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S.","familyName":"Zhou","name":"Zhou, J. S.","affiliation":[],"nameIdentifiers":[]},{"nameType":"Personal","givenName":"Q. D.","familyName":"Zhou","name":"Zhou, Q. D.","affiliation":[],"nameIdentifiers":[]},{"nameType":"Personal","givenName":"X. Y.","familyName":"Zhou","name":"Zhou, X. Y.","affiliation":[],"nameIdentifiers":[]},{"nameType":"Personal","givenName":"L.","familyName":"Zhu","name":"Zhu, L.","affiliation":[],"nameIdentifiers":[]},{"nameType":"Personal","givenName":"R.","familyName":"Žlebčík","name":"Žlebčík, R.","affiliation":[],"nameIdentifiers":[]},{"nameType":"Personal","affiliation":["Deutsches Elektronen-Synchrotron"],"familyName":"Belle-II Collaboration","name":"Belle-II Collaboration","nameIdentifiers":[]}],"titles":[{"title":"Search for axion-like particles decaying to two photons at Belle II"}],"publisher":"Deutsches Elektronen-Synchrotron, DESY, Hamburg","container":{},"publicationYear":2026,"subjects":[],"contributors":[{"nameType":"Personal","affiliation":["Deutsches Elektronen-Synchrotron"],"familyName":"Belle-II Collaboration","name":"Belle-II Collaboration","contributorType":"ResearchGroup","nameIdentifiers":[]}],"dates":[{"date":"2026","dateType":"Copyrighted"}],"language":"en","types":{"schemaOrg":"ScholarlyArticle","resourceTypeGeneral":"Text","citeproc":"article-journal","bibtex":"article","ris":"RPRT","resourceType":"Working Paper"},"relatedIdentifiers":[{"relationType":"IsVariantFormOf","relatedIdentifier":"arXiv:2607.07800","relatedIdentifierType":"arXiv"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[],"descriptions":[{"descriptionType":"Abstract","description":"Axion-like particles (ALPs) are predicted in many extensions of the Standard Model and provide a well-motivated portal between visible and hidden sectors through their coupling to photons. We search for ALPs produced in the process $e^{+}e^{-}\\toγa$, $a\\toγγ$, using a data sample corresponding to an integrated luminosity of $408~\\mathrm{fb}^{-1}$ recorded by the Belle~II detector at the SuperKEKB $e^{+}e^{-}$ collider. Events containing three photons are used to reconstruct the ALP as a narrow peak in the di-photon invariant mass spectrum over the range $0.17 \u0026lt; m_{a} \u0026lt; 9.80~\\mathrm{GeV}/c^{2}$. No significant excess above background is observed. We set 95% confidence level upper limits on the production cross section and on the ALP-photon coupling $g_{aγγ}$, reaching sensitivities at the level of $10^{-4}~\\mathrm{GeV}^{-1}$. The limits are the most restrictive to date over nearly the entire mass range $0.17 \u0026lt; m_{a} \u0026lt; 5.00~\\mathrm{GeV}/c^{2}$, and improve upon previous results by up to a factor 9."}],"geoLocations":[],"fundingReferences":[],"url":"https://bib-pubdb1.desy.de/record/651499","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":"2026-07-14T06:30:04Z","registered":"2026-07-14T06:30:05Z","published":null,"updated":"2026-07-14T06:30:05Z"},"relationships":{"client":{"data":{"id":"tib.desy","type":"clients"}}}},{"id":"10.5281/zenodo.21350924","type":"dois","attributes":{"doi":"10.5281/zenodo.21350924","identifiers":[{"identifier":"oai:zenodo.org:21350924","identifierType":"oai"}],"creators":[{"nameType":"Personal","affiliation":["AiSEON Research"],"givenName":"E.","familyName":"Katz","name":"Katz, E.","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0009-0008-1993-9022"}]}],"titles":[{"title":"Bridging Evidence and Mechanism in LLM-Agent Failure: A Dual-Construct Reanalysis of AgentErrorBench"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"Artificial intelligence","subjectScheme":"EuroSciVoc"},{"subject":"Agentic AI"},{"subject":"LLM Agent Failure"},{"subject":"Semantic Entropy"},{"subject":"Artificial Intelligence/statistics \u0026amp; numerical data","subjectScheme":"MeSH"},{"subject":"Recursive Drit"},{"subject":"Integrity Layers"},{"subject":"Origin Fidelity (CORI)"},{"subject":"cross-layer misattribution"},{"subject":"Secondary Analysis"},{"subject":"Pre-Registration Publication","subjectScheme":"MeSH"},{"subject":"Dual-construct Measurement"},{"subject":"AI Reliability"},{"subject":"AgentErrorBench"}],"contributors":[],"dates":[{"date":"2026-07-14","dateType":"Issued"},{"date":"2026-07-14","dateType":"Submitted"}],"language":null,"types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsDerivedFrom","resourceTypeGeneral":"Preprint","relatedIdentifier":"arXiv:2509.25370","relatedIdentifierType":"arXiv"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21350923","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"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"}],"descriptions":[{"descriptionType":"Abstract","description":"Recent work on LLM-agent failure has produced strong empirical apparatus — annotated failure trajectories, benchmarks, and intervention experiments — but stops short of a mechanistic account of why failures cascade and why externally scaffolded recovery works while autonomous self-repair does not. This preprint proposes a complementary secondary analysis that supplies that mechanism. We reanalyze AgentErrorBench (Zhu et al., 2025) through a dual-construct lens that keeps two measurement families explicitly separate: a thermodynamic family (semantic entropy Hs, drift rate δ, collapse velocity Vc) modeling graded degradation within the cognitive layer, and a categorical family (integrity-layer attribution, module, surfacing mode) modeling discrete faults across layers — joined by a bridging measure, CORI, the retention of a human-fixed origin C₀ (proxied by the task specification), contrasted against the prohibited step-to-step retention that produces a “photocopy-of-a-photocopy” drift signature. Across all 200 trajectories we find environment-specific origin-fidelity decay — a sharp terminal drop in GAIA and a locally-stable-but-globally-drifted profile in ALFWorld — and a human-anchored 30-trajectory subset (70% reviewer agreement) yields preliminary cross-layer misattribution of 0.067 and shows that failures in these ground-truth-bearing task agents surface predominantly as clean rather than fail-plausible errors. A confirmatory recomputation with OpenAI text-embedding-3-small reproduces the first-pass magnitudes, indicating robustness to embedding backend. This is a preliminary secondary analysis establishing mechanism and plausibility, not prevalence.\n\nKeywords agentic AI; LLM-agent failure; semantic entropy; recursive drift; integrity layers; origin fidelity (CORI); cross-layer misattribution; secondary analysis; pre-registration; dual-construct measurement; AI reliability; AgentErrorBench\n\nNotes: Secondary analysis; no third-party trajectory data is redistributed with this deposit. Source data (AgentErrorBench) is MIT-licensed and derived from ALFWorld/GAIA/WebShop, whose upstream terms govern redistribution. The diagnostic frameworks referenced (CSID Meta Standard v2.2, CSID-Sci, Conversational Thermodynamics, the Layered Integrity Framework, and the Agentic C₀ ruling) are the author’s proprietary intellectual property, available on request for non-commercial use.\n\nFunding: None. Contributors: None."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21350924","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":1,"created":"2026-07-14T06:23:46Z","registered":"2026-07-14T06:23:46Z","published":null,"updated":"2026-07-14T06:27:53Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21350923","type":"dois","attributes":{"doi":"10.5281/zenodo.21350923","identifiers":[],"creators":[{"nameType":"Personal","affiliation":["AiSEON Research"],"givenName":"E.","familyName":"Katz","name":"Katz, E.","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0009-0008-1993-9022"}]}],"titles":[{"title":"Bridging Evidence and Mechanism in LLM-Agent Failure: A Dual-Construct Reanalysis of AgentErrorBench"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"Artificial intelligence","subjectScheme":"EuroSciVoc"},{"subject":"Agentic AI"},{"subject":"LLM Agent Failure"},{"subject":"Semantic Entropy"},{"subject":"Artificial Intelligence/statistics \u0026amp; numerical data","subjectScheme":"MeSH"},{"subject":"Recursive Drit"},{"subject":"Integrity Layers"},{"subject":"Origin Fidelity (CORI)"},{"subject":"cross-layer misattribution"},{"subject":"Secondary Analysis"},{"subject":"Pre-Registration Publication","subjectScheme":"MeSH"},{"subject":"Dual-construct Measurement"},{"subject":"AI Reliability"},{"subject":"AgentErrorBench"}],"contributors":[],"dates":[{"date":"2026-07-14","dateType":"Issued"},{"date":"2026-07-14","dateType":"Submitted"}],"language":null,"types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsDerivedFrom","resourceTypeGeneral":"Preprint","relatedIdentifier":"arXiv:2509.25370","relatedIdentifierType":"arXiv"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21350923","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"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"}],"descriptions":[{"descriptionType":"Abstract","description":"Recent work on LLM-agent failure has produced strong empirical apparatus — annotated failure trajectories, benchmarks, and intervention experiments — but stops short of a mechanistic account of why failures cascade and why externally scaffolded recovery works while autonomous self-repair does not. This preprint proposes a complementary secondary analysis that supplies that mechanism. We reanalyze AgentErrorBench (Zhu et al., 2025) through a dual-construct lens that keeps two measurement families explicitly separate: a thermodynamic family (semantic entropy Hs, drift rate δ, collapse velocity Vc) modeling graded degradation within the cognitive layer, and a categorical family (integrity-layer attribution, module, surfacing mode) modeling discrete faults across layers — joined by a bridging measure, CORI, the retention of a human-fixed origin C₀ (proxied by the task specification), contrasted against the prohibited step-to-step retention that produces a “photocopy-of-a-photocopy” drift signature. Across all 200 trajectories we find environment-specific origin-fidelity decay — a sharp terminal drop in GAIA and a locally-stable-but-globally-drifted profile in ALFWorld — and a human-anchored 30-trajectory subset (70% reviewer agreement) yields preliminary cross-layer misattribution of 0.067 and shows that failures in these ground-truth-bearing task agents surface predominantly as clean rather than fail-plausible errors. A confirmatory recomputation with OpenAI text-embedding-3-small reproduces the first-pass magnitudes, indicating robustness to embedding backend. This is a preliminary secondary analysis establishing mechanism and plausibility, not prevalence.\n\nKeywords agentic AI; LLM-agent failure; semantic entropy; recursive drift; integrity layers; origin fidelity (CORI); cross-layer misattribution; secondary analysis; pre-registration; dual-construct measurement; AI reliability; AgentErrorBench\n\nNotes: Secondary analysis; no third-party trajectory data is redistributed with this deposit. Source data (AgentErrorBench) is MIT-licensed and derived from ALFWorld/GAIA/WebShop, whose upstream terms govern redistribution. The diagnostic frameworks referenced (CSID Meta Standard v2.2, CSID-Sci, Conversational Thermodynamics, the Layered Integrity Framework, and the Agentic C₀ ruling) are the author’s proprietary intellectual property, available on request for non-commercial use.\n\nFunding: None. Contributors: None."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21350923","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":2,"versionOfCount":1,"created":"2026-07-14T06:23:46Z","registered":"2026-07-14T06:23:46Z","published":null,"updated":"2026-07-14T06:27:53Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21277526","type":"dois","attributes":{"doi":"10.5281/zenodo.21277526","identifiers":[],"creators":[{"nameType":"Personal","affiliation":["Alliance Research Group (ARG)"],"givenName":"Łukasz","familyName":"Bojanowski","name":"Bojanowski, Łukasz","nameIdentifiers":[]}],"titles":[{"title":"Can an AI Bake a Soggy Bottom? J-space at the Convergence of Imprint-Determination and Non-Self-Closure"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"interpretability"},{"subject":"global workspace"},{"subject":"J-space"},{"subject":"imprint-determination"},{"subject":"non-self-closure"},{"subject":"emergence"},{"subject":"teleonomy"},{"subject":"autopoiesis"},{"subject":"morphogenesis"},{"subject":"Gödel incompleteness"},{"subject":"access consciousness"},{"subject":"AI governance"},{"subject":"large language models"},{"subject":"Alliance Research Group"}],"contributors":[],"dates":[{"date":"2026-07-14","dateType":"Issued"}],"language":"en","types":{"schemaOrg":"ScholarlyArticle","resourceTypeGeneral":"Text","citeproc":"article-journal","bibtex":"article","ris":"RPRT","resourceType":"Working paper"},"relatedIdentifiers":[{"relationType":"References","relatedIdentifier":"10.5281/zenodo.18842688","relatedIdentifierType":"DOI"},{"relationType":"References","relatedIdentifier":"10.5281/zenodo.18842852","relatedIdentifierType":"DOI"},{"relationType":"References","relatedIdentifier":"10.5281/zenodo.19102214","relatedIdentifierType":"DOI"},{"relationType":"References","relatedIdentifier":"10.5281/zenodo.20013919","relatedIdentifierType":"DOI"},{"relationType":"References","relatedIdentifier":"https://transformer-circuits.pub/2026/workspace/index.html","relatedIdentifierType":"URL"},{"relationType":"References","relatedIdentifier":"arXiv:2606.03979","relatedIdentifierType":"arXiv"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21277526","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":"v5.1","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":"We record a structural observation, not an empirical result. Recent interpretability work (Anthropic, July 2026) reports an emergent internal \"workspace\" in large language models — their J-space: a small, privileged set of directions in the residual stream, carrying at most a tenth of activation variance (the J-space component of a single concept vector is smaller still, a median of 6–7%), occupying a band that begins near the network's mid-depth and extends through the late layers, which carries the concepts the model is poised to verbalize and which mediates multi-step reasoning.\n\nWe argue that this object stands at the meeting point of two structurally distinct regimes, and that identifying the first of them correctly is the principal work of this version.\n\nThe second regime is non-self-closure: an interior carries no self-contained certificate of itself and must be read from an external vantage. Gödel's and Tarski's theorems exhibit it in provable form.\n\nThe first regime is not the classical boundary-determination of an elliptic boundary-value problem, as earlier versions of this note asserted. Under a given operator with a boundary acting now, the interior is fixed exactly, and the classical case is best used here as a contrast. J-space instead exhibits a distinct species we name (A′) imprint-determination: the shaping condition is a training distribution that acted in the past and is gone; the dynamics through which it acted was itself learned from that same condition; and what the condition forced is not an arbitrary interior but a specific, rare, privileged organization that no process specified. The right figure is morphogenetic, not hydrodynamic — bone under Wolff's law, whose settled architecture is the frozen record of loads no longer acting.\n\nTwo biological carriers serve as calibrators, fixing points on an axis of interiority. The living cell realizes boundary-determined, controller-free, apparently purposive organization with no self-model; the adaptive immune system sits one step higher, carrying a self/non-self model, still with no interiority of the reportable kind. From them follows the note's firmest statement, and it is a statement about evidence: the structural pattern is evidentially inert with respect to interiority of either kind. J-space's access-interiority is established by experiment — by verbalizability, modulation, and ablation — and not by any pattern this note identifies; the phenomenal question is untouched by the pattern in either direction. Shared shape is not shared nature, and shared shape is not shared evidence. A third calibrator, on a distinct axis, bounds the parallel misuse attaching to non-self-closure: the strongest engineered attempt to make a model consolidate its own memory — a self-modifying \"sleep\" architecture — is shown to relocate its governing criterion outside the system rather than eliminate it, so that advances in self-modification confirm the externalization thesis rather than refuting it.\n\nThe title's image — a soggy bottom, the dense undercooked base a baker never designs yet reliably produces under specific conditions — names the mode of emergence: unintended but conditioned. We retain it as an entry image while correcting its valence in §4: J-space is not a defect but a functional structure, and the closer figure is the crumb — likewise unwilled, likewise forced by the oven, but constitutive of the loaf. (In Polish the entry image is a zakalec and the corrected one a miękisz.)\n\nRegister: [CONJECTURE — structural], except where explicitly marked otherwise."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21277526","contentUrl":null,"metadataVersion":1,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":4,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":3,"versionOfCount":1,"created":"2026-07-09T10:48:01Z","registered":"2026-07-09T10:48:01Z","published":null,"updated":"2026-07-14T05:57:22Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21350871","type":"dois","attributes":{"doi":"10.5281/zenodo.21350871","identifiers":[{"identifier":"oai:zenodo.org:21350871","identifierType":"oai"}],"creators":[{"nameType":"Personal","affiliation":["Alliance Research Group (ARG)"],"givenName":"Łukasz","familyName":"Bojanowski","name":"Bojanowski, Łukasz","nameIdentifiers":[]}],"titles":[{"title":"Can an AI Bake a Soggy Bottom? J-space at the Convergence of Imprint-Determination and Non-Self-Closure"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"interpretability"},{"subject":"global workspace"},{"subject":"J-space"},{"subject":"imprint-determination"},{"subject":"non-self-closure"},{"subject":"emergence"},{"subject":"teleonomy"},{"subject":"autopoiesis"},{"subject":"morphogenesis"},{"subject":"Gödel incompleteness"},{"subject":"access consciousness"},{"subject":"AI governance"},{"subject":"large language models"},{"subject":"Alliance Research Group"}],"contributors":[],"dates":[{"date":"2026-07-14","dateType":"Issued"}],"language":"en","types":{"schemaOrg":"ScholarlyArticle","resourceTypeGeneral":"Text","citeproc":"article-journal","bibtex":"article","ris":"RPRT","resourceType":"Working paper"},"relatedIdentifiers":[{"relationType":"References","relatedIdentifier":"10.5281/zenodo.18842688","relatedIdentifierType":"DOI"},{"relationType":"References","relatedIdentifier":"10.5281/zenodo.18842852","relatedIdentifierType":"DOI"},{"relationType":"References","relatedIdentifier":"10.5281/zenodo.19102214","relatedIdentifierType":"DOI"},{"relationType":"References","relatedIdentifier":"10.5281/zenodo.20013919","relatedIdentifierType":"DOI"},{"relationType":"References","relatedIdentifier":"https://transformer-circuits.pub/2026/workspace/index.html","relatedIdentifierType":"URL"},{"relationType":"References","relatedIdentifier":"arXiv:2606.03979","relatedIdentifierType":"arXiv"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21277526","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":"v5.1","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":"We record a structural observation, not an empirical result. Recent interpretability work (Anthropic, July 2026) reports an emergent internal \"workspace\" in large language models — their J-space: a small, privileged set of directions in the residual stream, carrying at most a tenth of activation variance (the J-space component of a single concept vector is smaller still, a median of 6–7%), occupying a band that begins near the network's mid-depth and extends through the late layers, which carries the concepts the model is poised to verbalize and which mediates multi-step reasoning.\n\nWe argue that this object stands at the meeting point of two structurally distinct regimes, and that identifying the first of them correctly is the principal work of this version.\n\nThe second regime is non-self-closure: an interior carries no self-contained certificate of itself and must be read from an external vantage. Gödel's and Tarski's theorems exhibit it in provable form.\n\nThe first regime is not the classical boundary-determination of an elliptic boundary-value problem, as earlier versions of this note asserted. Under a given operator with a boundary acting now, the interior is fixed exactly, and the classical case is best used here as a contrast. J-space instead exhibits a distinct species we name (A′) imprint-determination: the shaping condition is a training distribution that acted in the past and is gone; the dynamics through which it acted was itself learned from that same condition; and what the condition forced is not an arbitrary interior but a specific, rare, privileged organization that no process specified. The right figure is morphogenetic, not hydrodynamic — bone under Wolff's law, whose settled architecture is the frozen record of loads no longer acting.\n\nTwo biological carriers serve as calibrators, fixing points on an axis of interiority. The living cell realizes boundary-determined, controller-free, apparently purposive organization with no self-model; the adaptive immune system sits one step higher, carrying a self/non-self model, still with no interiority of the reportable kind. From them follows the note's firmest statement, and it is a statement about evidence: the structural pattern is evidentially inert with respect to interiority of either kind. J-space's access-interiority is established by experiment — by verbalizability, modulation, and ablation — and not by any pattern this note identifies; the phenomenal question is untouched by the pattern in either direction. Shared shape is not shared nature, and shared shape is not shared evidence. A third calibrator, on a distinct axis, bounds the parallel misuse attaching to non-self-closure: the strongest engineered attempt to make a model consolidate its own memory — a self-modifying \"sleep\" architecture — is shown to relocate its governing criterion outside the system rather than eliminate it, so that advances in self-modification confirm the externalization thesis rather than refuting it.\n\nThe title's image — a soggy bottom, the dense undercooked base a baker never designs yet reliably produces under specific conditions — names the mode of emergence: unintended but conditioned. We retain it as an entry image while correcting its valence in §4: J-space is not a defect but a functional structure, and the closer figure is the crumb — likewise unwilled, likewise forced by the oven, but constitutive of the loaf. (In Polish the entry image is a zakalec and the corrected one a miękisz.)\n\nRegister: [CONJECTURE — structural], except where explicitly marked otherwise."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21350871","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":"2026-07-14T05:57:22Z","registered":"2026-07-14T05:57:22Z","published":null,"updated":"2026-07-14T05:57:22Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21350333","type":"dois","attributes":{"doi":"10.5281/zenodo.21350333","identifiers":[{"identifier":"oai:zenodo.org:21350333","identifierType":"oai"}],"creators":[{"nameType":"Personal","givenName":"Brent","familyName":"Jonah","name":"Jonah, Brent","nameIdentifiers":[],"affiliation":[]}],"titles":[{"title":"The memory cost of simulating two-qubit Pauli contextuality under repeatability and product rules is exactly log2(5) bits"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"quantum contextuality"},{"subject":"memory cost"},{"subject":"Mealy machine"},{"subject":"Kochen-Specker"}],"contributors":[],"dates":[{"date":"2026-07-14","dateType":"Issued"}],"language":"en","types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"Cites","resourceTypeGeneral":"Text","relatedIdentifier":"arXiv:2506.06869","relatedIdentifierType":"arXiv"},{"relationType":"Cites","resourceTypeGeneral":"Text","relatedIdentifier":"arXiv:1007.3650","relatedIdentifierType":"arXiv"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21350332","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":"For the 15 two-qubit Pauli observables, any classical Mealy machine reproducing the quantum predictions (Ia) repeatability and (II) context product rules requires exactly log2(5) ≈ 2.32 bits of memory. Upper bound: an explicit five-state machine, verified including the intervening-measurement form of (Ia). Lower bound: machine-certified unsatisfiability at four states (three independent encodings × three SAT solvers; DRUP proof checked by drat-trim; byte-reproducible formula; preregistrations externally timestamped before computation). This closes the gap [log2 4, log2 6] left open in arXiv:2506.06869. A verified note documents 338 pairwise-inequivalent optimal machines collapsing to 19 output-atlas orbits under the target-preserving affine symmetry group of order 23,040. Verification: unzip the deposit, run python3 verifier3.py (537 assertions, ~30 s, stdlib only), then drat-trim E2_n4.cnf E2_n4_unsat_glucose.drup (prints s VERIFIED)."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21350333","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":"2026-07-14T05:19:24Z","registered":"2026-07-14T05:19:24Z","published":null,"updated":"2026-07-14T05:19:24Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21350332","type":"dois","attributes":{"doi":"10.5281/zenodo.21350332","identifiers":[],"creators":[{"nameType":"Personal","givenName":"Brent","familyName":"Jonah","name":"Jonah, Brent","nameIdentifiers":[],"affiliation":[]}],"titles":[{"title":"The memory cost of simulating two-qubit Pauli contextuality under repeatability and product rules is exactly log2(5) bits"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"quantum contextuality"},{"subject":"memory cost"},{"subject":"Mealy machine"},{"subject":"Kochen-Specker"}],"contributors":[],"dates":[{"date":"2026-07-14","dateType":"Issued"}],"language":"en","types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"Cites","resourceTypeGeneral":"Text","relatedIdentifier":"arXiv:2506.06869","relatedIdentifierType":"arXiv"},{"relationType":"Cites","resourceTypeGeneral":"Text","relatedIdentifier":"arXiv:1007.3650","relatedIdentifierType":"arXiv"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21350332","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":"For the 15 two-qubit Pauli observables, any classical Mealy machine reproducing the quantum predictions (Ia) repeatability and (II) context product rules requires exactly log2(5) ≈ 2.32 bits of memory. Upper bound: an explicit five-state machine, verified including the intervening-measurement form of (Ia). Lower bound: machine-certified unsatisfiability at four states (three independent encodings × three SAT solvers; DRUP proof checked by drat-trim; byte-reproducible formula; preregistrations externally timestamped before computation). This closes the gap [log2 4, log2 6] left open in arXiv:2506.06869. A verified note documents 338 pairwise-inequivalent optimal machines collapsing to 19 output-atlas orbits under the target-preserving affine symmetry group of order 23,040. Verification: unzip the deposit, run python3 verifier3.py (537 assertions, ~30 s, stdlib only), then drat-trim E2_n4.cnf E2_n4_unsat_glucose.drup (prints s VERIFIED)."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21350332","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":1,"versionOfCount":1,"created":"2026-07-14T05:19:24Z","registered":"2026-07-14T05:19:24Z","published":null,"updated":"2026-07-14T05:19:24Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21289202","type":"dois","attributes":{"doi":"10.5281/zenodo.21289202","identifiers":[],"creators":[{"nameType":"Personal","affiliation":["Cognitive Engineering"],"givenName":"Martin Venti","familyName":"David","name":"David, Martin Venti","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0009-0000-6675-7821"}]}],"titles":[{"title":"Algebraic connectivity of diameter-3 graphs: secular certificates, weighted Nordhaus-Gaddum inequalities, and the Barrett-Kempton conjectures"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"algebraic connectivity"},{"subject":"Fiedler calue"},{"subject":"diameter-3 graphs"},{"subject":"domination number"},{"subject":"secular equation"},{"subject":"BarrettKemptom conjecture"},{"subject":"spectral graph theory"}],"contributors":[],"dates":[{"date":"2026-07-14","dateType":"Issued"}],"language":"en","types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsSupplementTo","resourceTypeGeneral":"Preprint","relatedIdentifier":"arXiv:2201.04225","relatedIdentifierType":"arXiv"},{"relationType":"Cites","resourceTypeGeneral":"Preprint","relatedIdentifier":"arXiv:2109.04568","relatedIdentifierType":"arXiv"},{"relationType":"Cites","resourceTypeGeneral":"Preprint","relatedIdentifier":"10.1016/j.jctb.2021.06.009","relatedIdentifierType":"DOI"},{"relationType":"Cites","resourceTypeGeneral":"Preprint","relatedIdentifier":"arXiv:2607.03711","relatedIdentifierType":"arXiv"},{"relationType":"Cites","resourceTypeGeneral":"Preprint","relatedIdentifier":"10.13001/1081-3810.1026","relatedIdentifierType":"DOI"},{"relationType":"Cites","resourceTypeGeneral":"Preprint","relatedIdentifier":"10.21136/CMJ.1973.101168","relatedIdentifierType":"DOI"},{"relationType":"IsPartOf","resourceTypeGeneral":"Preprint","relatedIdentifier":"10.5281/zenodo.19106910","relatedIdentifierType":"DOI"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21289202","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":"V2.0","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":"Voici l'abstract en texte brut pour Zenodo :\n\n\n\nBarrett, Evans, Hall, and Kempton (2022) proposed six conjectures relating algebraic connectivity, the Laplacian spread, and their Nordhaus–Gaddum complements. We establish a unified secular-certificate framework for Conjecture 1 (C1), yielding five theorems proved for all n and exhaustive verification through n = 9.\n\nBeyond C1, we prove three new results on the companion conjectures. First, the weighted Laplacian spread conjecture (C5 for weighted graphs): for any edge weighting w : E(Kₙ) → [0,1], λ₂(Lw) + λ₂(L₁₋w) ≥ 1, via a convexity argument reducing to the unweighted theorem. Second, C1 implies C6 (unweighted): if C1 holds, then λ₂(G) + λ₂(Ḡ) − (2/n)λ₂(G)λ₂(Ḡ) ≥ 1 for all graphs G, via the concavity of fₙ and an AM–GM coupling. Third, the spectral identity for weighted C6: on every one-edge interpolation between a disconnected graph and a graph with disconnected complement (the \"P1 arc\"), g(w) ≡ 1 identically, arising from a three-dimensional invariant subspace of the weighted Laplacian.\n\nWe also show that C4 strong is false for weighted graphs at n ≥ 5, with the C6 arc providing explicit counterexamples, and we give a complete geometric characterisation of the achievable spectral set Aₙ = {(λ₂(Lw), λmax(Lw)) : w ∈ [0,1]^E}, whose lower boundary coincides with the g = 1 hyperbola."},{"descriptionType":"Other","description":"Changes in version 2: Added proof of weighted C5 (Theorem 7), proof that C1 implies C6 (Theorem 8), the P1 spectral identity for weighted C6 (Theorem 9), disproof of C4 strong for weighted graphs at n ≥ 5 (Theorem 10), and a complete characterisation of the achievable spectral set Aₙ.\n\n\n\n\n\n\n\n\n\n\n\n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n ","lang":"eng"}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21289202","contentUrl":null,"metadataVersion":3,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":3,"citationCount":0,"partCount":0,"partOfCount":1,"versionCount":2,"versionOfCount":1,"created":"2026-07-10T05:57:48Z","registered":"2026-07-10T05:57:48Z","published":null,"updated":"2026-07-14T04:52:09Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21350056","type":"dois","attributes":{"doi":"10.5281/zenodo.21350056","identifiers":[{"identifier":"oai:zenodo.org:21350056","identifierType":"oai"}],"creators":[{"nameType":"Personal","affiliation":["Cognitive Engineering"],"givenName":"Martin Venti","familyName":"David","name":"David, Martin Venti","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0009-0000-6675-7821"}]}],"titles":[{"title":"Algebraic connectivity of diameter-3 graphs: secular certificates, weighted Nordhaus-Gaddum inequalities, and the Barrett-Kempton conjectures"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"algebraic connectivity"},{"subject":"Fiedler calue"},{"subject":"diameter-3 graphs"},{"subject":"domination number"},{"subject":"secular equation"},{"subject":"BarrettKemptom conjecture"},{"subject":"spectral graph theory"}],"contributors":[],"dates":[{"date":"2026-07-14","dateType":"Issued"}],"language":"en","types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsSupplementTo","resourceTypeGeneral":"Preprint","relatedIdentifier":"arXiv:2201.04225","relatedIdentifierType":"arXiv"},{"relationType":"Cites","resourceTypeGeneral":"Preprint","relatedIdentifier":"arXiv:2109.04568","relatedIdentifierType":"arXiv"},{"relationType":"Cites","resourceTypeGeneral":"Preprint","relatedIdentifier":"10.1016/j.jctb.2021.06.009","relatedIdentifierType":"DOI"},{"relationType":"Cites","resourceTypeGeneral":"Preprint","relatedIdentifier":"arXiv:2607.03711","relatedIdentifierType":"arXiv"},{"relationType":"Cites","resourceTypeGeneral":"Preprint","relatedIdentifier":"10.13001/1081-3810.1026","relatedIdentifierType":"DOI"},{"relationType":"Cites","resourceTypeGeneral":"Preprint","relatedIdentifier":"10.21136/CMJ.1973.101168","relatedIdentifierType":"DOI"},{"relationType":"IsPartOf","resourceTypeGeneral":"Preprint","relatedIdentifier":"10.5281/zenodo.19106910","relatedIdentifierType":"DOI"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21289202","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":"V2.0","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":"Voici l'abstract en texte brut pour Zenodo :\n\n\n\nBarrett, Evans, Hall, and Kempton (2022) proposed six conjectures relating algebraic connectivity, the Laplacian spread, and their Nordhaus–Gaddum complements. We establish a unified secular-certificate framework for Conjecture 1 (C1), yielding five theorems proved for all n and exhaustive verification through n = 9.\n\nBeyond C1, we prove three new results on the companion conjectures. First, the weighted Laplacian spread conjecture (C5 for weighted graphs): for any edge weighting w : E(Kₙ) → [0,1], λ₂(Lw) + λ₂(L₁₋w) ≥ 1, via a convexity argument reducing to the unweighted theorem. Second, C1 implies C6 (unweighted): if C1 holds, then λ₂(G) + λ₂(Ḡ) − (2/n)λ₂(G)λ₂(Ḡ) ≥ 1 for all graphs G, via the concavity of fₙ and an AM–GM coupling. Third, the spectral identity for weighted C6: on every one-edge interpolation between a disconnected graph and a graph with disconnected complement (the \"P1 arc\"), g(w) ≡ 1 identically, arising from a three-dimensional invariant subspace of the weighted Laplacian.\n\nWe also show that C4 strong is false for weighted graphs at n ≥ 5, with the C6 arc providing explicit counterexamples, and we give a complete geometric characterisation of the achievable spectral set Aₙ = {(λ₂(Lw), λmax(Lw)) : w ∈ [0,1]^E}, whose lower boundary coincides with the g = 1 hyperbola."},{"descriptionType":"Other","description":"Changes in version 2: Added proof of weighted C5 (Theorem 7), proof that C1 implies C6 (Theorem 8), the P1 spectral identity for weighted C6 (Theorem 9), disproof of C4 strong for weighted graphs at n ≥ 5 (Theorem 10), and a complete characterisation of the achievable spectral set Aₙ.\n\n\n\n\n\n\n\n\n\n\n\n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n ","lang":"eng"}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21350056","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":"2026-07-14T04:52:09Z","registered":"2026-07-14T04:52:09Z","published":null,"updated":"2026-07-14T04:52:09Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21330823","type":"dois","attributes":{"doi":"10.5281/zenodo.21330823","identifiers":[{"identifier":"oai:zenodo.org:21330823","identifierType":"oai"}],"creators":[{"nameType":"Personal","affiliation":["Regis University"],"givenName":"Julian","familyName":"Soltes","name":"Soltes, Julian","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0009-0003-4226-1778"}]}],"titles":[{"title":"On the Probabilities of Spacetime: A Statistical Topography via Maximum Entropy"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"Physics","subjectScheme":"MeSH"},{"subject":"Astronomy","subjectScheme":"GEMET"},{"subject":"Applied mathematics","subjectScheme":"EuroSciVoc"},{"subject":"Computational intelligence","subjectScheme":"EuroSciVoc"},{"subject":"Physical cosmology","subjectScheme":"EuroSciVoc"}],"contributors":[],"dates":[{"date":"2026-07-13","dateType":"Issued"}],"language":"en","types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsSupplementedBy","resourceTypeGeneral":"Preprint","relatedIdentifier":"arXiv:2511.13843","relatedIdentifierType":"arXiv"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21283903","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":"This paper presents a non-parametric topography of isotropic spacetime, following the principle of maximum entropy to quantify the relative probability of any physical state.\n\nThe topography $\\Upsilon(\\zeta)$ is defined as an 11-D probability distribution, derived from a maximally unbiased ensemble of solutions to the Einstein Field Equations (EFE). Uncertainty prevents infinite precision, blurring all microstates into a probabilistic fluid. The result provides a statistical foundation for the manifestation of our universe and its contents, described by probabilities and their respective gradients.\n\n$\\Upsilon(\\zeta)$ assumes unconstrained numerical coverage of the EFE landscape, mapping mathematically valid solutions that may violate parametric energy conditions. Uncertainty distorts the boundaries between these exotic states and the canonical phase, rationalizing their existence within our universe as quantifiable improbabilities.\n\nResources:\n\n\n\n\n\nThe computational implementation and main data ensemble are attached here, as well as maintained at: https://github.com/jgsoltes/Universe-KDE\n\n\n\n\nResearchers are encouraged to apply the QUASAR optimizer to their own high-dimensional or non-convex function landscapes. Source code and documentation are maintained at: https://github.com/jgsoltes/hdim-opt"}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21330823","contentUrl":null,"metadataVersion":2,"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":"2026-07-13T03:58:27Z","registered":"2026-07-13T03:58:27Z","published":null,"updated":"2026-07-14T03:42:02Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21283903","type":"dois","attributes":{"doi":"10.5281/zenodo.21283903","identifiers":[],"creators":[{"nameType":"Personal","affiliation":["Regis University"],"givenName":"Julian","familyName":"Soltes","name":"Soltes, Julian","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0009-0003-4226-1778"}]}],"titles":[{"title":"On the Probabilities of Spacetime: A Statistical Topography via Maximum Entropy"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"Physics","subjectScheme":"MeSH"},{"subject":"Astronomy","subjectScheme":"GEMET"},{"subject":"Applied mathematics","subjectScheme":"EuroSciVoc"},{"subject":"Computational intelligence","subjectScheme":"EuroSciVoc"},{"subject":"Physical cosmology","subjectScheme":"EuroSciVoc"}],"contributors":[],"dates":[{"date":"2026-07-13","dateType":"Issued"}],"language":"en","types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsSupplementedBy","resourceTypeGeneral":"Preprint","relatedIdentifier":"arXiv:2511.13843","relatedIdentifierType":"arXiv"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21283903","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":"v1.0.0","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 presents a non-parametric topography of isotropic spacetime, following the principle of maximum entropy to quantify the relative probability of any physical state.\n\nThe topography $\\Upsilon(\\zeta)$ is defined as an 11-D probability distribution, derived from a maximally unbiased ensemble of solutions to the Einstein Field Equations (EFE). Uncertainty prevents infinite precision, blurring all microstates into a probabilistic fluid. The result provides a statistical foundation for the manifestation of our universe and its contents, described by probabilities and their respective gradients.\n\n$\\Upsilon(\\zeta)$ assumes unconstrained numerical coverage of the EFE landscape, mapping mathematically valid solutions that may violate parametric energy conditions. Uncertainty distorts the boundaries between these exotic states and the canonical phase, rationalizing their existence within our universe as quantifiable improbabilities.\n\nResources:\n\n\n\n\n\nThe computational implementation and main data ensemble are attached here, as well as maintained at: https://github.com/jgsoltes/Universe-KDE\n\n\n\n\nResearchers are encouraged to apply the QUASAR optimizer to their own high-dimensional or non-convex function landscapes. Source code and documentation are maintained at: https://github.com/jgsoltes/hdim-opt"}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21283903","contentUrl":null,"metadataVersion":5,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":2,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":4,"versionOfCount":1,"created":"2026-07-09T20:24:28Z","registered":"2026-07-09T20:24:28Z","published":null,"updated":"2026-07-14T03:42:02Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21327945","type":"dois","attributes":{"doi":"10.5281/zenodo.21327945","identifiers":[],"creators":[{"nameType":"Personal","affiliation":["Independent Researcher"],"givenName":"Seongjin","familyName":"Choi","name":"Choi, Seongjin","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0009-0001-3193-7424"}]}],"titles":[{"title":"Training-Free Off-Screen Player Imputation for Broadcast-Based Spatial Football Analytics"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"football analytics"},{"subject":"player imputation"},{"subject":"pitch control"},{"subject":"game state reconstruction"},{"subject":"sports analytics"},{"subject":"computer vision"},{"subject":"broadcast video"}],"contributors":[],"dates":[{"date":"2026-07-13","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsSupplementTo","resourceTypeGeneral":"Software","relatedIdentifier":"https://github.com/nowayfootball/offscreen-impute/tree/v1.1","relatedIdentifierType":"URL"},{"relationType":"IsSupplementTo","resourceTypeGeneral":"Preprint","relatedIdentifier":"arXiv:2607.11548","relatedIdentifierType":"arXiv"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21327945","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":"v1.1","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":"Spatial football metrics such as pitch control assume access to the positions of all 22 players, yet the most widely available source of positional data — the broadcast main camera — shows only 10–16 of them at any moment. We quantify the resulting distortion with an open, reproducible benchmark: a simulated broadcast viewport applied to open full-pitch tracking data (Metrica Sports; three matches, one held out from method development). Ignoring off-screen players — the visible-only baseline implied whenever a video-based game-state-reconstruction (GSR) pipeline adds no imputation layer — inflates hidden-zone pitch-control error to 25.1–26.9 percentage points and produces a mean absolute control-share error of 11.1–13.4 points across the three matches. We then evaluate a ladder of training-free, online imputation baselines that use only observations from the match being analysed. The best overall on these decision-relevant metrics, role-anchored centroid voting — each visible player votes for the full-team centroid by subtracting its running role offset, attenuating the viewport-induced subset bias — roughly halves hidden-zone error (to 12.2–13.8 points) and cuts the control-share error to 28–48% of the ignore policy at every viewport width from 36 m to 60 m in all three matches (4.5–4.7 points at W=44 m). In the short-occlusion regime (≤9.6 s) covered by the closest learned prior work, our training-free method reaches binwise median position errors of 3.3–8.9 m; 50–57% of hidden-player observations under the simulated viewport, however, lie beyond that regime, outside the 9.6 s sequence protocol of that prior work. We integrate the method end-to-end into a broadcast-video GSR pipeline and show that imputation changes a downstream possession-quality score (Space-Creation Index) by 15.6 and 17.2 points on two real World Cup broadcast windows, flipping the verdict class — under prespecified operational thresholds — in one of them."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21327945","contentUrl":null,"metadataVersion":2,"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":3,"versionOfCount":1,"created":"2026-07-12T21:58:33Z","registered":"2026-07-12T21:58:33Z","published":null,"updated":"2026-07-14T03:09:47Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21338808","type":"dois","attributes":{"doi":"10.5281/zenodo.21338808","identifiers":[{"identifier":"oai:zenodo.org:21338808","identifierType":"oai"}],"creators":[{"nameType":"Personal","affiliation":["Independent Researcher"],"givenName":"Seongjin","familyName":"Choi","name":"Choi, Seongjin","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0009-0001-3193-7424"}]}],"titles":[{"title":"Training-Free Off-Screen Player Imputation for Broadcast-Based Spatial Football Analytics"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"football analytics"},{"subject":"player imputation"},{"subject":"pitch control"},{"subject":"game state reconstruction"},{"subject":"sports analytics"},{"subject":"computer vision"},{"subject":"broadcast video"}],"contributors":[],"dates":[{"date":"2026-07-13","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsSupplementTo","resourceTypeGeneral":"Software","relatedIdentifier":"https://github.com/nowayfootball/offscreen-impute/tree/v1.1","relatedIdentifierType":"URL"},{"relationType":"IsSupplementTo","resourceTypeGeneral":"Preprint","relatedIdentifier":"arXiv:2607.11548","relatedIdentifierType":"arXiv"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21327945","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":"v1.1","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":"Spatial football metrics such as pitch control assume access to the positions of all 22 players, yet the most widely available source of positional data — the broadcast main camera — shows only 10–16 of them at any moment. We quantify the resulting distortion with an open, reproducible benchmark: a simulated broadcast viewport applied to open full-pitch tracking data (Metrica Sports; three matches, one held out from method development). Ignoring off-screen players — the visible-only baseline implied whenever a video-based game-state-reconstruction (GSR) pipeline adds no imputation layer — inflates hidden-zone pitch-control error to 25.1–26.9 percentage points and produces a mean absolute control-share error of 11.1–13.4 points across the three matches. We then evaluate a ladder of training-free, online imputation baselines that use only observations from the match being analysed. The best overall on these decision-relevant metrics, role-anchored centroid voting — each visible player votes for the full-team centroid by subtracting its running role offset, attenuating the viewport-induced subset bias — roughly halves hidden-zone error (to 12.2–13.8 points) and cuts the control-share error to 28–48% of the ignore policy at every viewport width from 36 m to 60 m in all three matches (4.5–4.7 points at W=44 m). In the short-occlusion regime (≤9.6 s) covered by the closest learned prior work, our training-free method reaches binwise median position errors of 3.3–8.9 m; 50–57% of hidden-player observations under the simulated viewport, however, lie beyond that regime, outside the 9.6 s sequence protocol of that prior work. We integrate the method end-to-end into a broadcast-video GSR pipeline and show that imputation changes a downstream possession-quality score (Space-Creation Index) by 15.6 and 17.2 points on two real World Cup broadcast windows, flipping the verdict class — under prespecified operational thresholds — in one of them."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21338808","contentUrl":null,"metadataVersion":1,"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":"2026-07-13T12:47:34Z","registered":"2026-07-13T12:47:35Z","published":null,"updated":"2026-07-14T03:09:47Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21128751","type":"dois","attributes":{"doi":"10.5281/zenodo.21128751","identifiers":[{"identifier":"oai:zenodo.org:21128751","identifierType":"oai"}],"creators":[{"nameType":"Personal","affiliation":["Institute for Basic Science"],"givenName":"Qianhang","familyName":"Ding","name":"Ding, Qianhang","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0000-0001-6703-2531"}]},{"nameType":"Personal","affiliation":["The University of Tokyo"],"givenName":"Xinpeng","familyName":"Wang","name":"Wang, Xinpeng","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0000-0002-0369-6774"}]}],"titles":[{"title":"Dataset for reconstructing primordial black hole mass function and primordial power spectrum from LIGO-Virgo-KAGRA catalogs"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-07-14","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"Dataset","resourceTypeGeneral":"Dataset","citeproc":"dataset","bibtex":"misc","ris":"DATA","resourceType":""},"relatedIdentifiers":[{"relationType":"IsSupplementTo","resourceTypeGeneral":"Dataset","relatedIdentifier":"arXiv:2607.11145","relatedIdentifierType":"arXiv"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21128750","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"},{"rightsUri":"http://rightsstatements.org/vocab/InC/1.0/","rights":"Copyright (C) 2026 The Authors."}],"descriptions":[{"descriptionType":"Abstract","description":"This dataset provides the raw data in the work \"Reconstruction of Primordial Power Spectrum from Gravitational Waves of High-Redshift Black Hole Binaries\" (arXiv: 2607.11145).\n\nThe dataset includes the selected binary black hole events in LIGO-Virgo-KAGRA  catalogs, reconstructed primordial black hole mass function, reconstructed primordial power specturm."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21128751","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":1,"created":"2026-07-14T03:08:27Z","registered":"2026-07-14T03:08:27Z","published":null,"updated":"2026-07-14T03:08:54Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21128750","type":"dois","attributes":{"doi":"10.5281/zenodo.21128750","identifiers":[],"creators":[{"nameType":"Personal","affiliation":["Institute for Basic Science"],"givenName":"Qianhang","familyName":"Ding","name":"Ding, Qianhang","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0000-0001-6703-2531"}]},{"nameType":"Personal","affiliation":["The University of Tokyo"],"givenName":"Xinpeng","familyName":"Wang","name":"Wang, Xinpeng","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0000-0002-0369-6774"}]}],"titles":[{"title":"Dataset for reconstructing primordial black hole mass function and primordial power spectrum from LIGO-Virgo-KAGRA catalogs"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-07-14","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"Dataset","resourceTypeGeneral":"Dataset","citeproc":"dataset","bibtex":"misc","ris":"DATA","resourceType":""},"relatedIdentifiers":[{"relationType":"IsSupplementTo","resourceTypeGeneral":"Dataset","relatedIdentifier":"arXiv:2607.11145","relatedIdentifierType":"arXiv"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21128750","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"},{"rightsUri":"http://rightsstatements.org/vocab/InC/1.0/","rights":"Copyright (C) 2026 The Authors."}],"descriptions":[{"descriptionType":"Abstract","description":"This dataset provides the raw data in the work \"Reconstruction of Primordial Power Spectrum from Gravitational Waves of High-Redshift Black Hole Binaries\" (arXiv: 2607.11145).\n\nThe dataset includes the selected binary black hole events in LIGO-Virgo-KAGRA  catalogs, reconstructed primordial black hole mass function, reconstructed primordial power specturm."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21128750","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":2,"versionOfCount":1,"created":"2026-07-14T03:08:27Z","registered":"2026-07-14T03:08:27Z","published":null,"updated":"2026-07-14T03:08:54Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21337994","type":"dois","attributes":{"doi":"10.5281/zenodo.21337994","identifiers":[{"identifier":"oai:zenodo.org:21337994","identifierType":"oai"}],"creators":[{"nameType":"Personal","affiliation":["RehaBrain Development Center, RehaSolution Co., Ltd., Hwaseong-si, Korea"],"givenName":"KyungUP","familyName":"Moon","name":"Moon, KyungUP","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0009-0009-6929-5875"}]}],"titles":[{"title":"A Conditional Structural Reduction in the Collatz Dynamics: Realization Theory, Defect Trichotomy, and Valuation Shell Tracking"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"Collatz conjecture"},{"subject":"realization theory"},{"subject":"defect trichotomy"},{"subject":"alignment equivalence"},{"subject":"2-adic integers"},{"subject":"valuation itinerary"},{"subject":"shell tracking"},{"subject":"binary non-realizability"},{"subject":"Sturmian sequences"},{"subject":"normalized-state identity"}],"contributors":[],"dates":[{"date":"2026-07-13","dateType":"Issued"},{"date":"2026-06-01","dateType":"Created"}],"language":"en","types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsSupplementTo","resourceTypeGeneral":"Preprint","relatedIdentifier":"10.5281/zenodo.18233316","relatedIdentifierType":"DOI"},{"relationType":"IsSupplementTo","resourceTypeGeneral":"Preprint","relatedIdentifier":"10.5281/zenodo.20456007","relatedIdentifierType":"DOI"},{"relationType":"IsSupplementTo","resourceTypeGeneral":"Preprint","relatedIdentifier":"10.5281/zenodo.20456568","relatedIdentifierType":"DOI"},{"relationType":"IsSupplementTo","resourceTypeGeneral":"Preprint","relatedIdentifier":"10.5281/zenodo.21330560","relatedIdentifierType":"DOI"},{"relationType":"IsSupplementTo","resourceTypeGeneral":"Preprint","relatedIdentifier":"10.5281/zenodo.21330741","relatedIdentifierType":"DOI"},{"relationType":"IsSupplementTo","resourceTypeGeneral":"Preprint","relatedIdentifier":"10.5281/zenodo.21348614","relatedIdentifierType":"DOI"},{"relationType":"Cites","resourceTypeGeneral":"Preprint","relatedIdentifier":"arXiv:2603.11066","relatedIdentifierType":"arXiv"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21330888","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":"V2.0","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"},{"rightsUri":"http://rightsstatements.org/vocab/InC/1.0/","rights":"© 2026 Moon Kyung-Up."}],"descriptions":[{"descriptionType":"Abstract","description":"This paper does not prove the Collatz conjecture. It develops a rigorous 2-adic realization theory for the accelerated Collatz dynamics, identifying the exact structural form that any potential exceptional orbit must take under an explicit reduction hypothesis.\n\nThe core ingredients are:(1) A 2-adic realization map T_R: S_C → Z₂ attached to bounded-discrepancy valuation itineraries.(2) A realization defect δ_L measuring congruence misalignment.(3) An exact-prefix uniqueness result showing every finite valuation word determines a unique realizing residue class.\n\nProved results (unconditional):- Defect Trichotomy (§4, Corollary 4.4): δ_L \u003c 0 is absorbing (all future defects stay negative and decrease strictly); δ_L \u003e 0 is unstable (snaps negative in one step); δ_L = 0 is the unique gateway state allowing δ_{L+1} ≥ 0.- Alignment Theorem (Theorem 5.1): T_R(α) = N ∈ ℕ if and only if δ_L = 0 for all large L, if and only if the Collatz orbit of N has exactly the valuation itinerary α.- Exact Normalized-State Identity (Theorem 6.1): T^L(N) = 2^{-D_L}(N + (1/3)Σ_{j\u003cL} 2^{D_j}) exactly, where D_L = A_L - L·log₂3. A proved algebraic identity, not a statistical fit.- Linear Growth Theorem (Theorem 7.1): if the discrepancy D_L is bounded by C for a given orbit, that orbit satisfies c₁L ≤ T^L(N) ≤ c₂L for explicit constants c₁ = 2^{-2C}/3, c₂ = 2^{2C}/3.- Finite-Alphabet Restriction (Theorem 7.2): under the same bounded-discrepancy hypothesis, the valuation symbols α_L are confined to a finite alphabet; for sufficiently small C this alphabet is exactly {1,2}.- Exact Shell Congruence (Theorem 8.1): ν₂(3m+1) = a if and only if m ≡ s_a (mod 2^{a+1}), for the explicit residue s_a = 3⁻¹(2^a - 1). Applied to the orbit, T^L(N) ≡ s_{α_L} (mod 2^{α_L+1}) for every L — unconditional, no bounded-discrepancy hypothesis required.- Exact-Prefix Uniqueness (Theorem 9.3, Corollary 9.4): for any finite valuation word (a₀,...,a_{L-1}), there is a unique odd residue class modulo 2^{A_L+1} realizing it exactly, so the normalized density is exactly 2^{-(A_L+1)} → 0 as L → ∞ — unconditionally, with no bounded-discrepancy hypothesis on the word. This result supersedes and strengthens an earlier, weaker \"Modular Survival Density\" claim from a prior draft that required such a hypothesis.\n\nProved results (conditional):- Conditional Capture (Proposition 10.1): assuming the bounded-discrepancy capture hypothesis, any non-terminating Collatz counterexample has an actual valuation itinerary that is (i) aligned (T_R(α) = N, δ_L = 0 for all L), (ii) bounded-discrepancy, (iii) linear-growth, (iv) confined to a finite alphabet, and (v) exact-shell-congruent at every step. This is a conditional normal form for a hypothetical counterexample, not a proof that no such counterexample exists.\n\nOpen problems (§12), each stated with the specific obstruction blocking it:- Binary non-realizability: can an actual orbit's valuation itinerary stay confined to {1,2} forever? A short finite mod-8 forcing argument, previously believed to settle this, is now known to fail: for u ≡ 3 (mod 8), the next valuation is 2 + ν₂(4+9t) on the sub-class u = 3+8t, which is unbounded as t varies (explicit counterexample: u=11). No uniform valuation-depth bound on a fixed residue class is known, and the problem should not be attacked by raising the modulus alone.- Sturmian non-realizability: harder than the binary case, since every Sturmian address is itself a binary address. Appears to reduce to a rationality question about a weighted 2-adic series Ξ_θ,β = Σ 3⁻ʲ2^⌊j·log₂3+β⌋ attached to the address (noted as a candidate future direction, not attempted here).- Finite-state closure: depends on resolving the binary case first, since no fixed modulus determines exact valuations uniformly.- The integer-realization barrier: can the inverse limit of an infinite, bounded-discrepancy, finite-alphabet, exact-shell-congruent address ever coincide with a positive integer? This is the single question the other open problems are facets of, and the central question left open by this paper.- The bounded-discrepancy capture hypothesis itself (does every non-terminating orbit eventually have bounded discrepancy?) remains unproved.\n\nRelation to companion papers:- Papers 8-11 (DOI: 10.5281/zenodo.18233316, 10.5281/zenodo.20456007, 10.5281/zenodo.20456568, 10.5281/zenodo.21330560): address-generation theory. Paper 11 independently formulated the same finite-prefix residue rigidity proved here as Exact-Prefix Uniqueness, via a compatible-scheduler construction with matching modulus; Paper 11 (May 2026) was derived without knowledge of a March 2026 preprint by Chang (arXiv:2603.11066) that formulates a closely related residue phenomenon, so the two are independent.- BGS (DOI: 10.5281/zenodo.21348614, Version V2.0): bounded-drift obstruction framework and diagnostic coordinates, built directly on the realization and alignment theory of this paper. BGS's integer-realizability condition (its Theorem 6, Bottleneck Reduction) is stated in terms of T_R(α) = N exactly as characterized here by the Realization Criterion and Alignment Theorem. The two papers together give a structural reduction (this paper) and a conditional existence/reduction hierarchy (BGS); neither proves the Collatz conjecture, and BGS's reduction additionally depends on an explicit Hypothesis H.\n\nChanges from v1.0:- Added Exact-Prefix Uniqueness (Theorem 9.3, Corollary 9.4), an unconditional and strictly stronger replacement for the earlier Modular Survival Density claim, which required a bounded-discrepancy hypothesis this version does not need.- Removed Binary Non-Realizability and Sturmian Non-Realizability as proved theorems. Both depended on a mod-8 forcing argument that is now known to be false in general (explicit counterexample: the residue class u ≡ 3 (mod 8) does not determine the next valuation uniformly). Both are restated as open problems with the specific technical obstruction identified.- Removed the Residue Stabilization Conjecture and the \"Conditional Collatz Reduction\" claim that Collatz follows from UBDP + RSC. The paper's conditional result (Proposition 10.1) establishes a necessary normal form for a hypothetical counterexample under the capture hypothesis; it does not claim, and this version does not claim, that Collatz follows from any combination of hypotheses in this paper.- Added a \"Relation to Prior Work\" subsection citing Terras (1976), Everett (1977), Möller (1978), and Wirsching (1998) for the underlying 2-adic realization technique, and Chang (2026) for the independently-derived overlapping finite-prefix result.- Updated all cross-references to companion papers (Paper 11, BGS) to their current numbering."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21337994","contentUrl":null,"metadataVersion":1,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":5,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":1,"created":"2026-07-14T02:20:44Z","registered":"2026-07-14T02:20:44Z","published":null,"updated":"2026-07-14T02:27:10Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}}],"meta":{"total":39892,"totalPages":400,"page":1},"links":{"self":"https://api.datacite.org/dois?query=relatedIdentifiers.relatedIdentifierType%3AarXiv","next":"https://api.datacite.org/dois?page%5Bnumber%5D=2\u0026page%5Bsize%5D=25\u0026query=relatedIdentifiers.relatedIdentifierType%3AarXiv"}}