeither arm met complete training qualification. Their parameter counts differ, 36 versus 108, so this comparison does not isolate a routing advantage or establish a certified geometric atlas.\n\n\nC150: fixed cyclic coupling\nDiagonal continuation passed 79/84 and cyclic coupling passed 80/84 in each round. Four cyclic-arm response failures remained.\nThe cyclic arm did not meet complete training qualification. Parameter counts differ, 108 versus 216; the pass-count gain alone does not identify its cause or establish generalisation.\n\n\nC154: fixed-direction diagnostic\nThe execution log reports 1,512 native metric records and 3,025 model forwards at two archived training positions. Finite objective changes differ substantially from the archived linear gradient prediction.\nA training-side numerical diagnostic. The discrepancy does not by itself establish an AD error, curvature bound, convergence result or causal failure explanation.\n\n\nC155: paired forward and precision diagnostic\nThe execution log reports 1,530 metric records and 3,062 model forwards. All 756 FP32 native/functional pairs have zero reported observation and KL differences. FP64 measurements cover two fixed training states.\nFinds no sampled FP32 forward-route discrepancy. It does not verify backward derivatives, establish FP64 ground truth or provide a complete 84-state FP64 qualification.\n\n\nC156: read-only precision-trajectory audit\nThe execution log reports verification of all 1,530 archived records, 588 physical point entries and seven coefficient tensors. At the two fixed states, FP64 coordinate-slope variation across the three registered scales is approximately 1/1,102 and 1/821 of the corresponding FP32 variation.\nRecomputes archived trajectory arithmetic without new model execution. Smaller variation at these scales is not an accuracy certificate or a general precision-superiority result. FP64 AD was not recomputed, and no full 84-state FP64 objective was available.\n\n\nC157: same-function FP64 directional AD/FD diagnostic\nSoftware delivered; formal GPT-2 result pending. The protocol specifies two fixed training states, 26 model forwards and 16 scalar reverse-mode calls.\nCompares AD and finite differences on an explicitly declared continuous FP64 physical chord between archived endpoints. This path is distinguished from the original coefficient-update and FP32-commit path. Delivery tests are not experimental capability evidence.\n\n\n\n\nAll 84 states used in the later training-side studies remain exposed training states, including identifiers that retain the historical word confirmation. Their original roles remain in the archival record, but historical names do not confer current validation eligibility. None of the listed diagnostics supplies a new qualified writer or an excluded-input pass.\n\nController scope. Line C currently evaluates writer proposals separately from GPT-2 B5 controller dispatch. Reported B5 reads, XOR dispatch, writeback and halting do not by themselves establish model-controlled execution of the current Line C writers.\n\n2.1 Four-Layer Validation Architecture\n\n\n\n\nLayer and target\nCapability to establish\nProspective acceptance requirements\nCurrent status\n\n\nI. Writing mechanisms — LC1: Correction-free frozen writing\nA frozen writer produces an accepted update in one proposal from prewrite information.\nComplete content, preservation and read-margin acceptance on all prospectively requested local states, under fixed thresholds, without online Jacobian construction, SVD, response repair, backtracking or teacher access. Retain every requested state and attempted proposal.\nLocal development target met in C35–C37. Independent confirmation of those specific results remains pending.\n\n\nI. Writing mechanisms — LC2: Excluded-input generalisation\nLC1-style correction-free writing extends to input classes excluded from writer development.\nFix the excluded-input split before fitting, normalisation, data-dependent priors, calibration and selection. Freeze the complete proposal procedure before excluded-input evaluation. Report training, new states from represented classes and excluded-input states separately. Require complete acceptance on the prospectively requested excluded-input cohort under unchanged gates, with every failure retained.\nOpen. C140’s 36-state training acceptance did not extend to complete C141 local confirmation. Subsequent development and diagnostics do not establish excluded-input acceptance.\n\n\nII. Scalability — LC3: Capacity and cost scaling\nThe interface supports a declared number of concurrently usable, independently addressable contents within fixed resource and preservation budgets.\nPreregister the content unit, addressing contract, a workload-justified capacity target (C_{\\min}\\geq4), and at least three distinct concurrent-load levels including one content and (C_{\\min}). Require complete acceptance at every registered load, with matched acquisition, overwrite and preservation tests. Account separately for preparation, training, execution and verification, including failures, retries, hardware, precision, elapsed time and peak memory.\nOpen. No usable-capacity or cost-scaling result is established. Kernel dimension is not a usable-capacity estimate.\n\n\nII. Scalability — LC4: Cross-model and broader-domain extension\nThe declared interface and acceptance contract replicate beyond one model family and parameter domain.\nEvaluate at least two distinct model families, with at least two model sizes within one family. Declare coordinates, metrics and budgets for every instance. A broader-parameter-domain claim additionally requires at least two explicitly different update domains. Require matched acceptance on every instance in the preregistered replication matrix; retain failures and report preservation, interference and cost separately.\nOpen. Current Line C evidence remains within the recorded GPT-2 LoRA-B domain. Results from other research tracks require an explicit matched protocol before contributing to this target.\n\n\nIII. Temporal retention — LC5: Continual learning and cumulative drift\nSuccessive acquisitions remain usable while earlier acquisitions and protected capabilities satisfy fixed retention constraints.\nPreregister at least three acquisition stages and a terminal evaluation. Evaluate acquisition at every stage and all earlier acquisitions after every later stage, against frozen historical references. Require every stage and terminal evaluation to satisfy fixed acquisition, retention, interference and cumulative-drift budgets. Report every attempt, failure and rollback.\nOpen. Accepted individual writes and repeated measurements of one frozen state do not establish retention across sustained acquisition sequences.\n\n\nIV. Computational control — LC6: Internalised writable-weight computation\nWithin a declared model boundary, the model specifies addressing, update generation and write control across bounded, causally linked computations, demonstrating weights as computational operators, addressable state and writable computational storage.\nDemonstrate at least two causally linked write cycles: a later cycle must read earlier written state and use it to determine a subsequent address, update or control decision. Verify this dependence through preregistered state interventions and matched controls. Attribute every semantic decision to the model or Runtime. Require auditable writes, correct rollback and satisfaction of fixed quality, preservation and cost budgets across all preregistered executions.\nOpen. Frozen writer modules generate proposals and an external Runtime commits them. The required model-controlled causal read–write cycle has not been established.\n\n\n\n\nThese coverage floors are minimum protocol requirements, not claims of practical scale. Four concurrent contents do not establish useful large-memory capacity; two model families do not establish universal portability; three acquisition stages do not establish lifelong learning; and two linked write cycles do not establish long-sequence stability or Turing completeness. Conclusions remain bounded by the tested workloads, sequence lengths, update domains and model instances. Claims at hundred-billion-parameter scale require direct evidence at that scale, together with the relevant capacity, transfer and retention evidence.\n\n2.2 Claim-Dependent Dependencies\n\nLC1 is the functional root: each higher-level claim requires the relevant correction-free acceptance contract to hold within that claim’s own evaluation scope. C35–C37’s local result does not automatically establish this prerequisite for a different model, parameter domain or workload.\n\nBeyond this root, the targets may proceed concurrently. LC3 and LC4 need not wait for LC2, and bounded LC6 control experiments need not wait for a lifelong-learning demonstration. Composite claims require the corresponding evidence jointly:\n\n\n\n\n\nExcluded-input continual learning requires LC2 and LC5 evidence, with LC1-style acceptance maintained throughout the declared sequence.\n\n\n\n\nCross-model capacity or cost scaling requires both LC3 and LC4 evidence under matched contracts.\n\n\n\n\nModel-controlled continual acquisition requires LC5 and LC6 evidence; an excluded-input version additionally requires LC2.\n\n\n\n\nLarge-scale autonomous writable-weight computation requires the applicable capacity, cross-model or scale, retention and control evidence. Passing one target does not establish the others.\n\n\n\nThese dependencies attach to claims, not experimental numbering. A later C-number denotes a later run, not a higher validated capability.\n\n2.3 Shared Accounting and Protocol Constraints\n\nAttempt accounting and preparation eligibility. Every prospectively requested state remains in the primary denominator. Rejected proposals and preparation failures remain recorded failures of the declared evaluation. Preparation validity and writer performance on valid preparations must also be reported separately: an invalid preparation is not automatically evidence of a valid-domain writer failure, and a valid-only subset cannot replace the full requested denominator.\n\nFrozen execution versus offline development. Offline fitting, calibration and diagnostic backpropagation must be explicitly attributed and costed. They are distinct from the evaluated frozen proposal, which must satisfy its declared restrictions on online derivatives, repair, backtracking and teacher access. A diagnostic derivative check does not itself qualify a writer.\n\nExposure and exclusion accounting. Once states or outcomes have informed fitting, normalisation, priors, calibration, architecture choice or selection, that information belongs to development. Exposed states cannot be renamed as new unseen confirmation data. A new excluded-input study must disclose relevant historical access and specify what remains excluded; refitting a writer does not erase prior programme-level exposure.\n\nFailure recovery versus acceptance and retention. Retries or rollbacks cannot convert a failed original proposal into an LC1 success. Under LC5, acquisition subsequently removed by rollback cannot be credited as retained acquisition. Recovery performance may be reported separately.\n\nModel–Runtime boundary. Declare before evaluation whether each frozen writer, router and controller belongs to the model under study or is an externally fitted auxiliary module. Current writer results do not establish that GPT-2 itself generates the corresponding control decisions. A Runtime may mechanically apply parameter updates, enforce a fixed contract, log events and restore declared state. Runtime-generated semantic addressing, proposal content, repair or task branching receives no model-internalisation credit. External physical commitment alone neither establishes nor rules out LC6; the decisive issue is the demonstrated source of semantic control.\n\nAuditability and rollback scope. Record the proposed and applied updates, addressed coordinates, decision provenance and acceptance outcomes. Specify which parameter, memory and execution-state components rollback covers, and verify restoration of each declared component. Restoration of selected weights must not be presented as reversal of unspecified external effects.\n\nNumerical and evidential scope. Report precision, references, finite-difference scales, derivative paths and relevant numerical tolerances explicitly. Archive arithmetic does not independently establish measurement accuracy, chronology or non-access. Agreement between forward routes does not certify backward derivatives; smaller finite-scale variation does not establish an error bound. Numerical diagnostics remain separate from content, preservation and read-margin acceptance.\n\nCurrent boundary. The evidence establishes bounded local frozen-writing development results and a growing record of training, confirmation failures and numerical diagnostics. LC2 remains open until a frozen complete procedure satisfies a prospectively declared excluded-input evaluation with the required isolation, unchanged acceptance gates and full failure accounting.\n\n \n\n\n3. Mathematical Framework: Zero Modes, Controllability and Finite-Step Preservation\n\nWhy constrained controllability? Reducing a training loss does not by itself establish that an intended content change is compatible with preserving specified model responses. Programmable parametric memory requires both objectives to be declared: what should change, and what should remain within tolerance.\n\nThis introduces two overarching questions. Feasibility asks whether a compatible update exists. Construction asks how to compute and execute it. Backpropagation supplies derivatives; the constraints determine which changes those derivatives can support.\n\nLet \\(R(\\theta)\\) denote protected responses and \\(H(\\theta)\\) content readouts. At a fixed parameter state, the first-order feasibility problem is\n\n\\[ J(\\theta)v=0, \\qquad DH(\\theta)v=b, \\qquad J=DR. \\]\n\nHere \\(v\\) is a parameter direction and \\(b\\) the desired infinitesimal readout change. The first equation preserves the declared responses to first order; the second changes the content.\n\nThe distinction between a zero infimum and its nontrivial attainment is motivated by A Principle of Physical Realizability: Attainability and Local Zero Modes, which introduces Principle R. Here, that distinction is specialised to a declared neural response map. The results below follow from their stated assumptions; the controllability and finite-step results do not require Principle R.\n\nSection 3.7 summarises how the mathematical conditions connect to operational questions and experimental evidence.\n\n3.1 Declared Coordinates, Responses and Response Geometry\n\nLet \\(\\theta\\in\\mathcal L\\subseteq\\mathbb R^d\\) denote the variable coordinates of a declared parameter chart. In the restricted LoRA-B implementation, base-model parameters, LoRA-A and the chart specification remain fixed; only the declared LoRA-B coordinates vary.\n\nLet\n\n\\[ R:\\mathcal L\\to\\mathbb R^p, \\qquad H:\\mathcal L\\to\\mathbb R^q \\]\n\nbe the protected-response map and address-readout map. Their derivatives are taken within the declared chart:\n\n\\[ J(\\theta)=DR(\\theta)\\in\\mathbb R^{p\\times d}, \\qquad DH(\\theta)\\in\\mathbb R^{q\\times d}. \\]\n\nDerivatives are understood through extensions to open neighbourhoods of the states under consideration. Parameter coordinates use the Euclidean metric unless another metric is declared. The notation \\(\\|\\cdot\\|_2\\) denotes the Euclidean vector norm or its induced matrix norm; \\(\\|\\cdot\\|_\\infty\\) denotes the maximum absolute coordinate. For a matrix \\(M\\), \\(\\sigma_+(M)\\) denotes its positive singular values.\n\nProtected-response specification. One construction uses an anchor-averaged response,\n\n\\[ R(\\theta)=\\frac1{|A|}\\sum_{x\\in A}Sf_\\theta(x), \\]\n\nwhere \\(A\\) is a fixed nonempty finite anchor set, \\(f_\\theta(x)\\) the declared model output and \\(S\\) a fixed output selector. Averaging can permit cancellation between anchors. Preserving this average does not establish a matching per-anchor bound; such bounds require a stacked response specification or separate checks.\n\nReadouts and target-relative margins. For binary access under a fixed prompt \\(x\\), define\n\n\\[ h_x(\\theta)=z_1(\\theta;x)-z_0(\\theta;x), \\]\n\nwhere \\(z_0,z_1\\) are the logits of the declared readout tokens. The target-relative margin for \\(y\\in\\{0,1\\}\\) is\n\n\\[ m_x(\\theta;y)=(2y-1)h_x(\\theta). \\]\n\nA positive margin favours the requested symbol for either target. The components of \\(H\\) may be raw readout contrasts \\(h_x\\), target-relative margins for a fixed operation, or another explicitly declared smooth readout. Section 3.6 relates finite readout changes to margin attainment.\n\nAccess prompts, readout-token definitions, aggregation rules and decoding conventions, including tie handling, are fixed before evaluation and remain unchanged during writing and overwriting.\n\nResponse geometry within the chart. A fixed affine parameterisation\n\n\\[ w(\\theta)=w_0+T\\theta \\]\n\ngives\n\n\\[ J(\\theta)=DR_{\\mathrm{full}}(w(\\theta))T. \\]\n\nThe parameterisation is an embedding when \\(T\\) has full column rank. Its affine form does not imply that the response map is linear.\n\nChoose a fixed symmetric positive-definite output metric \\(G_O\\in\\mathbb R^{p\\times p}\\), and define\n\n\\[ \\|a\\|_{G_O}=\\sqrt{a^\\top G_Oa}, \\qquad a\\in\\mathbb R^p. \\]\n\nThe response-induced quadratic form is\n\n\\[ g_R(\\theta)=J(\\theta)^\\top G_OJ(\\theta). \\]\n\nEquivalently,\n\n\\[ g_R(\\theta) = T^\\top DR_{\\mathrm{full}}(w(\\theta))^\\top G_O\\,DR_{\\mathrm{full}}(w(\\theta))T. \\]\n\nSince \\(G_O\\succ0\\),\n\n\\[ g_R(\\theta)\\succeq0, \\qquad v^\\top g_R(\\theta)v=\\|J(\\theta)v\\|_{G_O}^2, \\qquad \\ker g_R(\\theta)=\\ker J(\\theta). \\]\n\nPositive semidefiniteness also holds when \\(G_O\\succeq0\\); positive definiteness ensures the stated kernel equality.\n\nRegularity conventions. The constants \\(L_R,L_K,L_j\\) bound changes in \\(DR,\\nabla K,\\nabla H_j\\), respectively, using Euclidean norms. Each bound must hold along the entire update segment to which it is applied. Constants may vary between segments and are then indexed by \\(\\ell\\). A uniform bound must be valid on a declared region containing every relevant segment. Sampled curvature estimates are diagnostics unless established as bounds.\n\n3.2 Response-Induced Zero Modes and Nontrivial Attainment\n\nThis section distinguishes a direction that preserves responses to first order at one state from a nonconstant curve that preserves them throughout its motion.\n\nNonnegativity of the response cost. Define\n\n\\[ F_R(\\theta,v) = \\sqrt{v^\\top g_R(\\theta)v} = \\|J(\\theta)v\\|_{G_O}. \\]\n\nBy §3.1,\n\n\\[ F_R(\\theta,v)\\ge0, \\qquad F_R(\\theta,v)=0 \\iff J(\\theta)v=0. \\]\n\nFor fixed \\(\\theta\\), \\(F_R(\\theta,\\cdot)\\) is the seminorm induced by \\(g_R(\\theta)\\). It is a norm precisely when \\(\\ker J(\\theta)=\\{0\\}\\).\n\nThe pointwise kernel dimension is\n\n\\[ \\dim\\ker J(\\theta)=d-\\operatorname{rank}J(\\theta). \\]\n\nA nonzero first-order response-preserving direction therefore exists whenever \\(\\operatorname{rank}J(\\theta)\u003cd\\). In particular, \\(p\u003cd\\) is sufficient. This is a direct linear-algebraic conclusion.\n\nFor fixed \\(v\\in\\ker J(\\theta)\\), a valid Jacobian Lipschitz bound along the update segment gives\n\n\\[ \\|R(\\theta+\\eta v)-R(\\theta)\\|_2 \\le \\frac{L_R}{2}\\eta^2\\|v\\|_2^2, \\qquad \\eta\\ge0. \\]\n\nThis follows from Lemma 1 in §3.5. A pointwise kernel direction therefore controls the leading response change, without establishing exact preservation under a finite straight step.\n\nFrom pointwise zero modes to zero-cost curves. Let \\(\\Gamma\\) be a declared class of absolutely continuous curves\n\n\\[ \\gamma:[0,1]\\to\\mathcal L. \\]\n\nAssume \\(R\\) is continuously differentiable on an open neighbourhood of their images, and define\n\n\\[ E[\\gamma] = \\int_0^1F_R(\\gamma(t),\\dot\\gamma(t))\\,dt. \\]\n\nThe integrand is measurable, with \\(\\dot\\gamma\\) defined arbitrarily on its null exceptional set. Its nonnegativity implies that a zero integral forces it to vanish almost everywhere. This implication does not establish that a nonconstant zero-cost curve exists.\n\nThe following conditions distinguish nonnegative cost, arbitrarily small cost, and actual zero-cost motion:\n\n\n\n\n\nZ1 — Nonnegativity:\n\\[ F_R\\ge0, \\qquad F_R(\\theta,0)=0. \\]\n\n\n\nZ2 — Zero nonconstant infimum: the nonconstant subclass of \\(\\Gamma\\) is nonempty and\n\\[ \\inf_{\\substack{\\gamma\\in\\Gamma\\\\ \\gamma\\ \\mathrm{nonconstant}}} E[\\gamma]=0. \\]\n\n\n\nZ3 — Nontrivial attainment: there exists a nonconstant \\(\\gamma_*\\in\\Gamma\\) such that\n\\[ E[\\gamma_*]=0. \\]\n\n\nZ1 holds by construction. Under Z1, Z3 implies Z2, but Z2 does not imply Z3. Principle R motivates an attainment requirement in its declared domain; it does not make Z3 an unconditional consequence of nonnegativity.\n\nHere \\(\\operatorname{Leb}\\) denotes one-dimensional Lebesgue measure on \\([0,1]\\). The positive-measure statement below concerns curve-parameter values \\(t\\), not ambient parameter-space volume or arc-length measure.\n\nProposition 1 — Zero-cost attainment yields nontrivial kernel motion.\n\nUnder the assumptions above, Z3 implies\n\n\\[ J(\\gamma_*(t))\\dot\\gamma_*(t)=0 \\quad\\text{for almost every }t, \\]\n\nand\n\n\\[ \\operatorname{Leb} \\left( \\left\\{ t\\in[0,1]: \\dot\\gamma_*(t)\\text{ exists}, \\ \\dot\\gamma_*(t)\\ne0, \\ J(\\gamma_*(t))\\dot\\gamma_*(t)=0 \\right\\} \\right)\u003e0. \\]\n\nFurthermore,\n\n\\[ R(\\gamma_*(t))=R(\\gamma_*(0)) \\qquad\\text{for every }t\\in[0,1]. \\]\n\nProof. The nonnegative measurable integrand has zero integral, so \\(F_R(\\gamma_*,\\dot\\gamma_*)=0\\) almost everywhere. Positive definiteness of \\(G_O\\) gives \\(J\\dot\\gamma_*=0\\) almost everywhere. An absolutely continuous curve whose derivative vanishes almost everywhere is constant. Nonconstancy therefore implies that \\(\\dot\\gamma_*\\ne0\\) on a set of positive Lebesgue measure. Intersecting that set with the full-measure kernel condition proves the second assertion. The chain rule and absolute continuity of \\(R\\circ\\gamma_*\\) give response constancy.\n\nRemark — Endpoint lower bound. For any \\(\\gamma\\in\\Gamma\\),\n\n\\[ E[\\gamma] \\ge \\|R(\\gamma(1))-R(\\gamma(0))\\|_{G_O}. \\]\n\nIndeed,\n\n\\[ R(\\gamma(1))-R(\\gamma(0)) = \\int_0^1J(\\gamma(t))\\dot\\gamma(t)\\,dt, \\]\n\nand the integral triangle inequality gives the bound.\n\nRemark — Zero infimum and pointwise kernels do not establish attainment. Let \\(R(\\theta)=\\theta\\), \\(G_O=1\\), and let \\(\\Gamma\\) contain\n\n\\[ \\gamma_\\epsilon(t)=\\epsilon t, \\qquad \\epsilon\u003e0. \\]\n\nThen\n\n\\[ E[\\gamma_\\epsilon]=\\epsilon\\to0, \\]\n\nbut \\(J=1\\) has no nonzero kernel, and every zero-cost absolutely continuous curve is constant.\n\nFor \\(R(\\theta)=\\theta^2\\), the kernel at zero is all of \\(\\mathbb R\\), and\n\n\\[ E[\\gamma_\\epsilon]=\\epsilon^2\\to0. \\]\n\nNevertheless, a zero-cost curve must have constant \\(R\\), and no nonconstant continuous curve in \\(\\mathbb R\\) can remain in a fibre of \\(\\theta^2\\). Thus a curve class containing this family satisfies Z2 but not Z3.\n\nA sufficient local geometric condition is that \\(R\\) be \\(C^1\\) with constant rank \\(r_0\u003cd\\) on a neighbourhood. The constant-rank theorem gives local response fibres of dimension \\(d-r_0\\), containing nonconstant response-preserving curves. Z3 additionally requires \\(\\Gamma\\) to admit such curves.\n\nDependencies of the subsequent results. Neither Z2 nor Z3 is required below. Proposition 2 uses \\(J\\) and \\(DH\\) at a single state. Proposition 3 uses \\(J\\) and \\(\\lambda\u003e0\\). Propositions 4–8 use Lemma 1 and their stated regularity, derivative and budget conditions.\n\n3.3 Zero Modes and Readout Controllability\n\nA response-preserving direction supports memory writing only if it changes a declared readout.\n\nFix a state \\(\\theta\\). Let the columns of\n\n\\[ N\\in\\mathbb R^{d\\times k}, \\qquad k=d-\\operatorname{rank}J, \\]\n\nform an orthonormal basis for \\(\\ker J\\). Define\n\n\\[ C=DH(\\theta)N\\in\\mathbb R^{q\\times k}. \\]\n\nProposition 2 — Response-preserving readout controllability.\n\nFor a desired infinitesimal readout change \\(b\\in\\mathbb R^q\\), the system\n\n\\[ Jv=0, \\qquad DH(\\theta)v=b \\]\n\nhas a solution if and only if\n\n\\[ b\\in\\operatorname{Im}C. \\]\n\nWhen feasible, its minimum-Euclidean-norm solution is\n\n\\[ v_{\\min}=NC^\\dagger b, \\]\n\nwhere \\(C^\\dagger\\) is the Moore–Penrose pseudoinverse.\n\nProof. Every \\(v\\in\\ker J\\) has a unique representation \\(v=N\\xi\\), with \\(\\|v\\|_2=\\|\\xi\\|_2\\). The readout equation becomes \\(C\\xi=b\\), whose minimum-norm solution is \\(C^\\dagger b\\).\n\nConsequences — Rank, conditioning and basis independence. If \\(\\operatorname{rank}C=q\\), every \\(b\\in\\mathbb R^q\\) is attainable in the linearised model, and\n\n\\[ \\|v_{\\min}\\|_2 \\le \\frac{\\|b\\|_2}{\\sigma_{\\min}(C)}, \\]\n\nwhere \\(\\sigma_{\\min}(C)\\) is its smallest positive singular value. Full row rank requires\n\n\\[ q\\le d-\\operatorname{rank}J, \\]\n\nbut this dimension condition is not sufficient.\n\nThe rank of \\(C\\) counts independently controllable first-order readout directions. Its singular values describe their conditioning and the displacement required to realise them.\n\nReplacing \\(N\\) by \\(NQ\\), with \\(Q\\) orthogonal, replaces \\(C\\) by \\(CQ\\) without changing its image, rank or singular values. Since\n\n\\[ (CQ)^\\dagger=Q^\\top C^\\dagger, \\]\n\nthe minimum-norm parameter direction is unchanged.\n\nThe bridge from zero modes to writing is\n\n\\[ \\exists v\\in\\ker J: DH(\\theta)v\\ne0 \\iff C\\ne0. \\]\n\nIf \\(C=0\\), first-order readout control vanishes at that state, although higher-order changes may remain possible.\n\nCorollary 1 — Selective first-order writing.\n\nFor scalar readout \\(H_i\\), let \\(B_i\\) stack the rows of \\(J\\) and \\(DH_j\\) for all \\(j\\ne i\\). For any prescribed \\(a_i\\ne0\\),\n\n\\[ B_iv_i=0, \\qquad DH_iv_i=a_i \\]\n\nis feasible if and only if\n\n\\[ DH_i\\notin\\operatorname{rowspan}B_i. \\]\n\nEquivalently,\n\n\\[ a_ie_i\\in\\operatorname{Im}C, \\]\n\nwhere \\(e_i\\) is the \\(i\\)-th coordinate vector in readout space.\n\nLet \\(Q_i\\) be the Euclidean orthogonal projector onto \\(\\ker B_i\\), and define\n\n\\[ d_i = \\|Q_iDH_i^\\top\\|_2 = \\operatorname{dist} \\bigl(DH_i,\\operatorname{rowspan}B_i\\bigr). \\]\n\nWhen \\(d_i\u003e0\\),\n\n\\[ v_{i,\\min} = \\frac{a_i}{d_i^2}Q_iDH_i^\\top, \\qquad \\|v_{i,\\min}\\|_2=\\frac{|a_i|}{d_i}. \\]\n\nProof. Restricting to \\(\\ker B_i\\) replaces the readout covector by \\(Q_iDH_i^\\top\\). A nonzero target is feasible precisely when this projection is nonzero. The minimum-norm solution follows from the Cauchy–Schwarz inequality, with equality along the projected direction.\n\nRemark — Numerical feasibility. Numerical rank estimates alone are not feasibility certificates. Computed directions should be accompanied by residuals, conditioning information and the required displacement norm.\n\n3.4 Regularised Near-Kernel Updates and Leakage\n\nA regularised near-kernel operator retains kernel components and attenuates components that change protected responses.\n\nFor \\(\\lambda\u003e0\\), define\n\n\\[ P_\\lambda = I_d-J^\\top(JJ^\\top+\\lambda I_p)^{-1}J = \\lambda(J^\\top J+\\lambda I_d)^{-1}. \\]\n\nIt acts as the identity on \\(\\ker J\\). Along a right singular direction with positive singular value \\(s\\), it scales the component by\n\n\\[ \\frac{\\lambda}{s^2+\\lambda}. \\]\n\nProposition 3 — Spectral leakage bound.\n\nThe operator satisfies\n\n\\[ \\|P_\\lambda\\|_2\\le1, \\qquad \\|JP_\\lambda\\|_2\\le\\frac{\\sqrt\\lambda}{2}. \\]\n\nFor \\(J\\ne0\\),\n\n\\[ \\|JP_\\lambda\\|_2 = \\max_{s\\in\\sigma_+(J)} \\frac{s\\lambda}{s^2+\\lambda}. \\]\n\nFor \\(J=0\\), the leakage is zero.\n\nProof. Apply a singular-value decomposition of \\(J\\). The positive singular values of \\(JP_\\lambda\\) are \\(s\\lambda/(s^2+\\lambda)\\). This expression is at most \\(\\sqrt\\lambda/2\\), with its scalar maximum attained at \\(s=\\sqrt\\lambda\\).\n\nCorollary 2 — Unnormalised descent and leakage.\n\nLet\n\n\\[ u=-P_\\lambda g, \\qquad g=\\nabla L_{\\mathrm{write}}(\\theta). \\]\n\nThen\n\n\\[ \\|u\\|_2\\le\\|g\\|_2, \\qquad \\|Ju\\|_2\\le\\frac{\\sqrt\\lambda}{2}\\|g\\|_2. \\]\n\nWhen \\(g\\ne0\\),\n\n\\[ g^\\top u=-g^\\top P_\\lambda g\u003c0. \\]\n\nProof. The norm bounds follow from Proposition 3. Positive definiteness of \\(P_\\lambda=\\lambda(J^\\top J+\\lambda I_d)^{-1}\\) gives strict descent.\n\nRemark — The regularised operator is not a projector. The identity\n\n\\[ JP_\\lambda = \\lambda(JJ^\\top+\\lambda I_p)^{-1}J \\]\n\nshows that, whenever \\(J\\ne0\\),\n\n\\[ JP_\\lambda\\ne0, \\qquad P_\\lambda^2\\ne P_\\lambda. \\]\n\nFor \\(J=0\\), \\(P_\\lambda=I_d\\).\n\nRemark — Normalisation changes the leakage statement. For\n\n\\[ \\widehat u = -\\frac{P_\\lambda g}{\\|P_\\lambda g\\|_2}, \\qquad g\\ne0, \\]\n\none has\n\n\\[ \\|J\\widehat u\\|_2 = \\frac{\\|JP_\\lambda g\\|_2}{\\|P_\\lambda g\\|_2} \\le \\min\\left\\{ \\|J\\|_2,\\, \\frac{\\sqrt\\lambda}{2} \\frac{\\|g\\|_2}{\\|P_\\lambda g\\|_2} \\right\\}. \\]\n\nNormalisation preserves the descent sign but can remove the attenuation of the unnormalised direction. If \\(g\\) lies along a right singular direction with singular value \\(s\u003e0\\), then\n\n\\[ \\|J\\widehat u\\|_2=s. \\]\n\nFor an actual step \\(\\delta\\theta=\\alpha\\widehat u\\),\n\n\\[ \\|J\\delta\\theta\\|_2 = \\alpha\\|J\\widehat u\\|_2, \\qquad \\alpha\\ge0. \\]\n\nRemark — Algorithmic scope. Feature-null restrictions, covariance preconditioning, metric projection onto a parameter-norm ball, normalisation, backtracking and response correction are distinct operations. Bounds must apply to the actual displacement produced by the specified algorithm.\n\nProposition 3 is an exact-arithmetic statement and does not by itself certify a floating-point implementation. The weighted-metric extension and numerical error bounds are given in Appendix A.\n\nSection 3.5 combines first-order leakage with curvature to obtain finite-step budget conditions. Modified directions require the corresponding leakage estimate for their actual displacement.\n\n3.5 Finite-Step Response and KL Preservation\n\nFirst-order compatibility identifies candidate directions. Finite admissibility additionally depends on curvature and the remaining budgets. The following lemma supplies the common remainder estimate used here and in §3.6.\n\nLemma 1 — Taylor remainder along an update segment.\n\nLet \\(F\\) be a continuously differentiable map into \\(\\mathbb R^a\\), defined on an open neighbourhood of the segment\n\n\\[ \\{\\theta+tv:0\\le t\\le\\eta\\}, \\qquad \\eta\\ge0. \\]\n\nSuppose\n\n\\[ \\|DF(\\theta+tv)-DF(\\theta)\\|_2 \\le Lt\\|v\\|_2 \\qquad(0\\le t\\le\\eta), \\]\n\nwith \\(L\\ge0\\). Then\n\n\\[ F(\\theta+\\eta v) = F(\\theta)+\\eta DF(\\theta)v+e_F, \\]\n\nwhere\n\n\\[ \\|e_F\\|_2 \\le \\frac L2\\eta^2\\|v\\|_2^2. \\]\n\nFor vector-valued \\(F\\),\n\n\\[ \\|e_F\\|_\\infty \\le \\|e_F\\|_2 \\le \\frac L2\\eta^2\\|v\\|_2^2. \\]\n\nFor scalar-valued \\(F\\), the same bound holds with \\(|e_F|\\).\n\nProof. The fundamental theorem of calculus gives\n\n\\[ e_F = \\int_0^\\eta [DF(\\theta+tv)-DF(\\theta)]v\\,dt. \\]\n\nTaking norms and integrating yields\n\n\\[ \\|e_F\\|_2 \\le \\int_0^\\eta Lt\\|v\\|_2^2\\,dt = \\frac L2\\eta^2\\|v\\|_2^2. \\]\n\nThis lemma requires no kernel or selectivity constraint. It applies to \\(R\\), \\(K\\) and each \\(H_j\\) under their respective regularity assumptions.\n\nDeclared budgets. Fix a reference state \\(\\theta_{\\mathrm{ref}}\\), and define\n\n\\[ K(\\theta) = \\frac1{|A|} \\sum_{x\\in A} D_{\\mathrm{KL}} \\left( p_{\\theta_{\\mathrm{ref}}}(\\cdot\\mid x) \\,\\middle\\|\\, p_\\theta(\\cdot\\mid x) \\right). \\]\n\nThe anchor set, distribution and KL convention are declared before evaluation. This average does not imply a uniform per-anchor bound.\n\nFor target response \\(r\\) and budgets \\(\\varepsilon_R,\\varepsilon_{\\mathrm{KL}}\\ge0\\), define\n\n\\[ \\mathcal F(r) = \\left\\{ \\theta\\in\\mathcal L: \\|R(\\theta)-r\\|_\\infty\\le\\varepsilon_R, \\quad K(\\theta)\\le\\varepsilon_{\\mathrm{KL}} \\right\\}. \\]\n\nParameter-norm, resource and content constraints are specified separately.\n\nConsider\n\n\\[ \\theta^+=\\theta+\\eta u, \\qquad \\eta\\ge0. \\]\n\nResponse budget\n\nProposition 4 — Finite-step response preservation.\n\nSuppose \\(R\\) satisfies Lemma 1 on the entire update segment, with constant \\(L_R\\). Define\n\n\\[ \\rho_R = \\varepsilon_R-\\|R(\\theta)-r\\|_\\infty. \\]\n\nThen\n\n\\[ \\|R(\\theta^+)-r\\|_\\infty \\le \\|R(\\theta)-r\\|_\\infty + \\eta\\|Ju\\|_\\infty + \\frac{L_R}{2}\\eta^2\\|u\\|_2^2. \\]\n\nConsequently,\n\n\\[ \\eta\\|Ju\\|_\\infty + \\frac{L_R}{2}\\eta^2\\|u\\|_2^2 \\le\\rho_R \\]\n\nis sufficient for the response budget.\n\nProof. Apply Lemma 1 to \\(R\\) and use the triangle inequality.\n\nConsequences — Step bounds. For \\(Ju=0\\), \\(\\rho_R\u003e0\\), \\(L_R\u003e0\\) and \\(u\\ne0\\),\n\n\\[ \\eta \\le \\frac{\\sqrt{2\\rho_R/L_R}}{\\|u\\|_2} \\]\n\nis sufficient, subject to the segment conditions.\n\nFor \\(u=-P_\\lambda g\\), Corollary 2 and\n\n\\[ \\|Ju\\|_\\infty\\le\\|Ju\\|_2 \\]\n\ngive the more conservative sufficient condition\n\n\\[ \\eta\\frac{\\sqrt\\lambda}{2}\\|g\\|_2 + \\frac{L_R}{2}\\eta^2\\|g\\|_2^2 \\le\\rho_R. \\]\n\nFor a normalised direction, use its actual \\(\\|J\\widehat u\\|_\\infty\\) and \\(\\|\\widehat u\\|_2=1\\).\n\nRemark — Uniform curvature bounds. Suppose \\(R\\) is \\(C^2\\) on an open neighbourhood of a compact convex region \\(U\\) containing the segment. Define\n\n\\[ M_R = \\sup_{\\xi\\in U} \\sup_{\\|v_1\\|_2=\\|v_2\\|_2=1} \\|D^2R(\\xi)[v_1,v_2]\\|_2. \\]\n\nThen \\(L_R=M_R\\) is valid throughout \\(U\\), including the kernel-direction bound in §3.2. Under the affine parameterisation,\n\n\\[ D^2R(\\theta)[v_1,v_2] = D^2R_{\\mathrm{full}}(w(\\theta))[Tv_1,Tv_2]. \\]\n\nKL budget and joint admissibility\n\nProposition 5 — Finite-step KL preservation.\n\nSuppose \\(K\\) satisfies the scalar version of Lemma 1 on the entire update segment, with constant \\(L_K\\). Define\n\n\\[ \\rho_K=\\varepsilon_{\\mathrm{KL}}-K(\\theta). \\]\n\nThen\n\n\\[ K(\\theta^+) \\le K(\\theta) + \\eta\\nabla K(\\theta)^\\top u + \\frac{L_K}{2}\\eta^2\\|u\\|_2^2. \\]\n\nTherefore,\n\n\\[ \\eta\\nabla K(\\theta)^\\top u + \\frac{L_K}{2}\\eta^2\\|u\\|_2^2 \\le\\rho_K \\]\n\nis sufficient for the KL budget.\n\nProof. Apply Lemma 1 to the scalar map \\(K\\) and use its upper remainder bound.\n\nCorollary 3 — Joint finite admissibility.\n\nUnder Propositions 4 and 5, if \\(\\theta^+\\in\\mathcal L\\) and\n\n\\[ \\eta\\|Ju\\|_\\infty + \\frac{L_R}{2}\\eta^2\\|u\\|_2^2 \\le\\rho_R, \\]\\[ \\eta\\nabla K(\\theta)^\\top u + \\frac{L_K}{2}\\eta^2\\|u\\|_2^2 \\le\\rho_K, \\]\n\nthen\n\n\\[ \\boxed{\\theta^+\\in\\mathcal F(r).} \\]\n\nProof. The two propositions establish the response and KL inequalities; chart membership completes the definition of \\(\\mathcal F(r)\\).\n\nSuccessful writing additionally requires the declared content margins and separate parameter-norm or resource constraints.\n\nRemark — Reference-state KL behaviour. At a differentiable interior reference state,\n\n\\[ K(\\theta_{\\mathrm{ref}})=0, \\qquad \\nabla K(\\theta_{\\mathrm{ref}})=0. \\]\n\nProposition 5 therefore gives\n\n\\[ K(\\theta_{\\mathrm{ref}}+\\eta u) \\le \\frac{L_K}{2}\\eta^2\\|u\\|_2^2 \\]\n\nwhenever the bound holds along that segment.\n\nRemark — Local Fisher interpretation. Define\n\n\\[ w_{\\mathrm{ref}}=w(\\theta_{\\mathrm{ref}}). \\]\n\nUnder smoothness, fixed-support and differentiation-under-expectation conditions,\n\n\\[ \\nabla_\\theta^2K(\\theta_{\\mathrm{ref}}) = T^\\top\\mathcal I_A(w_{\\mathrm{ref}})T, \\]\n\nwhere\n\n\\[ \\mathcal I_A(w_{\\mathrm{ref}}) = \\frac1{|A|} \\sum_{x\\in A} \\mathbb E_{y\\sim p_{w_{\\mathrm{ref}}}(\\cdot\\mid x)} [s_x(y)s_x(y)^\\top], \\]\n\nand\n\n\\[ s_x(y) = \\left. \\nabla_w\\log p_w(y\\mid x) \\right|_{w=w_{\\mathrm{ref}}}. \\]\n\nConsequently,\n\n\\[ K(\\theta_{\\mathrm{ref}}+\\delta) = \\frac12 \\delta^\\top T^\\top\\mathcal I_A(w_{\\mathrm{ref}})T\\delta + o(\\|\\delta\\|_2^2). \\]\n\nThe distribution must match the declared KL measurement. Final-token KL and full-sequence KL are different quantities. The reference Hessian describes the leading local quadratic cost; its largest eigenvalue alone does not bound curvature over a finite region. This interpretation is not an additional premise of the finite-step inequalities and does not identify an arbitrary optimisation metric with Fisher information.\n\n3.6 Selective Writes, Composition and Response Correction\n\nSelective finite writes\n\nProposition 6 — Finite-step selective writing.\n\nAt the current state \\(\\theta\\), suppose\n\n\\[ Jv_i=0, \\qquad DH_iv_i=a_i, \\qquad DH_jv_i=0 \\quad(j\\ne i). \\]\n\nThe condition \\(Jv_i=0\\) is included for first-order response compatibility; the readout bounds below do not require it.\n\nLet \\(\\eta\\ge0\\). Suppose the segment lies in the declared chart and each relevant \\(H_j\\) satisfies Lemma 1 there, with constant \\(L_j\\).\n\nThen, for \\(j\\ne i\\),\n\n\\[ |H_j(\\theta+\\eta v_i)-H_j(\\theta)| \\le \\frac{L_j}{2}\\eta^2\\|v_i\\|_2^2, \\]\n\nand\n\n\\[ \\left| H_i(\\theta+\\eta v_i)-H_i(\\theta)-\\eta a_i \\right| \\le \\frac{L_i}{2}\\eta^2\\|v_i\\|_2^2. \\]\n\nWhen \\(a_i\u003e0\\), an increase of at least \\(\\Delta\u003e0\\) is guaranteed if\n\n\\[ \\eta a_i - \\frac{L_i}{2}\\eta^2\\|v_i\\|_2^2 \\ge\\Delta. \\]\n\nIf the unselected first-order condition is approximate,\n\n\\[ |DH_jv_i|\\le\\tau_j, \\]\n\nthen\n\n\\[ |H_j(\\theta+\\eta v_i)-H_j(\\theta)| \\le \\eta\\tau_j + \\frac{L_j}{2}\\eta^2\\|v_i\\|_2^2. \\]\n\nProof. Apply the scalar version of Lemma 1 to each \\(H_j\\) and substitute the exact or approximate readout derivative constraints.\n\nConsequence — Binary margin attainment. Suppose \\(H_i=h_{x_i}\\), with target \\(y_i\\) fixed during the operation. Set\n\n\\[ s_i=2y_i-1, \\qquad m_i(\\theta)=s_iH_i(\\theta). \\]\n\nChoose the direction so that\n\n\\[ s_i a_i\u003e0. \\]\n\nThen\n\n\\[ m_i(\\theta+\\eta v_i) \\ge m_i(\\theta) + \\eta s_i a_i - \\frac{L_i}{2}\\eta^2\\|v_i\\|_2^2. \\]\n\nA margin threshold \\(\\mu_i\\) is attained if\n\n\\[ \\eta s_i a_i - \\frac{L_i}{2}\\eta^2\\|v_i\\|_2^2 \\ge \\mu_i-m_i(\\theta). \\]\n\nOne may instead apply Proposition 6 directly to a target-relative margin readout, holding its target fixed while differentiating. The step must also meet the preservation and parameter constraints.\n\nAccumulated interference and preservation budgets\n\nProposition 7 — Cumulative readout interference.\n\nConsider \\(m\\) updates,\n\n\\[ \\theta_{\\ell+1} = \\theta_\\ell+\\eta_\\ell v_\\ell, \\qquad \\ell=0,\\ldots,m-1, \\qquad \\eta_\\ell\\ge0. \\]\n\nSuppose readout \\(j\\) is unselected throughout and\n\n\\[ |DH_j(\\theta_\\ell)v_\\ell| \\le\\tau_{j,\\ell} \\]\n\nat each current state. Assume every segment lies in the declared chart and \\(H_j\\) satisfies Lemma 1 on that segment with constant \\(L_{j,\\ell}\\). Then\n\n\\[ |H_j(\\theta_m)-H_j(\\theta_0)| \\le \\sum_{\\ell=0}^{m-1} \\left[ \\eta_\\ell\\tau_{j,\\ell} + \\frac{L_{j,\\ell}}2 \\eta_\\ell^2\\|v_\\ell\\|_2^2 \\right]. \\]\n\nProof. Lemma 1 bounds each readout increment by its first-order term and remainder. Sum these bounds and use the triangle inequality. No condition \\(J(\\theta_\\ell)v_\\ell=0\\) is required.\n\nFor \\(m=1\\), Proposition 7 reproduces the approximate unselected-readout bound in Proposition 6, without requiring a response-kernel constraint.\n\nCorollary 4 — Cumulative response and KL bounds.\n\nFor the same sequence, let\n\n\\[ J_\\ell=DR(\\theta_\\ell). \\]\n\nSuppose every segment satisfies the assumptions of Propositions 4 and 5, with constants \\(L_{R,\\ell}\\) and \\(L_{K,\\ell}\\). Keep the target response \\(r\\), reference state \\(\\theta_{\\mathrm{ref}}\\), KL measurement and budgets fixed throughout the sequence.\n\nDefine\n\n\\[ A_\\ell = \\eta_\\ell\\|J_\\ell v_\\ell\\|_\\infty + \\frac{L_{R,\\ell}}2 \\eta_\\ell^2\\|v_\\ell\\|_2^2, \\]\n\nand\n\n\\[ B_\\ell = \\eta_\\ell\\nabla K(\\theta_\\ell)^\\top v_\\ell + \\frac{L_{K,\\ell}}2 \\eta_\\ell^2\\|v_\\ell\\|_2^2. \\]\n\nFor every prefix \\(n=1,\\ldots,m\\),\n\n\\[ \\|R(\\theta_n)-r\\|_\\infty \\le \\|R(\\theta_0)-r\\|_\\infty + \\sum_{\\ell=0}^{n-1}A_\\ell, \\]\n\nand\n\n\\[ K(\\theta_n) \\le K(\\theta_0) + \\sum_{\\ell=0}^{n-1}B_\\ell. \\]\n\nConsequently, if \\(\\theta_0\\in\\mathcal F(r)\\), every \\(\\theta_n\\in\\mathcal L\\), and\n\n\\[ \\sum_{\\ell=0}^{m-1}A_\\ell \\le \\varepsilon_R-\\|R(\\theta_0)-r\\|_\\infty, \\]\n\ntogether with\n\n\\[ \\sum_{\\ell=0}^{n-1}B_\\ell \\le \\varepsilon_{\\mathrm{KL}}-K(\\theta_0) \\qquad(n=1,\\ldots,m), \\]\n\nthen\n\n\\[ \\theta_n\\in\\mathcal F(r) \\qquad(n=0,\\ldots,m). \\]\n\nProof. Sum the one-step bounds from Propositions 4 and 5. Since \\(A_\\ell\\ge0\\), the total response condition bounds every response prefix. The signed KL increments require their stated prefix conditions. Chart membership completes admissibility.\n\nRemark — Mixed selected and unselected operations. Proposition 7 directly covers a readout left unselected throughout the sequence. For a sequence in which readout \\(j\\) is sometimes selected, declare a desired first-order change \\(a_{j,\\ell}\\), taking \\(a_{j,\\ell}=0\\) on unselected steps, and assume\n\n\\[ |DH_j(\\theta_\\ell)v_\\ell-a_{j,\\ell}| \\le\\tau_{j,\\ell}. \\]\n\nLemma 1 then gives\n\n\\[ \\left| H_j(\\theta_m)-H_j(\\theta_0) - \\sum_{\\ell=0}^{m-1}\\eta_\\ell a_{j,\\ell} \\right| \\le \\sum_{\\ell=0}^{m-1} \\left[ \\eta_\\ell\\tau_{j,\\ell} + \\frac{L_{j,\\ell}}2 \\eta_\\ell^2\\|v_\\ell\\|_2^2 \\right]. \\]\n\nThus composition can track deviations from declared changes as well as preservation of unselected contents.\n\nRemark — Sequence-level acceptance. The KL increments \\(B_\\ell\\) may be negative. A final-prefix condition alone does not guarantee that earlier states respected the KL budget. Prefix conditions, or direct statewise checks, are needed when every operation must remain admissible.\n\nDerivative constraints and regularity bounds must hold at the states and segments where updates occur. Constraints imposed only at the initial state do not establish these cumulative conclusions.\n\nNumerical response correction\n\nProposition 8 — Correction magnitude and response residual.\n\nAt a state \\(\\theta\\), let\n\n\\[ e=R(\\theta)-r, \\qquad J=DR(\\theta), \\]\n\nand define\n\n\\[ \\delta\\theta = -J^\\top(JJ^\\top+\\lambda I_p)^{-1}e, \\qquad \\lambda\u003e0. \\]\n\nThen\n\n\\[ \\|\\delta\\theta\\|_2 \\le \\frac{\\|e\\|_2}{2\\sqrt\\lambda}, \\]\n\nand\n\n\\[ e+J\\delta\\theta = \\lambda(JJ^\\top+\\lambda I_p)^{-1}e. \\]\n\nIf the correction segment lies in the declared chart and \\(R\\) satisfies Lemma 1 there with constant \\(L_R\\), then\n\n\\[ \\|R(\\theta+\\delta\\theta)-r\\|_\\infty \\le \\left\\| \\lambda(JJ^\\top+\\lambda I_p)^{-1}e \\right\\|_\\infty + \\frac{L_R}{2}\\|\\delta\\theta\\|_2^2. \\]\n\nProof. The singular values of the correction operator on positive singular directions are\n\n\\[ \\frac{s}{s^2+\\lambda}, \\]\n\nwhich are at most \\(1/(2\\sqrt\\lambda)\\). For \\(J=0\\), the correction operator is zero. The residual identity follows from\n\n\\[ I_p-JJ^\\top(JJ^\\top+\\lambda I_p)^{-1} = \\lambda(JJ^\\top+\\lambda I_p)^{-1}. \\]\n\nApply Lemma 1 with \\(\\eta=1\\) and \\(v=\\delta\\theta\\) to obtain the finite residual bound.\n\nConsequences — Curvature and content bounds. Substituting the correction-norm bound yields\n\n\\[ \\|R(\\theta+\\delta\\theta)-r\\|_\\infty \\le \\left\\| \\lambda(JJ^\\top+\\lambda I_p)^{-1}e \\right\\|_\\infty + \\frac{L_R}{8\\lambda}\\|e\\|_2^2. \\]\n\nFor a readout \\(H_j\\) satisfying Lemma 1 on the correction segment,\n\n\\[ |H_j(\\theta+\\delta\\theta)-H_j(\\theta)| \\le |DH_j(\\theta)\\delta\\theta| + \\frac{L_j}{2}\\|\\delta\\theta\\|_2^2, \\]\n\nand hence\n\n\\[ |H_j(\\theta+\\delta\\theta)-H_j(\\theta)| \\le \\frac{\\|DH_j(\\theta)\\|_2}{2\\sqrt\\lambda}\\|e\\|_2 + \\frac{L_j}{8\\lambda}\\|e\\|_2^2. \\]\n\nRemark — Regularisation and curvature. Along a positive left singular direction, the linear residual is attenuated by\n\n\\[ \\frac{\\lambda}{s^2+\\lambda}. \\]\n\nComponents orthogonal to \\(\\operatorname{Im}J\\) remain unchanged in the linearised model. Decreasing \\(\\lambda\\) improves attenuation on positive singular directions but weakens the uniform correction-norm bound as \\(1/\\sqrt\\lambda\\) and the resulting curvature bound as \\(1/\\lambda\\).\n\nThese are worst-case bounds, not claims that the actual correction diverges for a fixed \\(J\\). Its exact size depends on the singular spectrum and the components of \\(e\\). Finite nonlinear residual reduction requires the post-correction bound, or direct measurement, to improve on the current residual.\n\nCorrection steps enter Proposition 7 and Corollary 4 with\n\n\\[ \\eta_\\ell=1, \\qquad v_\\ell=\\delta\\theta_\\ell. \\]\n\nTheir acceptance depends on actual post-correction response, KL and content values. The quantity \\(\\|J\\delta\\theta\\|\\) measures the correction’s linear action, rather than the residual remaining after correction.\n\nRemark — Statewise correction and sequence accounting. Proposition 8 bounds the next residual using\n\n\\[ e_\\ell=R(\\theta_\\ell)-r. \\]\n\nIt can provide a tighter response bound than the generic additive estimate in Corollary 4. Incorporating it into sequence-level accounting requires measured or certified residual information, or a valid bound propagated over the possible residuals. An unknown residual cannot be substituted as though it were known. Numerical error in the computed correction must also be included when applying the bound to an implementation.\n\n3.7 From Mathematical Conditions to Operational Evidence\n\nThe framework separates five questions:\n\n\n\n\n\n\n\n\n\n\nQuestion\nMathematical criterion or bound\nResults\n\n\n\n\nZero modes\nNonzero \\(\\ker J\\), or an admitted nonconstant zero-cost curve\n§3.2; Proposition 1\n\n\nControllability\n\\(b\\in\\operatorname{Im}C\\), with conditioning and displacement requirements\nProposition 2\n\n\nFinite feasibility\nJoint response and KL conditions, chart membership and separate parameter constraints\nLemma 1; Propositions 3–5; Corollaries 2–3\n\n\nSelectivity\nSelective linear feasibility, finite interference and target-margin attainment\nLemma 1; Corollary 1; Proposition 6\n\n\nComposition\nCumulative readout, response and KL bounds, including selected operations and corrections\nLemma 1; Propositions 7–8; Corollary 4\n\n\n\n\n\n\n\nThree objects remain distinct: an ideal first-order kernel, a numerically computed candidate update, and a finite parameter state accepted by the measurement protocol.\n\nAn address is defined by its access rule. A kernel direction is a mechanism for changing the content returned by that rule. An endpoint atlas is a collection of separately instantiated parameter states; a shared state is one parameter point realising multiple addressed contents.\n\nThe central quantitative problem is to achieve enough readout change for reliable writing while keeping response drift, KL change and cross-address interference within budget. Kernel dimension alone does not determine usable memory capacity.\n\nThese local results organise the feasibility problem; they do not replace finite measurement. Experimental reports must identify the protected responses, access rules, tolerances, parameter domain, numerical procedure and evaluation coverage. Average-response preservation must be distinguished from per-prompt preservation, and development acceptance from independent confirmation.\n\nThe B0–B5 roadmap tests finite implementations of WRITE, OVERWRITE, SWAP, MOVE and RETURN, followed by their integration into computation and model-selected operation sequences. These capabilities are claimed only where the corresponding finite tests, controls and reproducibility evidence support them.\n\n \n\nAppendix A. Weighted Operators and Numerical Error\n\nA.1 Weighted Output Metric\n\nLet \\(G_O\\succ0\\) be the declared output metric and set\n\n\\[ \\widetilde J=G_O^{1/2}J. \\]\n\nApplying the regularised construction to \\(\\widetilde J\\) gives\n\n\\[ P_{\\lambda,G_O} = I_d-\\widetilde J^\\top (\\widetilde J\\widetilde J^\\top+\\lambda I_p)^{-1} \\widetilde J = \\lambda(g_R+\\lambda I_d)^{-1}. \\]\n\nProposition 3 applied to \\(\\widetilde J\\) yields\n\n\\[ \\|JP_{\\lambda,G_O}g\\|_{G_O} = \\|\\widetilde JP_{\\lambda,G_O}g\\|_2 \\le \\frac{\\sqrt\\lambda}{2}\\|g\\|_2. \\]\n\nThis construction weights protected-output changes while retaining the Euclidean metric on parameter coordinates. It does not identify a separately chosen covariance preconditioner or parameter-space metric with \\(g_R\\).\n\nA.2 Numerical Error in Candidate Updates\n\nProposition 3 concerns the exact operator and exact direction. Let\n\n\\[ u=-P_\\lambda g, \\qquad \\widetilde u=u+e_u \\]\n\nbe the computed unnormalised direction. Then\n\n\\[ \\|J\\widetilde u\\|_2 \\le \\frac{\\sqrt\\lambda}{2}\\|g\\|_2 + \\|J\\|_2\\|e_u\\|_2. \\]\n\nThus the exact leakage bound alone does not certify the computed direction. A valid numerical certificate requires control of the direction error, together with any error in the Jacobian used to evaluate leakage.\n\nIf \\(\\widetilde J\\) is a computed Jacobian, then\n\n\\[ \\|J\\widetilde u\\|_2 \\le \\|\\widetilde J\\widetilde u\\|_2 + \\|J-\\widetilde J\\|_2\\|\\widetilde u\\|_2. \\]\n\nFor a numerically computed correction \\(\\widetilde{\\delta\\theta}\\), Lemma 1 gives the directly applicable bound\n\n\\[ \\|R(\\theta+\\widetilde{\\delta\\theta})-r\\|_\\infty \\le \\|e+J\\widetilde{\\delta\\theta}\\|_\\infty + \\frac{L_R}{2}\\|\\widetilde{\\delta\\theta}\\|_2^2, \\]\n\nprovided the regularity bound holds on the actual correction segment.\n\nThese bounds separate exact operator properties from numerical implementation and finite nonlinear acceptance.\n\n4. Implementation, Evidence Access and Reproducibility\n\nEvery capability claim must identify its model and revision, parameter chart, protocol, software version and machine-readable result records.\n\nReproducibility materials should specify access rules, protected responses, budgets, data partitions, controls, stopping conditions and acceptance criteria. Reported records should distinguish completed, failed and interrupted runs, and separate development evidence from independent confirmation.\n\nReading and evidence access\n\n\n\nAccompanying paper: A Programmable Address Space for Neural Memory, available as a PDF attached to this record.\n\nConceptual background: A Principle of Physical Realizability: Attainability and Local Zero Modes.\n\nPublic code, protocols and evidence: github.com/papasop/fibre-nav.\n\nQwen development implementation: Maintained in a private Hugging Face repository; it is not currently publicly accessible.\n\n\nPublic reproducibility claims are limited to the materials available for inspection and execution. Results from private development implementations remain separately identified until the corresponding source, protocols and evidence are released."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.23296718","contentUrl":null,"metadataVersion":102,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":1,"created":"2026-10-11T10:24:49Z","registered":"2026-10-11T10:24:50Z","published":null,"updated":"2026-10-24T05:56:42Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.22097583","type":"dois","attributes":{"doi":"10.5281/zenodo.22097583","identifiers":[],"creators":[{"nameType":"Personal","givenName":"Li","familyName":"Y.Y.N.","name":"Y.Y.N., Li","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0009-0002-6471-139x"}],"affiliation":[]}],"titles":[{"title":"In-Weight Computing"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-10-11","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":""},"relatedIdentifiers":[{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.22174576","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.22097584","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.22134068","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.22167245","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.22171619","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.22618024","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.22638458","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.22142878","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.22158703","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.22206983","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.22105024","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.22641200","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.23296718","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[{"descriptionType":"Abstract","description":"1. Overview and Research Positioning\n\n\n\nEarly connectionist formalisms treated connection topology and computational state as fundamentally unified (McCulloch and Pitts, 1943). In contrast, constrained by the physical limitations of early discrete electronics, stored-program computing formalized a foundational separation between computational operators and mutable state at both physical and operational levels (von Neumann, 1945)—a pragmatic engineering compromise that sacrificed endogenous unity to secure manufacturability and deterministic execution. This architectural division remains the default assumption of modern mainstream deep learning: in standard fixed-weight inference, learned parameters are relegated to immutable, read-only operators, while the evolution of all dynamic, mutable state is offloaded entirely to transient activations, recurrent vectors, and external attention key-value caches.\n\nWe investigate a complementary computational organization:  In-Weight Computing. In this setting, selected parameter coordinates serve as addressable, writable state while continuing to participate in the model's computational operators. We formulate a parameter-level framework in which declared readout maps and state-transition relations specify stored contents, functional addresses, and the intended effects of write operations. Geometrically,  the framework connects continuous parameter updates to declared discrete state transitions through constrained subspace projections, providing a testable operational interface between neural representations and symbolic state manipulation. Auditability and rollback are specified through update records and explicit criteria for restoring declared parameter and memory states.\n\nHinton \u0026 Plaut (1987), Ba et al. (2016), and Schlag et al. (2021) successively introduced the concepts of fast weights and fast weight programmers, establishing a viable pathway for storing and manipulating information through dynamic adjustments of connection weights. We share this broad objective and focus on a constrained writable interface: requested changes to stored content, preservation of declared baseline responses, and readout requirements are specified and evaluated together. The distinction lies in these explicit interface requirements and their validation,  rather than in a general opposition to fast-weight update mechanisms.\n\nMathematically, writing is formulated as a constrained inverse problem: construct an update within the selected parameter domain that realizes the requested state change while satisfying specified response-error and Kullback–Leibler (KL) divergence budgets on declared evaluation inputs and output distributions. Response-Jacobian null spaces and near-kernel operators provide local, first-order geometric constructions. Geometric conditions do not, by themselves, guarantee finite-update acceptance. They depend on nonlinear residuals and numerical error; we therefore state geometric conditions separately from empirical acceptance criteria, with explicit coordinates, domains, and tolerances.\n\n2. Current Evidence and Validation Targets\n\nEvidence snapshot: 23 October 2026. Each capability claim is restricted to its recorded model, parameter coordinates, protocol, workload and evaluation scope. Layers I–IV organize the research questions; LC1–LC6 denote validation targets; C-numbered identifiers denote experimental runs. The targets form a claim-dependent partial order rather than a strictly serial ladder. The prospective coverage requirements below guide future evaluations and do not retroactively change earlier experimental decisions.\n\nLC1: local development target met. C35–C37 meet the declared LC1 local development acceptance target with both frozen composite writers. Each final proposal uses prewrite information and requires no online Jacobian construction, singular value decomposition (SVD), postwrite response correction, backtracking or teacher fallback. Offline fitting and calibration remain part of writer preparation. Independent archival and model-level confirmation of those specific local results remains pending; subsequent audits of other experiments do not discharge that requirement.\n\nLC2: open. C140 achieved complete acceptance on its declared 36-state training cohort in each of two rounds. Its frozen writer subsequently passed 42/48 prospectively declared local confirmation states in each C141 round, retaining six response-preservation failures. C142 completed a read-only audit that retained the C141 failure decision. Later training-side comparisons and numerical diagnostics provide additional development evidence, but no successful excluded-input acceptance result has been established.\n\nEvidence provenance. The present update distinguishes original-archive-backed records for C141, C142, C148 and C150 from supplied execution-log evidence for C154–C156. The latter records report completed diagnostics or audits, but their original result ZIPs have not been independently reverified for this update. C157 software has been delivered; its formal GPT-2 execution result is pending. Archive consistency, fresh model replay and capability acceptance are separate evidence levels.\n\nThe earlier development record remains relevant. C63 reported acceptance on 108/108 training states but only 38/48 prospectively declared new states from trained input classes; ten failed response preservation. On a different twelve-state cohort, C136 passed 11/12 and C137 passed 12/12 under the unchanged response budget of 0.002. C138 V2 then encountered 22 preparation failures among 24 requested confirmation states; frozen C137 passed 1/24 overall and one of the two valid preparations. C139 changed those exposed coordinates through a declared projected-preparation construction: all 24 projected preparations passed, and frozen C137 passed 23/24. These development results neither rescue the original C138 coordinates nor constitute independent confirmation.  All 24 projected states subsequently entered C140 training.\n\nThe following selected record separates training qualification, confirmation boundaries and numerical diagnostics.\n\n\n\n\nRun\nRecorded result\nInterpretation and boundary\n\n\nC140: expanded training acceptance\nRaw, frozen C137 and fixed-final C140 proposals passed 26/36, 35/36 and 36/36 respectively in each of two rounds. C140’s maximum response drift was approximately 0.00180817.\nComplete acceptance on the declared training cohort. All 36 states participated in development; the two rounds do not constitute 72 independent states. The tighter 0.00125 training response target was met on 23/36 states and is not a uniform established margin.\n\n\nC141: frozen local confirmation\nOn 48 new local states from the three represented input classes, raw, frozen C137 and frozen C140 proposals passed 32/48, 40/48 and 42/48 respectively in each round. Six C140 response failures remained.\nThe complete local confirmation target was not met. These are seen-class new-state results, not excluded-class generalisation. All exposed confirmation states are ineligible for reuse as unseen evaluation data.\n\n\nC142: read-only confirmation audit\nThe completed archive, tensor and arithmetic audit retained C141_FROZEN_KERNEL_LOCAL_CONFIRMATION_FAILURE.\nConfirms the audited archival consistency and arithmetic within its scope; it does not independently replay GPT-2 or reclassify the parent failure.\n\n\nC148: global and context-routed development\nGlobal continuation and fixed context routing both passed 79/84 exposed training states in each round.\nNeither arm met complete training qualification. Their parameter counts differ, 36 versus 108, so this comparison does not isolate a routing advantage or establish a certified geometric atlas.\n\n\nC150: fixed cyclic coupling\nDiagonal continuation passed 79/84 and cyclic coupling passed 80/84 in each round. Four cyclic-arm response failures remained.\nThe cyclic arm did not meet complete training qualification. Parameter counts differ, 108 versus 216; the pass-count gain alone does not identify its cause or establish generalisation.\n\n\nC154: fixed-direction diagnostic\nThe execution log reports 1,512 native metric records and 3,025 model forwards at two archived training positions. Finite objective changes differ substantially from the archived linear gradient prediction.\nA training-side numerical diagnostic. The discrepancy does not by itself establish an AD error, curvature bound, convergence result or causal failure explanation.\n\n\nC155: paired forward and precision diagnostic\nThe execution log reports 1,530 metric records and 3,062 model forwards. All 756 FP32 native/functional pairs have zero reported observation and KL differences. FP64 measurements cover two fixed training states.\nFinds no sampled FP32 forward-route discrepancy. It does not verify backward derivatives, establish FP64 ground truth or provide a complete 84-state FP64 qualification.\n\n\nC156: read-only precision-trajectory audit\nThe execution log reports verification of all 1,530 archived records, 588 physical point entries and seven coefficient tensors. At the two fixed states, FP64 coordinate-slope variation across the three registered scales is approximately 1/1,102 and 1/821 of the corresponding FP32 variation.\nRecomputes archived trajectory arithmetic without new model execution. Smaller variation at these scales is not an accuracy certificate or a general precision-superiority result. FP64 AD was not recomputed, and no full 84-state FP64 objective was available.\n\n\nC157: same-function FP64 directional AD/FD diagnostic\nSoftware delivered; formal GPT-2 result pending. The protocol specifies two fixed training states, 26 model forwards and 16 scalar reverse-mode calls.\nCompares AD and finite differences on an explicitly declared continuous FP64 physical chord between archived endpoints. This path is distinguished from the original coefficient-update and FP32-commit path. Delivery tests are not experimental capability evidence.\n\n\n\n\nAll 84 states used in the later training-side studies remain exposed training states, including identifiers that retain the historical word confirmation. Their original roles remain in the archival record, but historical names do not confer current validation eligibility. None of the listed diagnostics supplies a new qualified writer or an excluded-input pass.\n\nController scope. Line C currently evaluates writer proposals separately from GPT-2 B5 controller dispatch. Reported B5 reads, XOR dispatch, writeback and halting do not by themselves establish model-controlled execution of the current Line C writers.\n\n2.1 Four-Layer Validation Architecture\n\n\n\n\nLayer and target\nCapability to establish\nProspective acceptance requirements\nCurrent status\n\n\nI. Writing mechanisms — LC1: Correction-free frozen writing\nA frozen writer produces an accepted update in one proposal from prewrite information.\nComplete content, preservation and read-margin acceptance on all prospectively requested local states, under fixed thresholds, without online Jacobian construction, SVD, response repair, backtracking or teacher access. Retain every requested state and attempted proposal.\nLocal development target met in C35–C37. Independent confirmation of those specific results remains pending.\n\n\nI. Writing mechanisms — LC2: Excluded-input generalisation\nLC1-style correction-free writing extends to input classes excluded from writer development.\nFix the excluded-input split before fitting, normalisation, data-dependent priors, calibration and selection. Freeze the complete proposal procedure before excluded-input evaluation. Report training, new states from represented classes and excluded-input states separately. Require complete acceptance on the prospectively requested excluded-input cohort under unchanged gates, with every failure retained.\nOpen. C140’s 36-state training acceptance did not extend to complete C141 local confirmation. Subsequent development and diagnostics do not establish excluded-input acceptance.\n\n\nII. Scalability — LC3: Capacity and cost scaling\nThe interface supports a declared number of concurrently usable, independently addressable contents within fixed resource and preservation budgets.\nPreregister the content unit, addressing contract, a workload-justified capacity target (C_{\\min}\\geq4), and at least three distinct concurrent-load levels including one content and (C_{\\min}). Require complete acceptance at every registered load, with matched acquisition, overwrite and preservation tests. Account separately for preparation, training, execution and verification, including failures, retries, hardware, precision, elapsed time and peak memory.\nOpen. No usable-capacity or cost-scaling result is established. Kernel dimension is not a usable-capacity estimate.\n\n\nII. Scalability — LC4: Cross-model and broader-domain extension\nThe declared interface and acceptance contract replicate beyond one model family and parameter domain.\nEvaluate at least two distinct model families, with at least two model sizes within one family. Declare coordinates, metrics and budgets for every instance. A broader-parameter-domain claim additionally requires at least two explicitly different update domains. Require matched acceptance on every instance in the preregistered replication matrix; retain failures and report preservation, interference and cost separately.\nOpen. Current Line C evidence remains within the recorded GPT-2 LoRA-B domain. Results from other research tracks require an explicit matched protocol before contributing to this target.\n\n\nIII. Temporal retention — LC5: Continual learning and cumulative drift\nSuccessive acquisitions remain usable while earlier acquisitions and protected capabilities satisfy fixed retention constraints.\nPreregister at least three acquisition stages and a terminal evaluation. Evaluate acquisition at every stage and all earlier acquisitions after every later stage, against frozen historical references. Require every stage and terminal evaluation to satisfy fixed acquisition, retention, interference and cumulative-drift budgets. Report every attempt, failure and rollback.\nOpen. Accepted individual writes and repeated measurements of one frozen state do not establish retention across sustained acquisition sequences.\n\n\nIV. Computational control — LC6: Internalised writable-weight computation\nWithin a declared model boundary, the model specifies addressing, update generation and write control across bounded, causally linked computations, demonstrating weights as computational operators, addressable state and writable computational storage.\nDemonstrate at least two causally linked write cycles: a later cycle must read earlier written state and use it to determine a subsequent address, update or control decision. Verify this dependence through preregistered state interventions and matched controls. Attribute every semantic decision to the model or Runtime. Require auditable writes, correct rollback and satisfaction of fixed quality, preservation and cost budgets across all preregistered executions.\nOpen. Frozen writer modules generate proposals and an external Runtime commits them. The required model-controlled causal read–write cycle has not been established.\n\n\n\n\nThese coverage floors are minimum protocol requirements, not claims of practical scale. Four concurrent contents do not establish useful large-memory capacity; two model families do not establish universal portability; three acquisition stages do not establish lifelong learning; and two linked write cycles do not establish long-sequence stability or Turing completeness. Conclusions remain bounded by the tested workloads, sequence lengths, update domains and model instances. Claims at hundred-billion-parameter scale require direct evidence at that scale, together with the relevant capacity, transfer and retention evidence.\n\n2.2 Claim-Dependent Dependencies\n\nLC1 is the functional root: each higher-level claim requires the relevant correction-free acceptance contract to hold within that claim’s own evaluation scope. C35–C37’s local result does not automatically establish this prerequisite for a different model, parameter domain or workload.\n\nBeyond this root, the targets may proceed concurrently. LC3 and LC4 need not wait for LC2, and bounded LC6 control experiments need not wait for a lifelong-learning demonstration. Composite claims require the corresponding evidence jointly:\n\n\n\n\n\nExcluded-input continual learning requires LC2 and LC5 evidence, with LC1-style acceptance maintained throughout the declared sequence.\n\n\n\n\nCross-model capacity or cost scaling requires both LC3 and LC4 evidence under matched contracts.\n\n\n\n\nModel-controlled continual acquisition requires LC5 and LC6 evidence; an excluded-input version additionally requires LC2.\n\n\n\n\nLarge-scale autonomous writable-weight computation requires the applicable capacity, cross-model or scale, retention and control evidence. Passing one target does not establish the others.\n\n\n\nThese dependencies attach to claims, not experimental numbering. A later C-number denotes a later run, not a higher validated capability.\n\n2.3 Shared Accounting and Protocol Constraints\n\nAttempt accounting and preparation eligibility. Every prospectively requested state remains in the primary denominator. Rejected proposals and preparation failures remain recorded failures of the declared evaluation. Preparation validity and writer performance on valid preparations must also be reported separately: an invalid preparation is not automatically evidence of a valid-domain writer failure, and a valid-only subset cannot replace the full requested denominator.\n\nFrozen execution versus offline development. Offline fitting, calibration and diagnostic backpropagation must be explicitly attributed and costed. They are distinct from the evaluated frozen proposal, which must satisfy its declared restrictions on online derivatives, repair, backtracking and teacher access. A diagnostic derivative check does not itself qualify a writer.\n\nExposure and exclusion accounting. Once states or outcomes have informed fitting, normalisation, priors, calibration, architecture choice or selection, that information belongs to development. Exposed states cannot be renamed as new unseen confirmation data. A new excluded-input study must disclose relevant historical access and specify what remains excluded; refitting a writer does not erase prior programme-level exposure.\n\nFailure recovery versus acceptance and retention. Retries or rollbacks cannot convert a failed original proposal into an LC1 success. Under LC5, acquisition subsequently removed by rollback cannot be credited as retained acquisition. Recovery performance may be reported separately.\n\nModel–Runtime boundary. Declare before evaluation whether each frozen writer, router and controller belongs to the model under study or is an externally fitted auxiliary module. Current writer results do not establish that GPT-2 itself generates the corresponding control decisions. A Runtime may mechanically apply parameter updates, enforce a fixed contract, log events and restore declared state. Runtime-generated semantic addressing, proposal content, repair or task branching receives no model-internalisation credit. External physical commitment alone neither establishes nor rules out LC6; the decisive issue is the demonstrated source of semantic control.\n\nAuditability and rollback scope. Record the proposed and applied updates, addressed coordinates, decision provenance and acceptance outcomes. Specify which parameter, memory and execution-state components rollback covers, and verify restoration of each declared component. Restoration of selected weights must not be presented as reversal of unspecified external effects.\n\nNumerical and evidential scope. Report precision, references, finite-difference scales, derivative paths and relevant numerical tolerances explicitly. Archive arithmetic does not independently establish measurement accuracy, chronology or non-access. Agreement between forward routes does not certify backward derivatives; smaller finite-scale variation does not establish an error bound. Numerical diagnostics remain separate from content, preservation and read-margin acceptance.\n\nCurrent boundary. The evidence establishes bounded local frozen-writing development results and a growing record of training, confirmation failures and numerical diagnostics. LC2 remains open until a frozen complete procedure satisfies a prospectively declared excluded-input evaluation with the required isolation, unchanged acceptance gates and full failure accounting.\n\n \n\n\n3. Mathematical Framework: Zero Modes, Controllability and Finite-Step Preservation\n\nWhy constrained controllability? Reducing a training loss does not by itself establish that an intended content change is compatible with preserving specified model responses. Programmable parametric memory requires both objectives to be declared: what should change, and what should remain within tolerance.\n\nThis introduces two overarching questions. Feasibility asks whether a compatible update exists. Construction asks how to compute and execute it. Backpropagation supplies derivatives; the constraints determine which changes those derivatives can support.\n\nLet \\(R(\\theta)\\) denote protected responses and \\(H(\\theta)\\) content readouts. At a fixed parameter state, the first-order feasibility problem is\n\n\\[ J(\\theta)v=0, \\qquad DH(\\theta)v=b, \\qquad J=DR. \\]\n\nHere \\(v\\) is a parameter direction and \\(b\\) the desired infinitesimal readout change. The first equation preserves the declared responses to first order; the second changes the content.\n\nThe distinction between a zero infimum and its nontrivial attainment is motivated by A Principle of Physical Realizability: Attainability and Local Zero Modes, which introduces Principle R. Here, that distinction is specialised to a declared neural response map. The results below follow from their stated assumptions; the controllability and finite-step results do not require Principle R.\n\nSection 3.7 summarises how the mathematical conditions connect to operational questions and experimental evidence.\n\n3.1 Declared Coordinates, Responses and Response Geometry\n\nLet \\(\\theta\\in\\mathcal L\\subseteq\\mathbb R^d\\) denote the variable coordinates of a declared parameter chart. In the restricted LoRA-B implementation, base-model parameters, LoRA-A and the chart specification remain fixed; only the declared LoRA-B coordinates vary.\n\nLet\n\n\\[ R:\\mathcal L\\to\\mathbb R^p, \\qquad H:\\mathcal L\\to\\mathbb R^q \\]\n\nbe the protected-response map and address-readout map. Their derivatives are taken within the declared chart:\n\n\\[ J(\\theta)=DR(\\theta)\\in\\mathbb R^{p\\times d}, \\qquad DH(\\theta)\\in\\mathbb R^{q\\times d}. \\]\n\nDerivatives are understood through extensions to open neighbourhoods of the states under consideration. Parameter coordinates use the Euclidean metric unless another metric is declared. The notation \\(\\|\\cdot\\|_2\\) denotes the Euclidean vector norm or its induced matrix norm; \\(\\|\\cdot\\|_\\infty\\) denotes the maximum absolute coordinate. For a matrix \\(M\\), \\(\\sigma_+(M)\\) denotes its positive singular values.\n\nProtected-response specification. One construction uses an anchor-averaged response,\n\n\\[ R(\\theta)=\\frac1{|A|}\\sum_{x\\in A}Sf_\\theta(x), \\]\n\nwhere \\(A\\) is a fixed nonempty finite anchor set, \\(f_\\theta(x)\\) the declared model output and \\(S\\) a fixed output selector. Averaging can permit cancellation between anchors. Preserving this average does not establish a matching per-anchor bound; such bounds require a stacked response specification or separate checks.\n\nReadouts and target-relative margins. For binary access under a fixed prompt \\(x\\), define\n\n\\[ h_x(\\theta)=z_1(\\theta;x)-z_0(\\theta;x), \\]\n\nwhere \\(z_0,z_1\\) are the logits of the declared readout tokens. The target-relative margin for \\(y\\in\\{0,1\\}\\) is\n\n\\[ m_x(\\theta;y)=(2y-1)h_x(\\theta). \\]\n\nA positive margin favours the requested symbol for either target. The components of \\(H\\) may be raw readout contrasts \\(h_x\\), target-relative margins for a fixed operation, or another explicitly declared smooth readout. Section 3.6 relates finite readout changes to margin attainment.\n\nAccess prompts, readout-token definitions, aggregation rules and decoding conventions, including tie handling, are fixed before evaluation and remain unchanged during writing and overwriting.\n\nResponse geometry within the chart. A fixed affine parameterisation\n\n\\[ w(\\theta)=w_0+T\\theta \\]\n\ngives\n\n\\[ J(\\theta)=DR_{\\mathrm{full}}(w(\\theta))T. \\]\n\nThe parameterisation is an embedding when \\(T\\) has full column rank. Its affine form does not imply that the response map is linear.\n\nChoose a fixed symmetric positive-definite output metric \\(G_O\\in\\mathbb R^{p\\times p}\\), and define\n\n\\[ \\|a\\|_{G_O}=\\sqrt{a^\\top G_Oa}, \\qquad a\\in\\mathbb R^p. \\]\n\nThe response-induced quadratic form is\n\n\\[ g_R(\\theta)=J(\\theta)^\\top G_OJ(\\theta). \\]\n\nEquivalently,\n\n\\[ g_R(\\theta) = T^\\top DR_{\\mathrm{full}}(w(\\theta))^\\top G_O\\,DR_{\\mathrm{full}}(w(\\theta))T. \\]\n\nSince \\(G_O\\succ0\\),\n\n\\[ g_R(\\theta)\\succeq0, \\qquad v^\\top g_R(\\theta)v=\\|J(\\theta)v\\|_{G_O}^2, \\qquad \\ker g_R(\\theta)=\\ker J(\\theta). \\]\n\nPositive semidefiniteness also holds when \\(G_O\\succeq0\\); positive definiteness ensures the stated kernel equality.\n\nRegularity conventions. The constants \\(L_R,L_K,L_j\\) bound changes in \\(DR,\\nabla K,\\nabla H_j\\), respectively, using Euclidean norms. Each bound must hold along the entire update segment to which it is applied. Constants may vary between segments and are then indexed by \\(\\ell\\). A uniform bound must be valid on a declared region containing every relevant segment. Sampled curvature estimates are diagnostics unless established as bounds.\n\n3.2 Response-Induced Zero Modes and Nontrivial Attainment\n\nThis section distinguishes a direction that preserves responses to first order at one state from a nonconstant curve that preserves them throughout its motion.\n\nNonnegativity of the response cost. Define\n\n\\[ F_R(\\theta,v) = \\sqrt{v^\\top g_R(\\theta)v} = \\|J(\\theta)v\\|_{G_O}. \\]\n\nBy §3.1,\n\n\\[ F_R(\\theta,v)\\ge0, \\qquad F_R(\\theta,v)=0 \\iff J(\\theta)v=0. \\]\n\nFor fixed \\(\\theta\\), \\(F_R(\\theta,\\cdot)\\) is the seminorm induced by \\(g_R(\\theta)\\). It is a norm precisely when \\(\\ker J(\\theta)=\\{0\\}\\).\n\nThe pointwise kernel dimension is\n\n\\[ \\dim\\ker J(\\theta)=d-\\operatorname{rank}J(\\theta). \\]\n\nA nonzero first-order response-preserving direction therefore exists whenever \\(\\operatorname{rank}J(\\theta)\u003cd\\). In particular, \\(p\u003cd\\) is sufficient. This is a direct linear-algebraic conclusion.\n\nFor fixed \\(v\\in\\ker J(\\theta)\\), a valid Jacobian Lipschitz bound along the update segment gives\n\n\\[ \\|R(\\theta+\\eta v)-R(\\theta)\\|_2 \\le \\frac{L_R}{2}\\eta^2\\|v\\|_2^2, \\qquad \\eta\\ge0. \\]\n\nThis follows from Lemma 1 in §3.5. A pointwise kernel direction therefore controls the leading response change, without establishing exact preservation under a finite straight step.\n\nFrom pointwise zero modes to zero-cost curves. Let \\(\\Gamma\\) be a declared class of absolutely continuous curves\n\n\\[ \\gamma:[0,1]\\to\\mathcal L. \\]\n\nAssume \\(R\\) is continuously differentiable on an open neighbourhood of their images, and define\n\n\\[ E[\\gamma] = \\int_0^1F_R(\\gamma(t),\\dot\\gamma(t))\\,dt. \\]\n\nThe integrand is measurable, with \\(\\dot\\gamma\\) defined arbitrarily on its null exceptional set. Its nonnegativity implies that a zero integral forces it to vanish almost everywhere. This implication does not establish that a nonconstant zero-cost curve exists.\n\nThe following conditions distinguish nonnegative cost, arbitrarily small cost, and actual zero-cost motion:\n\n\n\n\n\nZ1 — Nonnegativity:\n\\[ F_R\\ge0, \\qquad F_R(\\theta,0)=0. \\]\n\n\n\nZ2 — Zero nonconstant infimum: the nonconstant subclass of \\(\\Gamma\\) is nonempty and\n\\[ \\inf_{\\substack{\\gamma\\in\\Gamma\\\\ \\gamma\\ \\mathrm{nonconstant}}} E[\\gamma]=0. \\]\n\n\n\nZ3 — Nontrivial attainment: there exists a nonconstant \\(\\gamma_*\\in\\Gamma\\) such that\n\\[ E[\\gamma_*]=0. \\]\n\n\nZ1 holds by construction. Under Z1, Z3 implies Z2, but Z2 does not imply Z3. Principle R motivates an attainment requirement in its declared domain; it does not make Z3 an unconditional consequence of nonnegativity.\n\nHere \\(\\operatorname{Leb}\\) denotes one-dimensional Lebesgue measure on \\([0,1]\\). The positive-measure statement below concerns curve-parameter values \\(t\\), not ambient parameter-space volume or arc-length measure.\n\nProposition 1 — Zero-cost attainment yields nontrivial kernel motion.\n\nUnder the assumptions above, Z3 implies\n\n\\[ J(\\gamma_*(t))\\dot\\gamma_*(t)=0 \\quad\\text{for almost every }t, \\]\n\nand\n\n\\[ \\operatorname{Leb} \\left( \\left\\{ t\\in[0,1]: \\dot\\gamma_*(t)\\text{ exists}, \\ \\dot\\gamma_*(t)\\ne0, \\ J(\\gamma_*(t))\\dot\\gamma_*(t)=0 \\right\\} \\right)\u003e0. \\]\n\nFurthermore,\n\n\\[ R(\\gamma_*(t))=R(\\gamma_*(0)) \\qquad\\text{for every }t\\in[0,1]. \\]\n\nProof. The nonnegative measurable integrand has zero integral, so \\(F_R(\\gamma_*,\\dot\\gamma_*)=0\\) almost everywhere. Positive definiteness of \\(G_O\\) gives \\(J\\dot\\gamma_*=0\\) almost everywhere. An absolutely continuous curve whose derivative vanishes almost everywhere is constant. Nonconstancy therefore implies that \\(\\dot\\gamma_*\\ne0\\) on a set of positive Lebesgue measure. Intersecting that set with the full-measure kernel condition proves the second assertion. The chain rule and absolute continuity of \\(R\\circ\\gamma_*\\) give response constancy.\n\nRemark — Endpoint lower bound. For any \\(\\gamma\\in\\Gamma\\),\n\n\\[ E[\\gamma] \\ge \\|R(\\gamma(1))-R(\\gamma(0))\\|_{G_O}. \\]\n\nIndeed,\n\n\\[ R(\\gamma(1))-R(\\gamma(0)) = \\int_0^1J(\\gamma(t))\\dot\\gamma(t)\\,dt, \\]\n\nand the integral triangle inequality gives the bound.\n\nRemark — Zero infimum and pointwise kernels do not establish attainment. Let \\(R(\\theta)=\\theta\\), \\(G_O=1\\), and let \\(\\Gamma\\) contain\n\n\\[ \\gamma_\\epsilon(t)=\\epsilon t, \\qquad \\epsilon\u003e0. \\]\n\nThen\n\n\\[ E[\\gamma_\\epsilon]=\\epsilon\\to0, \\]\n\nbut \\(J=1\\) has no nonzero kernel, and every zero-cost absolutely continuous curve is constant.\n\nFor \\(R(\\theta)=\\theta^2\\), the kernel at zero is all of \\(\\mathbb R\\), and\n\n\\[ E[\\gamma_\\epsilon]=\\epsilon^2\\to0. \\]\n\nNevertheless, a zero-cost curve must have constant \\(R\\), and no nonconstant continuous curve in \\(\\mathbb R\\) can remain in a fibre of \\(\\theta^2\\). Thus a curve class containing this family satisfies Z2 but not Z3.\n\nA sufficient local geometric condition is that \\(R\\) be \\(C^1\\) with constant rank \\(r_0\u003cd\\) on a neighbourhood. The constant-rank theorem gives local response fibres of dimension \\(d-r_0\\), containing nonconstant response-preserving curves. Z3 additionally requires \\(\\Gamma\\) to admit such curves.\n\nDependencies of the subsequent results. Neither Z2 nor Z3 is required below. Proposition 2 uses \\(J\\) and \\(DH\\) at a single state. Proposition 3 uses \\(J\\) and \\(\\lambda\u003e0\\). Propositions 4–8 use Lemma 1 and their stated regularity, derivative and budget conditions.\n\n3.3 Zero Modes and Readout Controllability\n\nA response-preserving direction supports memory writing only if it changes a declared readout.\n\nFix a state \\(\\theta\\). Let the columns of\n\n\\[ N\\in\\mathbb R^{d\\times k}, \\qquad k=d-\\operatorname{rank}J, \\]\n\nform an orthonormal basis for \\(\\ker J\\). Define\n\n\\[ C=DH(\\theta)N\\in\\mathbb R^{q\\times k}. \\]\n\nProposition 2 — Response-preserving readout controllability.\n\nFor a desired infinitesimal readout change \\(b\\in\\mathbb R^q\\), the system\n\n\\[ Jv=0, \\qquad DH(\\theta)v=b \\]\n\nhas a solution if and only if\n\n\\[ b\\in\\operatorname{Im}C. \\]\n\nWhen feasible, its minimum-Euclidean-norm solution is\n\n\\[ v_{\\min}=NC^\\dagger b, \\]\n\nwhere \\(C^\\dagger\\) is the Moore–Penrose pseudoinverse.\n\nProof. Every \\(v\\in\\ker J\\) has a unique representation \\(v=N\\xi\\), with \\(\\|v\\|_2=\\|\\xi\\|_2\\). The readout equation becomes \\(C\\xi=b\\), whose minimum-norm solution is \\(C^\\dagger b\\).\n\nConsequences — Rank, conditioning and basis independence. If \\(\\operatorname{rank}C=q\\), every \\(b\\in\\mathbb R^q\\) is attainable in the linearised model, and\n\n\\[ \\|v_{\\min}\\|_2 \\le \\frac{\\|b\\|_2}{\\sigma_{\\min}(C)}, \\]\n\nwhere \\(\\sigma_{\\min}(C)\\) is its smallest positive singular value. Full row rank requires\n\n\\[ q\\le d-\\operatorname{rank}J, \\]\n\nbut this dimension condition is not sufficient.\n\nThe rank of \\(C\\) counts independently controllable first-order readout directions. Its singular values describe their conditioning and the displacement required to realise them.\n\nReplacing \\(N\\) by \\(NQ\\), with \\(Q\\) orthogonal, replaces \\(C\\) by \\(CQ\\) without changing its image, rank or singular values. Since\n\n\\[ (CQ)^\\dagger=Q^\\top C^\\dagger, \\]\n\nthe minimum-norm parameter direction is unchanged.\n\nThe bridge from zero modes to writing is\n\n\\[ \\exists v\\in\\ker J: DH(\\theta)v\\ne0 \\iff C\\ne0. \\]\n\nIf \\(C=0\\), first-order readout control vanishes at that state, although higher-order changes may remain possible.\n\nCorollary 1 — Selective first-order writing.\n\nFor scalar readout \\(H_i\\), let \\(B_i\\) stack the rows of \\(J\\) and \\(DH_j\\) for all \\(j\\ne i\\). For any prescribed \\(a_i\\ne0\\),\n\n\\[ B_iv_i=0, \\qquad DH_iv_i=a_i \\]\n\nis feasible if and only if\n\n\\[ DH_i\\notin\\operatorname{rowspan}B_i. \\]\n\nEquivalently,\n\n\\[ a_ie_i\\in\\operatorname{Im}C, \\]\n\nwhere \\(e_i\\) is the \\(i\\)-th coordinate vector in readout space.\n\nLet \\(Q_i\\) be the Euclidean orthogonal projector onto \\(\\ker B_i\\), and define\n\n\\[ d_i = \\|Q_iDH_i^\\top\\|_2 = \\operatorname{dist} \\bigl(DH_i,\\operatorname{rowspan}B_i\\bigr). \\]\n\nWhen \\(d_i\u003e0\\),\n\n\\[ v_{i,\\min} = \\frac{a_i}{d_i^2}Q_iDH_i^\\top, \\qquad \\|v_{i,\\min}\\|_2=\\frac{|a_i|}{d_i}. \\]\n\nProof. Restricting to \\(\\ker B_i\\) replaces the readout covector by \\(Q_iDH_i^\\top\\). A nonzero target is feasible precisely when this projection is nonzero. The minimum-norm solution follows from the Cauchy–Schwarz inequality, with equality along the projected direction.\n\nRemark — Numerical feasibility. Numerical rank estimates alone are not feasibility certificates. Computed directions should be accompanied by residuals, conditioning information and the required displacement norm.\n\n3.4 Regularised Near-Kernel Updates and Leakage\n\nA regularised near-kernel operator retains kernel components and attenuates components that change protected responses.\n\nFor \\(\\lambda\u003e0\\), define\n\n\\[ P_\\lambda = I_d-J^\\top(JJ^\\top+\\lambda I_p)^{-1}J = \\lambda(J^\\top J+\\lambda I_d)^{-1}. \\]\n\nIt acts as the identity on \\(\\ker J\\). Along a right singular direction with positive singular value \\(s\\), it scales the component by\n\n\\[ \\frac{\\lambda}{s^2+\\lambda}. \\]\n\nProposition 3 — Spectral leakage bound.\n\nThe operator satisfies\n\n\\[ \\|P_\\lambda\\|_2\\le1, \\qquad \\|JP_\\lambda\\|_2\\le\\frac{\\sqrt\\lambda}{2}. \\]\n\nFor \\(J\\ne0\\),\n\n\\[ \\|JP_\\lambda\\|_2 = \\max_{s\\in\\sigma_+(J)} \\frac{s\\lambda}{s^2+\\lambda}. \\]\n\nFor \\(J=0\\), the leakage is zero.\n\nProof. Apply a singular-value decomposition of \\(J\\). The positive singular values of \\(JP_\\lambda\\) are \\(s\\lambda/(s^2+\\lambda)\\). This expression is at most \\(\\sqrt\\lambda/2\\), with its scalar maximum attained at \\(s=\\sqrt\\lambda\\).\n\nCorollary 2 — Unnormalised descent and leakage.\n\nLet\n\n\\[ u=-P_\\lambda g, \\qquad g=\\nabla L_{\\mathrm{write}}(\\theta). \\]\n\nThen\n\n\\[ \\|u\\|_2\\le\\|g\\|_2, \\qquad \\|Ju\\|_2\\le\\frac{\\sqrt\\lambda}{2}\\|g\\|_2. \\]\n\nWhen \\(g\\ne0\\),\n\n\\[ g^\\top u=-g^\\top P_\\lambda g\u003c0. \\]\n\nProof. The norm bounds follow from Proposition 3. Positive definiteness of \\(P_\\lambda=\\lambda(J^\\top J+\\lambda I_d)^{-1}\\) gives strict descent.\n\nRemark — The regularised operator is not a projector. The identity\n\n\\[ JP_\\lambda = \\lambda(JJ^\\top+\\lambda I_p)^{-1}J \\]\n\nshows that, whenever \\(J\\ne0\\),\n\n\\[ JP_\\lambda\\ne0, \\qquad P_\\lambda^2\\ne P_\\lambda. \\]\n\nFor \\(J=0\\), \\(P_\\lambda=I_d\\).\n\nRemark — Normalisation changes the leakage statement. For\n\n\\[ \\widehat u = -\\frac{P_\\lambda g}{\\|P_\\lambda g\\|_2}, \\qquad g\\ne0, \\]\n\none has\n\n\\[ \\|J\\widehat u\\|_2 = \\frac{\\|JP_\\lambda g\\|_2}{\\|P_\\lambda g\\|_2} \\le \\min\\left\\{ \\|J\\|_2,\\, \\frac{\\sqrt\\lambda}{2} \\frac{\\|g\\|_2}{\\|P_\\lambda g\\|_2} \\right\\}. \\]\n\nNormalisation preserves the descent sign but can remove the attenuation of the unnormalised direction. If \\(g\\) lies along a right singular direction with singular value \\(s\u003e0\\), then\n\n\\[ \\|J\\widehat u\\|_2=s. \\]\n\nFor an actual step \\(\\delta\\theta=\\alpha\\widehat u\\),\n\n\\[ \\|J\\delta\\theta\\|_2 = \\alpha\\|J\\widehat u\\|_2, \\qquad \\alpha\\ge0. \\]\n\nRemark — Algorithmic scope. Feature-null restrictions, covariance preconditioning, metric projection onto a parameter-norm ball, normalisation, backtracking and response correction are distinct operations. Bounds must apply to the actual displacement produced by the specified algorithm.\n\nProposition 3 is an exact-arithmetic statement and does not by itself certify a floating-point implementation. The weighted-metric extension and numerical error bounds are given in Appendix A.\n\nSection 3.5 combines first-order leakage with curvature to obtain finite-step budget conditions. Modified directions require the corresponding leakage estimate for their actual displacement.\n\n3.5 Finite-Step Response and KL Preservation\n\nFirst-order compatibility identifies candidate directions. Finite admissibility additionally depends on curvature and the remaining budgets. The following lemma supplies the common remainder estimate used here and in §3.6.\n\nLemma 1 — Taylor remainder along an update segment.\n\nLet \\(F\\) be a continuously differentiable map into \\(\\mathbb R^a\\), defined on an open neighbourhood of the segment\n\n\\[ \\{\\theta+tv:0\\le t\\le\\eta\\}, \\qquad \\eta\\ge0. \\]\n\nSuppose\n\n\\[ \\|DF(\\theta+tv)-DF(\\theta)\\|_2 \\le Lt\\|v\\|_2 \\qquad(0\\le t\\le\\eta), \\]\n\nwith \\(L\\ge0\\). Then\n\n\\[ F(\\theta+\\eta v) = F(\\theta)+\\eta DF(\\theta)v+e_F, \\]\n\nwhere\n\n\\[ \\|e_F\\|_2 \\le \\frac L2\\eta^2\\|v\\|_2^2. \\]\n\nFor vector-valued \\(F\\),\n\n\\[ \\|e_F\\|_\\infty \\le \\|e_F\\|_2 \\le \\frac L2\\eta^2\\|v\\|_2^2. \\]\n\nFor scalar-valued \\(F\\), the same bound holds with \\(|e_F|\\).\n\nProof. The fundamental theorem of calculus gives\n\n\\[ e_F = \\int_0^\\eta [DF(\\theta+tv)-DF(\\theta)]v\\,dt. \\]\n\nTaking norms and integrating yields\n\n\\[ \\|e_F\\|_2 \\le \\int_0^\\eta Lt\\|v\\|_2^2\\,dt = \\frac L2\\eta^2\\|v\\|_2^2. \\]\n\nThis lemma requires no kernel or selectivity constraint. It applies to \\(R\\), \\(K\\) and each \\(H_j\\) under their respective regularity assumptions.\n\nDeclared budgets. Fix a reference state \\(\\theta_{\\mathrm{ref}}\\), and define\n\n\\[ K(\\theta) = \\frac1{|A|} \\sum_{x\\in A} D_{\\mathrm{KL}} \\left( p_{\\theta_{\\mathrm{ref}}}(\\cdot\\mid x) \\,\\middle\\|\\, p_\\theta(\\cdot\\mid x) \\right). \\]\n\nThe anchor set, distribution and KL convention are declared before evaluation. This average does not imply a uniform per-anchor bound.\n\nFor target response \\(r\\) and budgets \\(\\varepsilon_R,\\varepsilon_{\\mathrm{KL}}\\ge0\\), define\n\n\\[ \\mathcal F(r) = \\left\\{ \\theta\\in\\mathcal L: \\|R(\\theta)-r\\|_\\infty\\le\\varepsilon_R, \\quad K(\\theta)\\le\\varepsilon_{\\mathrm{KL}} \\right\\}. \\]\n\nParameter-norm, resource and content constraints are specified separately.\n\nConsider\n\n\\[ \\theta^+=\\theta+\\eta u, \\qquad \\eta\\ge0. \\]\n\nResponse budget\n\nProposition 4 — Finite-step response preservation.\n\nSuppose \\(R\\) satisfies Lemma 1 on the entire update segment, with constant \\(L_R\\). Define\n\n\\[ \\rho_R = \\varepsilon_R-\\|R(\\theta)-r\\|_\\infty. \\]\n\nThen\n\n\\[ \\|R(\\theta^+)-r\\|_\\infty \\le \\|R(\\theta)-r\\|_\\infty + \\eta\\|Ju\\|_\\infty + \\frac{L_R}{2}\\eta^2\\|u\\|_2^2. \\]\n\nConsequently,\n\n\\[ \\eta\\|Ju\\|_\\infty + \\frac{L_R}{2}\\eta^2\\|u\\|_2^2 \\le\\rho_R \\]\n\nis sufficient for the response budget.\n\nProof. Apply Lemma 1 to \\(R\\) and use the triangle inequality.\n\nConsequences — Step bounds. For \\(Ju=0\\), \\(\\rho_R\u003e0\\), \\(L_R\u003e0\\) and \\(u\\ne0\\),\n\n\\[ \\eta \\le \\frac{\\sqrt{2\\rho_R/L_R}}{\\|u\\|_2} \\]\n\nis sufficient, subject to the segment conditions.\n\nFor \\(u=-P_\\lambda g\\), Corollary 2 and\n\n\\[ \\|Ju\\|_\\infty\\le\\|Ju\\|_2 \\]\n\ngive the more conservative sufficient condition\n\n\\[ \\eta\\frac{\\sqrt\\lambda}{2}\\|g\\|_2 + \\frac{L_R}{2}\\eta^2\\|g\\|_2^2 \\le\\rho_R. \\]\n\nFor a normalised direction, use its actual \\(\\|J\\widehat u\\|_\\infty\\) and \\(\\|\\widehat u\\|_2=1\\).\n\nRemark — Uniform curvature bounds. Suppose \\(R\\) is \\(C^2\\) on an open neighbourhood of a compact convex region \\(U\\) containing the segment. Define\n\n\\[ M_R = \\sup_{\\xi\\in U} \\sup_{\\|v_1\\|_2=\\|v_2\\|_2=1} \\|D^2R(\\xi)[v_1,v_2]\\|_2. \\]\n\nThen \\(L_R=M_R\\) is valid throughout \\(U\\), including the kernel-direction bound in §3.2. Under the affine parameterisation,\n\n\\[ D^2R(\\theta)[v_1,v_2] = D^2R_{\\mathrm{full}}(w(\\theta))[Tv_1,Tv_2]. \\]\n\nKL budget and joint admissibility\n\nProposition 5 — Finite-step KL preservation.\n\nSuppose \\(K\\) satisfies the scalar version of Lemma 1 on the entire update segment, with constant \\(L_K\\). Define\n\n\\[ \\rho_K=\\varepsilon_{\\mathrm{KL}}-K(\\theta). \\]\n\nThen\n\n\\[ K(\\theta^+) \\le K(\\theta) + \\eta\\nabla K(\\theta)^\\top u + \\frac{L_K}{2}\\eta^2\\|u\\|_2^2. \\]\n\nTherefore,\n\n\\[ \\eta\\nabla K(\\theta)^\\top u + \\frac{L_K}{2}\\eta^2\\|u\\|_2^2 \\le\\rho_K \\]\n\nis sufficient for the KL budget.\n\nProof. Apply Lemma 1 to the scalar map \\(K\\) and use its upper remainder bound.\n\nCorollary 3 — Joint finite admissibility.\n\nUnder Propositions 4 and 5, if \\(\\theta^+\\in\\mathcal L\\) and\n\n\\[ \\eta\\|Ju\\|_\\infty + \\frac{L_R}{2}\\eta^2\\|u\\|_2^2 \\le\\rho_R, \\]\\[ \\eta\\nabla K(\\theta)^\\top u + \\frac{L_K}{2}\\eta^2\\|u\\|_2^2 \\le\\rho_K, \\]\n\nthen\n\n\\[ \\boxed{\\theta^+\\in\\mathcal F(r).} \\]\n\nProof. The two propositions establish the response and KL inequalities; chart membership completes the definition of \\(\\mathcal F(r)\\).\n\nSuccessful writing additionally requires the declared content margins and separate parameter-norm or resource constraints.\n\nRemark — Reference-state KL behaviour. At a differentiable interior reference state,\n\n\\[ K(\\theta_{\\mathrm{ref}})=0, \\qquad \\nabla K(\\theta_{\\mathrm{ref}})=0. \\]\n\nProposition 5 therefore gives\n\n\\[ K(\\theta_{\\mathrm{ref}}+\\eta u) \\le \\frac{L_K}{2}\\eta^2\\|u\\|_2^2 \\]\n\nwhenever the bound holds along that segment.\n\nRemark — Local Fisher interpretation. Define\n\n\\[ w_{\\mathrm{ref}}=w(\\theta_{\\mathrm{ref}}). \\]\n\nUnder smoothness, fixed-support and differentiation-under-expectation conditions,\n\n\\[ \\nabla_\\theta^2K(\\theta_{\\mathrm{ref}}) = T^\\top\\mathcal I_A(w_{\\mathrm{ref}})T, \\]\n\nwhere\n\n\\[ \\mathcal I_A(w_{\\mathrm{ref}}) = \\frac1{|A|} \\sum_{x\\in A} \\mathbb E_{y\\sim p_{w_{\\mathrm{ref}}}(\\cdot\\mid x)} [s_x(y)s_x(y)^\\top], \\]\n\nand\n\n\\[ s_x(y) = \\left. \\nabla_w\\log p_w(y\\mid x) \\right|_{w=w_{\\mathrm{ref}}}. \\]\n\nConsequently,\n\n\\[ K(\\theta_{\\mathrm{ref}}+\\delta) = \\frac12 \\delta^\\top T^\\top\\mathcal I_A(w_{\\mathrm{ref}})T\\delta + o(\\|\\delta\\|_2^2). \\]\n\nThe distribution must match the declared KL measurement. Final-token KL and full-sequence KL are different quantities. The reference Hessian describes the leading local quadratic cost; its largest eigenvalue alone does not bound curvature over a finite region. This interpretation is not an additional premise of the finite-step inequalities and does not identify an arbitrary optimisation metric with Fisher information.\n\n3.6 Selective Writes, Composition and Response Correction\n\nSelective finite writes\n\nProposition 6 — Finite-step selective writing.\n\nAt the current state \\(\\theta\\), suppose\n\n\\[ Jv_i=0, \\qquad DH_iv_i=a_i, \\qquad DH_jv_i=0 \\quad(j\\ne i). \\]\n\nThe condition \\(Jv_i=0\\) is included for first-order response compatibility; the readout bounds below do not require it.\n\nLet \\(\\eta\\ge0\\). Suppose the segment lies in the declared chart and each relevant \\(H_j\\) satisfies Lemma 1 there, with constant \\(L_j\\).\n\nThen, for \\(j\\ne i\\),\n\n\\[ |H_j(\\theta+\\eta v_i)-H_j(\\theta)| \\le \\frac{L_j}{2}\\eta^2\\|v_i\\|_2^2, \\]\n\nand\n\n\\[ \\left| H_i(\\theta+\\eta v_i)-H_i(\\theta)-\\eta a_i \\right| \\le \\frac{L_i}{2}\\eta^2\\|v_i\\|_2^2. \\]\n\nWhen \\(a_i\u003e0\\), an increase of at least \\(\\Delta\u003e0\\) is guaranteed if\n\n\\[ \\eta a_i - \\frac{L_i}{2}\\eta^2\\|v_i\\|_2^2 \\ge\\Delta. \\]\n\nIf the unselected first-order condition is approximate,\n\n\\[ |DH_jv_i|\\le\\tau_j, \\]\n\nthen\n\n\\[ |H_j(\\theta+\\eta v_i)-H_j(\\theta)| \\le \\eta\\tau_j + \\frac{L_j}{2}\\eta^2\\|v_i\\|_2^2. \\]\n\nProof. Apply the scalar version of Lemma 1 to each \\(H_j\\) and substitute the exact or approximate readout derivative constraints.\n\nConsequence — Binary margin attainment. Suppose \\(H_i=h_{x_i}\\), with target \\(y_i\\) fixed during the operation. Set\n\n\\[ s_i=2y_i-1, \\qquad m_i(\\theta)=s_iH_i(\\theta). \\]\n\nChoose the direction so that\n\n\\[ s_i a_i\u003e0. \\]\n\nThen\n\n\\[ m_i(\\theta+\\eta v_i) \\ge m_i(\\theta) + \\eta s_i a_i - \\frac{L_i}{2}\\eta^2\\|v_i\\|_2^2. \\]\n\nA margin threshold \\(\\mu_i\\) is attained if\n\n\\[ \\eta s_i a_i - \\frac{L_i}{2}\\eta^2\\|v_i\\|_2^2 \\ge \\mu_i-m_i(\\theta). \\]\n\nOne may instead apply Proposition 6 directly to a target-relative margin readout, holding its target fixed while differentiating. The step must also meet the preservation and parameter constraints.\n\nAccumulated interference and preservation budgets\n\nProposition 7 — Cumulative readout interference.\n\nConsider \\(m\\) updates,\n\n\\[ \\theta_{\\ell+1} = \\theta_\\ell+\\eta_\\ell v_\\ell, \\qquad \\ell=0,\\ldots,m-1, \\qquad \\eta_\\ell\\ge0. \\]\n\nSuppose readout \\(j\\) is unselected throughout and\n\n\\[ |DH_j(\\theta_\\ell)v_\\ell| \\le\\tau_{j,\\ell} \\]\n\nat each current state. Assume every segment lies in the declared chart and \\(H_j\\) satisfies Lemma 1 on that segment with constant \\(L_{j,\\ell}\\). Then\n\n\\[ |H_j(\\theta_m)-H_j(\\theta_0)| \\le \\sum_{\\ell=0}^{m-1} \\left[ \\eta_\\ell\\tau_{j,\\ell} + \\frac{L_{j,\\ell}}2 \\eta_\\ell^2\\|v_\\ell\\|_2^2 \\right]. \\]\n\nProof. Lemma 1 bounds each readout increment by its first-order term and remainder. Sum these bounds and use the triangle inequality. No condition \\(J(\\theta_\\ell)v_\\ell=0\\) is required.\n\nFor \\(m=1\\), Proposition 7 reproduces the approximate unselected-readout bound in Proposition 6, without requiring a response-kernel constraint.\n\nCorollary 4 — Cumulative response and KL bounds.\n\nFor the same sequence, let\n\n\\[ J_\\ell=DR(\\theta_\\ell). \\]\n\nSuppose every segment satisfies the assumptions of Propositions 4 and 5, with constants \\(L_{R,\\ell}\\) and \\(L_{K,\\ell}\\). Keep the target response \\(r\\), reference state \\(\\theta_{\\mathrm{ref}}\\), KL measurement and budgets fixed throughout the sequence.\n\nDefine\n\n\\[ A_\\ell = \\eta_\\ell\\|J_\\ell v_\\ell\\|_\\infty + \\frac{L_{R,\\ell}}2 \\eta_\\ell^2\\|v_\\ell\\|_2^2, \\]\n\nand\n\n\\[ B_\\ell = \\eta_\\ell\\nabla K(\\theta_\\ell)^\\top v_\\ell + \\frac{L_{K,\\ell}}2 \\eta_\\ell^2\\|v_\\ell\\|_2^2. \\]\n\nFor every prefix \\(n=1,\\ldots,m\\),\n\n\\[ \\|R(\\theta_n)-r\\|_\\infty \\le \\|R(\\theta_0)-r\\|_\\infty + \\sum_{\\ell=0}^{n-1}A_\\ell, \\]\n\nand\n\n\\[ K(\\theta_n) \\le K(\\theta_0) + \\sum_{\\ell=0}^{n-1}B_\\ell. \\]\n\nConsequently, if \\(\\theta_0\\in\\mathcal F(r)\\), every \\(\\theta_n\\in\\mathcal L\\), and\n\n\\[ \\sum_{\\ell=0}^{m-1}A_\\ell \\le \\varepsilon_R-\\|R(\\theta_0)-r\\|_\\infty, \\]\n\ntogether with\n\n\\[ \\sum_{\\ell=0}^{n-1}B_\\ell \\le \\varepsilon_{\\mathrm{KL}}-K(\\theta_0) \\qquad(n=1,\\ldots,m), \\]\n\nthen\n\n\\[ \\theta_n\\in\\mathcal F(r) \\qquad(n=0,\\ldots,m). \\]\n\nProof. Sum the one-step bounds from Propositions 4 and 5. Since \\(A_\\ell\\ge0\\), the total response condition bounds every response prefix. The signed KL increments require their stated prefix conditions. Chart membership completes admissibility.\n\nRemark — Mixed selected and unselected operations. Proposition 7 directly covers a readout left unselected throughout the sequence. For a sequence in which readout \\(j\\) is sometimes selected, declare a desired first-order change \\(a_{j,\\ell}\\), taking \\(a_{j,\\ell}=0\\) on unselected steps, and assume\n\n\\[ |DH_j(\\theta_\\ell)v_\\ell-a_{j,\\ell}| \\le\\tau_{j,\\ell}. \\]\n\nLemma 1 then gives\n\n\\[ \\left| H_j(\\theta_m)-H_j(\\theta_0) - \\sum_{\\ell=0}^{m-1}\\eta_\\ell a_{j,\\ell} \\right| \\le \\sum_{\\ell=0}^{m-1} \\left[ \\eta_\\ell\\tau_{j,\\ell} + \\frac{L_{j,\\ell}}2 \\eta_\\ell^2\\|v_\\ell\\|_2^2 \\right]. \\]\n\nThus composition can track deviations from declared changes as well as preservation of unselected contents.\n\nRemark — Sequence-level acceptance. The KL increments \\(B_\\ell\\) may be negative. A final-prefix condition alone does not guarantee that earlier states respected the KL budget. Prefix conditions, or direct statewise checks, are needed when every operation must remain admissible.\n\nDerivative constraints and regularity bounds must hold at the states and segments where updates occur. Constraints imposed only at the initial state do not establish these cumulative conclusions.\n\nNumerical response correction\n\nProposition 8 — Correction magnitude and response residual.\n\nAt a state \\(\\theta\\), let\n\n\\[ e=R(\\theta)-r, \\qquad J=DR(\\theta), \\]\n\nand define\n\n\\[ \\delta\\theta = -J^\\top(JJ^\\top+\\lambda I_p)^{-1}e, \\qquad \\lambda\u003e0. \\]\n\nThen\n\n\\[ \\|\\delta\\theta\\|_2 \\le \\frac{\\|e\\|_2}{2\\sqrt\\lambda}, \\]\n\nand\n\n\\[ e+J\\delta\\theta = \\lambda(JJ^\\top+\\lambda I_p)^{-1}e. \\]\n\nIf the correction segment lies in the declared chart and \\(R\\) satisfies Lemma 1 there with constant \\(L_R\\), then\n\n\\[ \\|R(\\theta+\\delta\\theta)-r\\|_\\infty \\le \\left\\| \\lambda(JJ^\\top+\\lambda I_p)^{-1}e \\right\\|_\\infty + \\frac{L_R}{2}\\|\\delta\\theta\\|_2^2. \\]\n\nProof. The singular values of the correction operator on positive singular directions are\n\n\\[ \\frac{s}{s^2+\\lambda}, \\]\n\nwhich are at most \\(1/(2\\sqrt\\lambda)\\). For \\(J=0\\), the correction operator is zero. The residual identity follows from\n\n\\[ I_p-JJ^\\top(JJ^\\top+\\lambda I_p)^{-1} = \\lambda(JJ^\\top+\\lambda I_p)^{-1}. \\]\n\nApply Lemma 1 with \\(\\eta=1\\) and \\(v=\\delta\\theta\\) to obtain the finite residual bound.\n\nConsequences — Curvature and content bounds. Substituting the correction-norm bound yields\n\n\\[ \\|R(\\theta+\\delta\\theta)-r\\|_\\infty \\le \\left\\| \\lambda(JJ^\\top+\\lambda I_p)^{-1}e \\right\\|_\\infty + \\frac{L_R}{8\\lambda}\\|e\\|_2^2. \\]\n\nFor a readout \\(H_j\\) satisfying Lemma 1 on the correction segment,\n\n\\[ |H_j(\\theta+\\delta\\theta)-H_j(\\theta)| \\le |DH_j(\\theta)\\delta\\theta| + \\frac{L_j}{2}\\|\\delta\\theta\\|_2^2, \\]\n\nand hence\n\n\\[ |H_j(\\theta+\\delta\\theta)-H_j(\\theta)| \\le \\frac{\\|DH_j(\\theta)\\|_2}{2\\sqrt\\lambda}\\|e\\|_2 + \\frac{L_j}{8\\lambda}\\|e\\|_2^2. \\]\n\nRemark — Regularisation and curvature. Along a positive left singular direction, the linear residual is attenuated by\n\n\\[ \\frac{\\lambda}{s^2+\\lambda}. \\]\n\nComponents orthogonal to \\(\\operatorname{Im}J\\) remain unchanged in the linearised model. Decreasing \\(\\lambda\\) improves attenuation on positive singular directions but weakens the uniform correction-norm bound as \\(1/\\sqrt\\lambda\\) and the resulting curvature bound as \\(1/\\lambda\\).\n\nThese are worst-case bounds, not claims that the actual correction diverges for a fixed \\(J\\). Its exact size depends on the singular spectrum and the components of \\(e\\). Finite nonlinear residual reduction requires the post-correction bound, or direct measurement, to improve on the current residual.\n\nCorrection steps enter Proposition 7 and Corollary 4 with\n\n\\[ \\eta_\\ell=1, \\qquad v_\\ell=\\delta\\theta_\\ell. \\]\n\nTheir acceptance depends on actual post-correction response, KL and content values. The quantity \\(\\|J\\delta\\theta\\|\\) measures the correction’s linear action, rather than the residual remaining after correction.\n\nRemark — Statewise correction and sequence accounting. Proposition 8 bounds the next residual using\n\n\\[ e_\\ell=R(\\theta_\\ell)-r. \\]\n\nIt can provide a tighter response bound than the generic additive estimate in Corollary 4. Incorporating it into sequence-level accounting requires measured or certified residual information, or a valid bound propagated over the possible residuals. An unknown residual cannot be substituted as though it were known. Numerical error in the computed correction must also be included when applying the bound to an implementation.\n\n3.7 From Mathematical Conditions to Operational Evidence\n\nThe framework separates five questions:\n\n\n\n\n\n\n\n\n\n\nQuestion\nMathematical criterion or bound\nResults\n\n\n\n\nZero modes\nNonzero \\(\\ker J\\), or an admitted nonconstant zero-cost curve\n§3.2; Proposition 1\n\n\nControllability\n\\(b\\in\\operatorname{Im}C\\), with conditioning and displacement requirements\nProposition 2\n\n\nFinite feasibility\nJoint response and KL conditions, chart membership and separate parameter constraints\nLemma 1; Propositions 3–5; Corollaries 2–3\n\n\nSelectivity\nSelective linear feasibility, finite interference and target-margin attainment\nLemma 1; Corollary 1; Proposition 6\n\n\nComposition\nCumulative readout, response and KL bounds, including selected operations and corrections\nLemma 1; Propositions 7–8; Corollary 4\n\n\n\n\n\n\n\nThree objects remain distinct: an ideal first-order kernel, a numerically computed candidate update, and a finite parameter state accepted by the measurement protocol.\n\nAn address is defined by its access rule. A kernel direction is a mechanism for changing the content returned by that rule. An endpoint atlas is a collection of separately instantiated parameter states; a shared state is one parameter point realising multiple addressed contents.\n\nThe central quantitative problem is to achieve enough readout change for reliable writing while keeping response drift, KL change and cross-address interference within budget. Kernel dimension alone does not determine usable memory capacity.\n\nThese local results organise the feasibility problem; they do not replace finite measurement. Experimental reports must identify the protected responses, access rules, tolerances, parameter domain, numerical procedure and evaluation coverage. Average-response preservation must be distinguished from per-prompt preservation, and development acceptance from independent confirmation.\n\nThe B0–B5 roadmap tests finite implementations of WRITE, OVERWRITE, SWAP, MOVE and RETURN, followed by their integration into computation and model-selected operation sequences. These capabilities are claimed only where the corresponding finite tests, controls and reproducibility evidence support them.\n\n \n\nAppendix A. Weighted Operators and Numerical Error\n\nA.1 Weighted Output Metric\n\nLet \\(G_O\\succ0\\) be the declared output metric and set\n\n\\[ \\widetilde J=G_O^{1/2}J. \\]\n\nApplying the regularised construction to \\(\\widetilde J\\) gives\n\n\\[ P_{\\lambda,G_O} = I_d-\\widetilde J^\\top (\\widetilde J\\widetilde J^\\top+\\lambda I_p)^{-1} \\widetilde J = \\lambda(g_R+\\lambda I_d)^{-1}. \\]\n\nProposition 3 applied to \\(\\widetilde J\\) yields\n\n\\[ \\|JP_{\\lambda,G_O}g\\|_{G_O} = \\|\\widetilde JP_{\\lambda,G_O}g\\|_2 \\le \\frac{\\sqrt\\lambda}{2}\\|g\\|_2. \\]\n\nThis construction weights protected-output changes while retaining the Euclidean metric on parameter coordinates. It does not identify a separately chosen covariance preconditioner or parameter-space metric with \\(g_R\\).\n\nA.2 Numerical Error in Candidate Updates\n\nProposition 3 concerns the exact operator and exact direction. Let\n\n\\[ u=-P_\\lambda g, \\qquad \\widetilde u=u+e_u \\]\n\nbe the computed unnormalised direction. Then\n\n\\[ \\|J\\widetilde u\\|_2 \\le \\frac{\\sqrt\\lambda}{2}\\|g\\|_2 + \\|J\\|_2\\|e_u\\|_2. \\]\n\nThus the exact leakage bound alone does not certify the computed direction. A valid numerical certificate requires control of the direction error, together with any error in the Jacobian used to evaluate leakage.\n\nIf \\(\\widetilde J\\) is a computed Jacobian, then\n\n\\[ \\|J\\widetilde u\\|_2 \\le \\|\\widetilde J\\widetilde u\\|_2 + \\|J-\\widetilde J\\|_2\\|\\widetilde u\\|_2. \\]\n\nFor a numerically computed correction \\(\\widetilde{\\delta\\theta}\\), Lemma 1 gives the directly applicable bound\n\n\\[ \\|R(\\theta+\\widetilde{\\delta\\theta})-r\\|_\\infty \\le \\|e+J\\widetilde{\\delta\\theta}\\|_\\infty + \\frac{L_R}{2}\\|\\widetilde{\\delta\\theta}\\|_2^2, \\]\n\nprovided the regularity bound holds on the actual correction segment.\n\nThese bounds separate exact operator properties from numerical implementation and finite nonlinear acceptance.\n\n4. Implementation, Evidence Access and Reproducibility\n\nEvery capability claim must identify its model and revision, parameter chart, protocol, software version and machine-readable result records.\n\nReproducibility materials should specify access rules, protected responses, budgets, data partitions, controls, stopping conditions and acceptance criteria. Reported records should distinguish completed, failed and interrupted runs, and separate development evidence from independent confirmation.\n\nReading and evidence access\n\n\n\nAccompanying paper: A Programmable Address Space for Neural Memory, available as a PDF attached to this record.\n\nConceptual background: A Principle of Physical Realizability: Attainability and Local Zero Modes.\n\nPublic code, protocols and evidence: github.com/papasop/fibre-nav.\n\nQwen development implementation: Maintained in a private Hugging Face repository; it is not currently publicly accessible.\n\n\nPublic reproducibility claims are limited to the materials available for inspection and execution. Results from private development implementations remain separately identified until the corresponding source, protocols and evidence are released."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.22097583","contentUrl":null,"metadataVersion":330,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":13,"versionOfCount":0,"created":"2026-08-25T14:31:51Z","registered":"2026-08-25T14:31:52Z","published":null,"updated":"2026-10-24T05:56:42Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.23610514","type":"dois","attributes":{"doi":"10.5281/zenodo.23610514","identifiers":[],"creators":[{"nameType":"Personal","givenName":"Shokhrukhbek","familyName":"Yuldoshev","name":"Yuldoshev, Shokhrukhbek","nameIdentifiers":[],"affiliation":[]}],"titles":[{"title":"TA'LIMDA AXBOROT XAVFSIZLIGINING HOZIRGI HOLATI"}],"publisher":"Zenodo","container":{},"publicationYear":2023,"subjects":[],"contributors":[],"dates":[{"date":"2023-10-20","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":""},"relatedIdentifiers":[{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.23610515","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.23610514","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T05:52:46Z","registered":"2026-10-24T05:52:46Z","published":null,"updated":"2026-10-24T05:52:46Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.23610515","type":"dois","attributes":{"doi":"10.5281/zenodo.23610515","identifiers":[{"identifier":"oai:zenodo.org:23610515","identifierType":"oai"}],"creators":[{"nameType":"Personal","givenName":"Shokhrukhbek","familyName":"Yuldoshev","name":"Yuldoshev, Shokhrukhbek","nameIdentifiers":[],"affiliation":[]}],"titles":[{"title":"TA'LIMDA AXBOROT XAVFSIZLIGINING HOZIRGI HOLATI"}],"publisher":"Zenodo","container":{},"publicationYear":2023,"subjects":[],"contributors":[],"dates":[{"date":"2023-10-20","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":""},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.23610514","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.23610515","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T05:52:46Z","registered":"2026-10-24T05:52:46Z","published":null,"updated":"2026-10-24T05:52:46Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.71781/36407","type":"dois","attributes":{"doi":"10.71781/36407","identifiers":[{"identifier":"https://hdl.handle.net/1866/46835","identifierType":"URI"}],"creators":[{"name":"Forget, Marilou","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"L’esthétique transductive de Gilbert Simondon. Vers une éthique de la culture"}],"publisher":"Université de Montréal","container":{},"publicationYear":2026,"subjects":[{"subject":"Philosophie"},{"subject":"Esthétique"},{"subject":"Individuation"},{"subject":"Technique"},{"subject":"Techno-esthétique"},{"subject":"Transduction"},{"subject":"Philosophy"},{"subject":"Aesthetics"},{"subject":"Technics"},{"subject":"Techno-esthetics"}],"contributors":[{"name":"Université de Montréal","contributorType":"HostingInstitution","affiliation":[],"nameIdentifiers":[]},{"name":"Dumouchel, Daniel","contributorType":"RelatedPerson","affiliation":[],"nameIdentifiers":[]}],"dates":[{"date":"2026-10-23","dateType":"Available"},{"date":"2026-10","dateType":"Issued"}],"language":"fr","types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":"Thèse ou mémoire / Thesis or Dissertation"},"relatedIdentifiers":[],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[],"descriptions":[{"descriptionType":"Abstract","description":"Gilbert Simondon est connu pour la richesse de ses réflexions sur l’individuation et la technique, mais de nombreuses facettes de son œuvre demeurent à explorer – en particulier sa pensée esthétique. Notre recherche a pour but de mettre en lumière cette dimension de la philosophie simondonienne, qui parcourt en filigrane l’ensemble de son œuvre. Les deux premiers chapitres du présent mémoire portent sur la théorie de l’individuation présentée dans L’individuation à la lumière des notions de forme et d’information, et sur la place discrète mais cruciale qu’y tient la notion d’« esthétisme ». Le troisième chapitre s’intéresse à la place de l’esthétique au sein du devenir des phases de la pensée, dont la description occupe la troisième partie de Du mode d’existence des objets techniques. Le quatrième chapitre aborde l’expérience esthétique à l’aune des cours de psychologie de Simondon, en particulier par rapport à sa théorie de l’imagination et de l’invention. Finalement, le cinquième chapitre tente une explicitation du sens axiontologique de l’esthétique simondonienne et de ses résonances actuelles, au prisme de la notion de techno-esthétique. Il apparaîtra que la question esthétique s’articule étroitement à celle du devenir de la culture."},{"descriptionType":"Abstract","description":"Gilbert Simondon is known for the depth of his insights on individuation and technics, but numerous aspects of his work are still to be explored – notably his aesthetic thought. Our research aims to shed light on this dimension of simondonian philosphy, which implicitly goes through his work. The first two chapters touch upon the theory of individuation laid out in Individuation in Light of Notions of Form and Information, as well as the crucial albeit subtle role held by the concept of « aesthetism ». The third chapter looks into the place of aesthetics in the becoming of thought, described in the third part of On the Mode of Existence of Technical Objects. The fourth chapter adresses the aesthetic experience in Simondon’s psychology courses, mainly with regard to his theory of imagination and invention. Lastly, the fifth chapter attempts an explanation of the axiontological meaning of simondonian aesthetics, and of its current resonance, through the concept of techno-aesthetics. Our research will show how aesthetics is linked to the becoming of culture."}],"geoLocations":[],"fundingReferences":[],"url":"https://umontreal.scholaris.ca/handle/1866/46835","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T05:00:21Z","registered":"2026-10-24T05:00:49Z","published":null,"updated":"2026-10-24T05:00:49Z"},"relationships":{"client":{"data":{"id":"umon.tbxpus","type":"clients"}}}},{"id":"10.71781/36399","type":"dois","attributes":{"doi":"10.71781/36399","identifiers":[{"identifier":"https://hdl.handle.net/1866/46820","identifierType":"URI"}],"creators":[{"name":"Allard, Marianne","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","schemeUri":"https://orcid.org","nameIdentifier":"https://orcid.org/0009-0007-6103-3390"}],"affiliation":[]}],"titles":[{"title":"Aspects novateurs de la mécanique des fluides appliquée à la biologie des coraux"}],"publisher":"Université de Montréal","container":{},"publicationYear":2026,"subjects":[{"subject":"coraux mous"},{"subject":"coraux durs"},{"subject":"polypes"},{"subject":"vibrations"},{"subject":"vibrations induites par vortex"},{"subject":"huile"},{"subject":"pétrole"},{"subject":"soft corals"},{"subject":"hard corals"},{"subject":"polyps"},{"subject":"vortex induced vibrations"},{"subject":"oil"},{"subject":"crude oil"}],"contributors":[{"name":"Université de Montréal","contributorType":"HostingInstitution","affiliation":[],"nameIdentifiers":[]},{"name":"Cameron, Christopher B.","contributorType":"RelatedPerson","affiliation":[],"nameIdentifiers":[]},{"name":"Viggiano, Bianca","contributorType":"RelatedPerson","affiliation":[],"nameIdentifiers":[]}],"dates":[{"date":"2026-10-23","dateType":"Available"},{"date":"2026-10","dateType":"Issued"}],"language":"fr","types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":"Thèse ou mémoire / Thesis or Dissertation"},"relatedIdentifiers":[],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[],"descriptions":[{"descriptionType":"Abstract","description":"Les coraux, étant des animaux filtreurs, sont indispensables aux écosystèmes marins, créant des points chauds de biodiversité. Les pressions humaines grandissantes sur les coraux menacent leur survie et crée un changement de dominance des coraux durs aux coraux mous. Cette étude révèle la présence de vibrations chez plusieurs espèces de coraux mous à partir de données récoltées en laboratoire et en plongée. Les paramètres principaux influençant la fréquence de vibration sont le diamètre des branches, la vitesse d’écoulement et la présence des polypes (structures servant à capturer la nourriture). La dynamique d’interaction entre les coraux et leur environnement changeant se verra modifiée dans les prochaines années en raison de l’augmentation de l’intensité des tempêtes liée aux changements climatiques, risquant d’impacter leur capacité d’alimentation. Les déversements pétroliers représentent également une menace importante pour les coraux. Leur toxicité a été démontrée dans des études précédentes, sans toutefois qu’une ingestion directe n’ait été observée. Dans cette étude, deux espèces de coraux mous et trois espèces de coraux durs ont été exposés à trois types d’huile différents (canola, poisson et moteur) pour évaluer leur réaction et leur interaction avec les gouttelettes d’huile. L’ingestion des trois huiles a été confirmée chez les coraux mous, et l’ingestion accidentelle de l’huile de canola a été constatée chez une espèce de corail dur. Les deux autres espèces de coraux durs ont montré un gonflement des polypes lors de l’exposition aux trois types d’huile. Les coraux mous sont donc potentiellement plus vulnérables aux déversements de pétrole, alors que les coraux durs pourraient servir d’indicateurs d’exposition. Cette étude est significative car elle est la première à se pencher sur ces deux aspects des menaces anthropiques sur les récifs coralliens."},{"descriptionType":"Abstract","description":"Corals are filter-feeding animals that play a vital role in marine ecosystems, creating biodiversity hotspots. Growing human pressures on corals are threatening their survival and creating a shift from hard to soft coral dominated reefs. This study revealed the presence of vibrations in several soft coral species, from diving and laboratory data. The main parameters influencing vibration frequency are branch diameter, water flow velocity, and the presence of polyps (structures that capture food particles). The fluid-structure interaction between the coral and its environment is expected to change in coming years due to stronger storms from climate change, potentially affecting their feeding capacity. Oil spills also pose a major threat to corals. While toxicity has been demonstrated in past studies, direct ingestion had not been observed. In this study, experiments were made exposing two soft coral species and three hard coral species to three oil types (canola, fish, and motor) to test their reaction and interaction with oil droplets. All three oils were ingested by soft corals, while only canola oil was accidentally ingested by one hard coral species. The other two hard coral species showed polyp swelling after exposure to all three oils. Soft corals may thus be more vulnerable to oil spills, while hard corals could serve as exposure indicators. This study is significant as it is the first to examine these two aspects of human threats on coral reefs."}],"geoLocations":[],"fundingReferences":[],"url":"https://umontreal.scholaris.ca/handle/1866/46820","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T05:00:19Z","registered":"2026-10-24T05:00:47Z","published":null,"updated":"2026-10-24T05:00:47Z"},"relationships":{"client":{"data":{"id":"umon.tbxpus","type":"clients"}}}},{"id":"10.71781/36398","type":"dois","attributes":{"doi":"10.71781/36398","identifiers":[{"identifier":"https://hdl.handle.net/1866/46819","identifierType":"URI"}],"creators":[{"name":"Mumford, Benjamin","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","schemeUri":"https://orcid.org","nameIdentifier":"https://orcid.org/0009-0002-1512-7189"}],"affiliation":[]}],"titles":[{"title":"The elemental composition of echinoderm ossicles : phylogeny, development, ecology and biomechanics"}],"publisher":"Université de Montréal","container":{},"publicationYear":2026,"subjects":[{"subject":"Échinodermes"},{"subject":"Stéréome"},{"subject":"Ossicules"},{"subject":"Biominéralisation"},{"subject":"Calcite riche en Mg"},{"subject":"MEB-EDS"},{"subject":"Spectroscopie Raman"},{"subject":"Analyse par activation neutronique"},{"subject":"Composition élémentaire"},{"subject":"Ambulacraria"},{"subject":"Echinodermata"},{"subject":"Stereom"},{"subject":"Ossicles"},{"subject":"Biomineralization"},{"subject":"High-Mg calcite"},{"subject":"SEM-EDS"},{"subject":"Raman spectroscopy"},{"subject":"Neutron activation analysis"},{"subject":"Elemental composition"}],"contributors":[{"name":"Université de Montréal","contributorType":"HostingInstitution","affiliation":[],"nameIdentifiers":[]},{"name":"Cameron, Christopher B.","contributorType":"RelatedPerson","affiliation":[],"nameIdentifiers":[]}],"dates":[{"date":"2026-10-23","dateType":"Available"},{"date":"2026-10","dateType":"Issued"}],"language":"en","types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":"Thèse ou mémoire / Thesis or Dissertation"},"relatedIdentifiers":[],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[],"descriptions":[{"descriptionType":"Abstract","description":"L’endosquelette des échinodermes constitue une caractéristique fondamentale de ce phylum, mais les contributions respectives de l’histoire évolutive, du développement, de l’écologie et de la biomécanique à sa composition élémentaire restent mal comprises. Dans cette étude, nous avons examiné la minéralogie et la composition élémentaire du squelette de 24 espèces représentant les cinq classes actuelles d’échinodermes, à l’aide de la spectroscopie Raman, de la microscopie électronique à balayage couplée à la spectroscopie à dispersion d’énergie des rayons X (MEB-EDS) et de l’analyse par activation neutronique instrumentale (AANI). Nous avons également étudié les influences potentielles du développement et de la fonction au moyen de comparaisons ontogénétiques et d’une expérience alimentaire contrôlée chez Pisaster ochraceus. La calcite constituait le seul polymorphe du carbonate de calcium observé chez tous les taxons échantillonnés, ce qui témoigne d’une forte conservation minéralogique chez les échinodermes actuels. Le magnésium était systématiquement incorporé au stéréome, tandis que les autres éléments traces (S, Al, Si, Ra, Rh et Th) étaient présents en faibles pourcentages massiques et leur distribution était limitée à certaines espèces. La composition en éléments traces ne présentait aucune structuration significative en fonction de la classe taxonomique, du groupe trophique ou de l’histoire phylogénétique. Elle semble plutôt être régulée à l’échelle de l’espèce. De même, aucune variation significative des pourcentages massiques n’a été observée entre les différentes trajectoires de développement au sein d’un ossicule, tandis que l’analyse d’ossicules juvéniles et adultes a révélé des variations de la composition élémentaire entre les stades de vie, visibles mais non significatives. Chez Pisaster ochraceus, l’exposition à des charges mécaniques faibles ou élevées, induites par une alimentation à base de proies molles ou dures, n’a entraîné aucune modification significative de la composition élémentaire des ossicules. Enfin, la détection d’éléments inattendus, notamment le soufre et le rhodium, ainsi que de l’or chez Evasterias troschelii et Psolus chitonoides, respectivement, souligne la nécessité de poursuivre les recherches sur l’incorporation des éléments traces au sein du phylum. Ces résultats étayent l’idée que le squelette des échinodermes se caractérise par une structure calcitique hautement conservée, sur laquelle se superposent de subtiles variations chimiques dépendantes du contexte, apportant ainsi de nouveaux éclairages sur l’évolution et la régulation de la biominéralisation chez les Echinodermata."},{"descriptionType":"Abstract","description":"The echinoderm endoskeleton is a defining feature of the phylum, yet the relative contributions of evolutionary history, development, ecology and biomechanics to its elemental composition remain poorly understood. Here, we investigated skeletal mineralogy and elemental composition across 24 species representing all five extant echinoderm classes using Raman spectroscopy, scanning electron microscopy coupled with energy-dispersive X-ray spectroscopy (SEM-EDS), and instrumental neutron activation analysis (NAA). We further examined potential developmental and functional influences through ontogenetic comparisons and a controlled feeding experiment in Pisaster ochraceus. Calcite was the sole calcium carbonate polymorph in all sampled taxa, supporting strong mineralogical conservation across extant echinoderms. Magnesium was consistently incorporated into stereom, whereas other trace elements (S, Al, Si, Ra, Rh, Th) occurred at low weight percentage and with restricted species distributions. Trace-element composition showed no significant structuring by class, feeding guild or phylogenetic history. Instead, it is regulated at species scales. Likewise, no significant weight percentage changes occurred across developmental pathways within an ossicle, with noticeable but non-significant shifts in elemental composition across life stages, determined by analysis of juvenile and adult ossicles. Pisaster ochraceus exposed to low versus high mechanical load by feeding on soft versus hard diets resulted in no significant change to ossicle elemental composition. Lastly, the inclusion of unexpected elements, sulphur and rhodium, and gold in Evasterias troschelii and Psolus chitonoides respectively, illustrate the need for continued investigation into trace element inclusion across the phyla. These findings support the view that the echinoderm skeleton is characterised by a highly conserved calcitic framework upon which subtle, context-dependent chemical variation is superimposed, providing new insight into the evolution and regulation of biomineralization across Echinodermata."}],"geoLocations":[],"fundingReferences":[],"url":"https://umontreal.scholaris.ca/handle/1866/46819","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T05:00:18Z","registered":"2026-10-24T05:00:45Z","published":null,"updated":"2026-10-24T05:00:45Z"},"relationships":{"client":{"data":{"id":"umon.tbxpus","type":"clients"}}}},{"id":"10.71781/36346","type":"dois","attributes":{"doi":"10.71781/36346","identifiers":[{"identifier":"https://hdl.handle.net/1866/46737","identifierType":"URI"}],"creators":[{"name":"Akplogan, Fiacre Sètondji Dibe","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","schemeUri":"https://orcid.org","nameIdentifier":"https://orcid.org/0009-0009-8695-8888"}],"affiliation":[]}],"titles":[{"title":"Développement des compétences en mobilisation des connaissances chez les personnes étudiantes universitaires dans des domaines liés à la santé"}],"publisher":"Université de Montréal","container":{},"publicationYear":2026,"subjects":[{"subject":"Compétences"},{"subject":"Mobilisation des connaissances"},{"subject":"Applications des connaissances"},{"subject":"Personnes étudiantes"},{"subject":"Cycles supérieurs"},{"subject":"Competencies"},{"subject":"Knowledge mobilization"},{"subject":"Knowledge translation"},{"subject":"Students"},{"subject":"Experiential learning"}],"contributors":[{"name":"Université de Montréal","contributorType":"HostingInstitution","affiliation":[],"nameIdentifiers":[]},{"name":"Lecours, Alexandra","contributorType":"RelatedPerson","affiliation":[],"nameIdentifiers":[]}],"dates":[{"date":"2026-10-23","dateType":"Available"},{"date":"2026-10","dateType":"Issued"}],"language":"fr","types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":"Thèse ou mémoire / Thesis or Dissertation"},"relatedIdentifiers":[],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[],"descriptions":[{"descriptionType":"Abstract","description":"La production scientifique au Québec a connu une croissance soutenue au cours des dernières années, mais l’utilisation de ces connaissances dans les milieux de pratique demeure limitée. Ce mémoire par article présente une étude visant à explorer le développement des compétences en mobilisation des connaissances chez des personnes étudiantes universitaires dans des domaines liés à la santé, en s’appuyant sur le modèle d’apprentissage expérientiel de David Kolb. S’inscrivant dans un devis qualitatif descriptif, douze entrevues semi-structurées ont été réalisées auprès de personnes étudiantes inscrites à la maîtrise ou au doctorat de recherche dans différentes universités québécoises. Une analyse thématique a permis d’identifier les compétences mobilisées ainsi que les barrières et facilitateurs influençant leur développement. Les résultats mettent en évidence dix compétences clés en mobilisation des connaissances. Ils révèlent que, bien que leur développement repose en grande partie sur une démarche individuelle, certaines phases du processus d’apprentissage sont contraintes par des limites structurelles et matérielles au sein des institutions universitaires. Nos résultats suggèrent l’intégration formelle de formations en mobilisation des connaissances dans les cursus académiques, un meilleur accès aux ressources financières, ainsi que la mise en place d’espaces de pratique favorisant l’expérimentation dans un environnement sécurisant. Enfin, des recherches futures pourraient explorer le rôle et les perceptions des directions de recherche dans le développement de ces compétences."},{"descriptionType":"Abstract","description":"Scientific research in Quebec has grown sustainably in recent years, but the use of this knowledge in practice settings remains limited. This dissertation by article presents a study aimed at exploring the development of knowledge mobilization competencies among graduate students in health-related fields, drawing on David Kolb’s experiential learning model. Using a descriptive qualitative design, twelve semi-structured interviews were conducted with students enrolled in master’s or doctoral research programs at various universities in Quebec. A thematic analysis identified the competencies utilized, as well as the barriers and facilitators influencing their development. The results highlight ten key competencies in knowledge mobilization. They reveal that, although the development of these competencies relies largely on individual initiative, certain phases of the learning process are constrained by structural and material limitations within academic institutions. Our findings suggest the formal integration of knowledge translation training into academic programs, improved access to financial resources, and the creation of practice spaces that encourage experimentation in a supportive environment. Future research could explore the role and perceptions of research leadership in the development of these competencies."}],"geoLocations":[],"fundingReferences":[],"url":"https://umontreal.scholaris.ca/handle/1866/46737","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T05:00:16Z","registered":"2026-10-24T05:00:44Z","published":null,"updated":"2026-10-24T05:00:44Z"},"relationships":{"client":{"data":{"id":"umon.tbxpus","type":"clients"}}}},{"id":"10.71781/36298","type":"dois","attributes":{"doi":"10.71781/36298","identifiers":[{"identifier":"https://hdl.handle.net/1866/46650","identifierType":"URI"}],"creators":[{"name":"Gavrila, Simona Erika","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"L’anxiété de performance scolaire chez les élèves du primaire"}],"publisher":"Université de Montréal","container":{},"publicationYear":2026,"subjects":[{"subject":"Anxiété de performance scolaire (APS)"},{"subject":"Élèves du primaire"},{"subject":"Modèle bioécologique (PPCT)"},{"subject":"Variables individuelles et environnementales"},{"subject":"Validation d’un questionnaire"},{"subject":"School performance anxiety (SPA)"},{"subject":"Elementary school students"},{"subject":"Bioecological model (PPCT)"},{"subject":"Individual and environmental variables"},{"subject":"Questionnaire validation"}],"contributors":[{"name":"Université de Montréal","contributorType":"HostingInstitution","affiliation":[],"nameIdentifiers":[]},{"name":"Borges, Cecilia","contributorType":"RelatedPerson","affiliation":[],"nameIdentifiers":[]},{"name":"Bowen, François","contributorType":"RelatedPerson","affiliation":[],"nameIdentifiers":[]}],"dates":[{"date":"2026-10-23","dateType":"Available"},{"date":"2026-10","dateType":"Issued"}],"language":"fr","types":{"schemaOrg":"Thesis","resourceTypeGeneral":"Dissertation","citeproc":"thesis","bibtex":"phdthesis","ris":"THES","resourceType":"Thèse ou mémoire / Thesis or Dissertation"},"relatedIdentifiers":[],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[],"descriptions":[{"descriptionType":"Abstract","description":"Cette thèse porte sur l’anxiété de performance scolaire (APS) chez les élèves du primaire francophones du Québec. Bien que fréquemment observée dans les milieux scolaires, l’APS demeure peu documentée à cet âge, tant sur le plan développemental que contextuel. S’appuyant sur le modèle bioécologique du développement humain (Processus–Personne–Contexte–Temps ; Bronfenbrenner et Morris, 2007), cette recherche vise à comprendre comment se caractérise l’APS chez les élèves du primaire, à travers les contextes où elle émerge, ses manifestations, ainsi que l’influence de variables individuelles (VI), notamment l’auto-efficacité, l’engagement scolaire, les buts d’accomplissement et le perfectionnisme, et de variables environnementales (VE), telles que les attentes parentales et enseignantes, les pratiques pédagogiques, le climat de classe et les normes sociales. Cette recherche repose sur un devis mixte convergent. Le volet quantitatif, réalisé auprès de 657 élèves de la 1re à la 6e année, a permis de valider un questionnaire inédit mesurant l’APS. Les analyses factorielles exploratoires (AFE) et confirmatoires (AFC) ont confirmé une structure à quatre facteurs (anxiété liée aux évaluations, manifestations de l’APS, VI associées à l’APS et VE associées à l’APS) ainsi que des indices de fidélité jugés satisfaisants. Le volet qualitatif, fondé sur 12 entretiens de groupe (N = 48), a permis d’approfondir la compréhension des expériences vécues de l’APS selon les différents cycles du primaire. Les situations d’évaluation constituent la principale situation anxiogène, particulièrement en 4e année, où la pression liée à la réussite devient plus marquée. Les manifestations cognitives, émotionnelles et physiologiques s’intensifient avec l’âge, et les filles rapportent des niveaux d’APS plus élevés que les garçons. L’analyse croisée souligne l’influence des attentes parentales, des pratiques pédagogiques, du climat de classe et du sentiment de compétence sur la construction de l’APS. Ces résultats mettent en évidence la dimension développementale et systémique de l’APS, conçue comme le produit d’interactions répétées entre la personne et son environnement. Ils ouvrent des perspectives pour la prévention en milieu scolaire et la formation du personnel enseignant, soutenues par la création d’un nouvel outil de mesure validé."},{"descriptionType":"Abstract","description":"This dissertation examines school performance anxiety (SPA) among French-speaking elementary school students in Quebec. Although frequently observed in educational settings, SPA remains insufficiently documented at this age from both developmental and contextual perspectives. Grounded in the bioecological model of human development (Process–Person–Context–Time; Bronfenbrenner \u0026amp; Morris, 2007), this study aims to understand how SPA is characterized among elementary school students through the contexts in which it emerges, its manifestations, and the influence of individual variables (IVs), including self-efficacy, school engagement, achievement goals, and perfectionism, as well as environmental variables (EVs), such as parental and teacher expectations, pedagogical practices, classroom climate, and social norms. This research is based on a convergent mixed-methods design. The quantitative component, conducted with 657 students from Grades 1 to 6, led to the validation of a new questionnaire designed to assess SPA. Exploratory and confirmatory factor analyses supported a fourfactor structure (evaluation-related anxiety, SPA manifestations, SPA-related individual variables, and SPA-related environmental variables) and satisfactory reliability indices. The qualitative component, based on 12 group interviews (N = 48), provided a deeper understanding of students’ lived experiences of SPA across elementary school cycles. Evaluation situations emerged as the primary anxiety-provoking context, particularly in Grade 4, where achievement-related pressure becomes more salient. Cognitive, emotional, and physiological manifestations intensified with age, and girls reported higher levels of SPA than boys. The integrated analysis highlights the influence of parental expectations, pedagogical practices, classroom climate, and perceived competence on the development of SPA. These findings underscore the developmental and systemic nature of SPA, conceptualized as the product of repeated interactions between the individual and their environment. They also offer promising avenues for schoolbased prevention and teacher training, supported by the development and validation of a new assessment instrument."}],"geoLocations":[],"fundingReferences":[],"url":"https://umontreal.scholaris.ca/handle/1866/46650","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-10-24T05:00:16Z","registered":"2026-10-24T05:00:41Z","published":null,"updated":"2026-10-24T05:00:41Z"},"relationships":{"client":{"data":{"id":"umon.tbxpus","type":"clients"}}}}],"meta":{"total":907491,"totalPages":400,"page":1},"links":{"self":"https://api.datacite.org/dois?resource-type-id=Dissertation","next":"https://api.datacite.org/dois?page%5Bnumber%5D=2\u0026page%5Bsize%5D=25\u0026resource-type-id=Dissertation"}}