{"data":[{"id":"10.5281/zenodo.22848467","type":"dois","attributes":{"doi":"10.5281/zenodo.22848467","identifiers":[{"identifier":"oai:zenodo.org:22848467","identifierType":"oai"}],"creators":[{"nameType":"Personal","affiliation":[{"affiliationIdentifier":"https://ror.org/02k3smh20","name":"University of Kentucky","affiliationIdentifierScheme":"ROR"}],"familyName":"Paul Rodgers","name":"Paul Rodgers","nameIdentifiers":[]}],"titles":[{"title":"The Damage-Tolerance Axis: Capacity Sparsity, Delocalisation, and the Mutation-Load Bound on Functional Fraction"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-09-19","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.22848466","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 manuscript proposes a single axis ordering physical, biological and engineered systems by their tolerance to damage, and identifies the quantity that sets position on it. We begin from a pair of systems ordinarily discussed in unrelated literatures — the cerebral cortex and a black hole horizon — and observe that both are two-dimensional surfaces whose capacity is set by area and whose interiors express the content they encode, and that both pose the identical question of whether content survives destruction of its container. They sit at opposite extremes of the fraction of their own capacity bound that they actually use, separated by fifty-nine orders of magnitude, and this accounts for why the same question receives opposite answers in the two cases. A single-term formulation of the axis is stated and then shown to fail on a case in the middle, and is corrected to require two terms, the second of which is already present in this framework. We then show that every system examined is internally heterogeneous — a small, brittle, addressed core embedded in a large, tolerant, delocalised bulk — and that the size of the core is set not by any counting argument but by mutation load, with the functional fraction bounded by the reciprocal of the per-generation mutation rate. This bound is tested out-of-sample on six organisms spanning four orders of magnitude in genome size, predicts their ordering correctly with a consistent offset rather than scatter, and renders the C-value paradox a forced consequence rather than a puzzle. We state plainly that the derivation is population genetics’ and the framing is this framework’s, and rank the result accordingly.The foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). 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We begin from a pair of systems ordinarily discussed in unrelated literatures — the cerebral cortex and a black hole horizon — and observe that both are two-dimensional surfaces whose capacity is set by area and whose interiors express the content they encode, and that both pose the identical question of whether content survives destruction of its container. They sit at opposite extremes of the fraction of their own capacity bound that they actually use, separated by fifty-nine orders of magnitude, and this accounts for why the same question receives opposite answers in the two cases. A single-term formulation of the axis is stated and then shown to fail on a case in the middle, and is corrected to require two terms, the second of which is already present in this framework. We then show that every system examined is internally heterogeneous — a small, brittle, addressed core embedded in a large, tolerant, delocalised bulk — and that the size of the core is set not by any counting argument but by mutation load, with the functional fraction bounded by the reciprocal of the per-generation mutation rate. This bound is tested out-of-sample on six organisms spanning four orders of magnitude in genome size, predicts their ordering correctly with a consistent offset rather than scatter, and renders the C-value paradox a forced consequence rather than a puzzle. We state plainly that the derivation is population genetics’ and the framing is this framework’s, and rank the result accordingly.The foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). 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This manuscript supplies the method. We give the operation converting a subdivided triad into a tetrahedron, and show it is edge identification rather than any spatial folding — a distinction that blocked the construction entirely until it was corrected. We derive the parity condition determining which subdivisions can close, and show that of the eight convex deltahedra only two have a face count that is a perfect square, giving exactly the two doubly magic nuclei A=4 and A=16. We derive the mass-number gaps at A=5 and A=8 by three independent routes each, and identify both as the first four-dimensional member of their respective polytope families. We give the regularity criterion, correcting an earlier and narrower triangularity criterion that does not survive inspection. We supply the composition rule — balancing nucleon count across a two-by-two grid of type against spin on both marginals — together with the three routes that failed before it, and report an out-of-sample test that the rule passes without having been aimed at it. Every result is counting. No reaction rate, cross-section, or binding energy is computed or required, and Section X states precisely which quantities are therefore unavailable.The foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). 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This manuscript supplies the method. We give the operation converting a subdivided triad into a tetrahedron, and show it is edge identification rather than any spatial folding — a distinction that blocked the construction entirely until it was corrected. We derive the parity condition determining which subdivisions can close, and show that of the eight convex deltahedra only two have a face count that is a perfect square, giving exactly the two doubly magic nuclei A=4 and A=16. We derive the mass-number gaps at A=5 and A=8 by three independent routes each, and identify both as the first four-dimensional member of their respective polytope families. We give the regularity criterion, correcting an earlier and narrower triangularity criterion that does not survive inspection. We supply the composition rule — balancing nucleon count across a two-by-two grid of type against spin on both marginals — together with the three routes that failed before it, and report an out-of-sample test that the rule passes without having been aimed at it. Every result is counting. No reaction rate, cross-section, or binding energy is computed or required, and Section X states precisely which quantities are therefore unavailable.The foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). The author directed this process, evaluated and selected among proposed derivations, and takes full responsibility for the accuracy and originality of the final work."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.22848458","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":0,"created":"2026-09-19T18:02:01Z","registered":"2026-09-19T18:02:01Z","published":null,"updated":"2026-09-19T18:02:01Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.22848442","type":"dois","attributes":{"doi":"10.5281/zenodo.22848442","identifiers":[],"creators":[{"nameType":"Personal","affiliation":[{"affiliationIdentifier":"https://ror.org/02k3smh20","name":"University of Kentucky","affiliationIdentifierScheme":"ROR"}],"familyName":"Paul Rodgers","name":"Paul Rodgers","nameIdentifiers":[]}],"titles":[{"title":"Reconstruction from a Degraded Record: Six Substrates, One Scaling Law, and a Dispute Six Fields Have Independently"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-09-19","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.22848443","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 manuscript identifies six substrates — individual memory, species lineages, externalised records, immune memory, the first generation of stars, and prion populations — which share a four-part mechanical structure, and among which no pair, to our knowledge, cites another. We specify the four mechanisms as an explicit screen, and validate it by applying it to cases that should fail: thermal equilibrium scores zero of four, sheared amorphous matter scores an intermediate two and a half, and stem cells score three of four in a manner that identifies precisely which mechanism is missing. We then derive, from this framework’s own commitment that any render of a record is necessarily partial, a scaling law governing all six: the more degraded the record, the more the reconstruction is determined by the template rather than by the record. We show this law is independently confirmed in four of the six fields, under four different names, by researchers not addressing one another. We supply a birth term that a companion manuscript’s earlier treatment lacked, deriving it from Bennett’s history-tape result rather than from biology, and show that a standard macroevolutionary survivorship formula then applies to memory unchanged. Three results that did not hold are recorded in full, including one prediction that failed outright on simulation and one correspondence that was stated backwards relative to the data.The foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). The author directed this process, evaluated and selected among proposed derivations, and takes full responsibility for the accuracy and originality of the final work."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.22848442","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":0,"created":"2026-09-19T18:00:16Z","registered":"2026-09-19T18:00:17Z","published":null,"updated":"2026-09-19T18:00:17Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.22848443","type":"dois","attributes":{"doi":"10.5281/zenodo.22848443","identifiers":[{"identifier":"oai:zenodo.org:22848443","identifierType":"oai"}],"creators":[{"nameType":"Personal","affiliation":[{"affiliationIdentifier":"https://ror.org/02k3smh20","name":"University of Kentucky","affiliationIdentifierScheme":"ROR"}],"familyName":"Paul Rodgers","name":"Paul Rodgers","nameIdentifiers":[]}],"titles":[{"title":"Reconstruction from a Degraded Record: Six Substrates, One Scaling Law, and a Dispute Six Fields Have Independently"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-09-19","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.22848442","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 manuscript identifies six substrates — individual memory, species lineages, externalised records, immune memory, the first generation of stars, and prion populations — which share a four-part mechanical structure, and among which no pair, to our knowledge, cites another. We specify the four mechanisms as an explicit screen, and validate it by applying it to cases that should fail: thermal equilibrium scores zero of four, sheared amorphous matter scores an intermediate two and a half, and stem cells score three of four in a manner that identifies precisely which mechanism is missing. We then derive, from this framework’s own commitment that any render of a record is necessarily partial, a scaling law governing all six: the more degraded the record, the more the reconstruction is determined by the template rather than by the record. We show this law is independently confirmed in four of the six fields, under four different names, by researchers not addressing one another. We supply a birth term that a companion manuscript’s earlier treatment lacked, deriving it from Bennett’s history-tape result rather than from biology, and show that a standard macroevolutionary survivorship formula then applies to memory unchanged. Three results that did not hold are recorded in full, including one prediction that failed outright on simulation and one correspondence that was stated backwards relative to the data.The foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). The author directed this process, evaluated and selected among proposed derivations, and takes full responsibility for the accuracy and originality of the final work."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.22848443","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":"2026-09-19T18:00:16Z","registered":"2026-09-19T18:00:16Z","published":null,"updated":"2026-09-19T18:00:17Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.22848420","type":"dois","attributes":{"doi":"10.5281/zenodo.22848420","identifiers":[],"creators":[{"nameType":"Personal","affiliation":[{"affiliationIdentifier":"https://ror.org/02k3smh20","name":"University of Kentucky","affiliationIdentifierScheme":"ROR"}],"familyName":"Paul Rodgers","name":"Paul Rodgers","nameIdentifiers":[]}],"titles":[{"title":"The Four Families: A Two-Axis Partition of System States by Operation Type"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-09-19","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.22848421","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 manuscript proposes a classification of system states by which of two operations a system performs: changing what is currently readable, and changing the record itself. Each operation is either present or absent, giving four families, and the partition is exhaustive by construction. We show the four families correspond to four things ordinarily treated as unrelated kinds — a law, noise, a process, and a memory — and that the correspondence is not loose: a standing law is exactly an access-change with no accompanying write, which is why a law has no history and therefore cannot depend on what came before. We give a formal criterion distinguishing the two operations (a gate is an idempotent endomorphism; an accumulation is not), demonstrate that the criterion catches a misclassification the informal version admitted, and identify a substructure within the fourth family — whether the gate is set from outside the record or by the record itself — which we argue is the structural difference between an archive and a mind. We state precisely what the partition’s exhaustiveness rests on, namely a closure argument limiting the operation set to two, and we separate that dependency from the classification’s usefulness, which does not require it. A prior-art survey finds every component of the scheme published in some field and the two-axis sort across them not found.\n\nThe foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). The author directed this process, evaluated and selected among proposed derivations, and takes full responsibility for the accuracy and originality of the final work."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.22848420","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":0,"created":"2026-09-19T17:58:47Z","registered":"2026-09-19T17:58:48Z","published":null,"updated":"2026-09-19T17:58:48Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.22848421","type":"dois","attributes":{"doi":"10.5281/zenodo.22848421","identifiers":[{"identifier":"oai:zenodo.org:22848421","identifierType":"oai"}],"creators":[{"nameType":"Personal","affiliation":[{"affiliationIdentifier":"https://ror.org/02k3smh20","name":"University of Kentucky","affiliationIdentifierScheme":"ROR"}],"familyName":"Paul Rodgers","name":"Paul Rodgers","nameIdentifiers":[]}],"titles":[{"title":"The Four Families: A Two-Axis Partition of System States by Operation Type"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-09-19","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.22848420","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 manuscript proposes a classification of system states by which of two operations a system performs: changing what is currently readable, and changing the record itself. 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We state precisely what the partition’s exhaustiveness rests on, namely a closure argument limiting the operation set to two, and we separate that dependency from the classification’s usefulness, which does not require it. A prior-art survey finds every component of the scheme published in some field and the two-axis sort across them not found.\n\nThe foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). 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This manuscript addresses the physical significance of the polarity not selected. We identify the unselected chirality with antimatter via the Feynman-Stueckelberg interpretation, and show that the corrected form of the Genesis Operator upgrades this identification from a proposed correspondence to a structural consequence: time reversal in quantum mechanics is implemented by an antiunitary operator, which is to say one incorporating complex conjugation, and conjugation is precisely the operation χ performs. We develop the resulting bipolar time structure, state explicitly that this structure is independent of the rendered/unrendered partition with which it has previously been conflated, and bound what the bipolarity does and does not license.\n\nThe foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. 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We further show this same mechanism generalizes cleanly to a substrate-independent form of the identical principle observed in plant epigenetic memory.\n\nThe foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). 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We draw a precise distinction, already established in real philosophy of mind, between irreducibility and randomness, and identify the specific compatibilist question this framework’s account leaves genuinely open.\n\nThe foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). 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Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). 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This manuscript addresses that question directly. We model the origin of structure as a single, dimensionless node whose neutral state is shown to be dynamically unstable under the substrate’s own governing relations, and whose resolution proceeds via a mechanism structurally identical to spontaneous symmetry breaking in established field theory. We give the resolved output its correct group-theoretic form, showing that chirality must enter as an orientation reversal rather than as a sign factor, and that the resulting output space is O(2) rather than U(1). 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This manuscript addresses that question directly. We model the origin of structure as a single, dimensionless node whose neutral state is shown to be dynamically unstable under the substrate’s own governing relations, and whose resolution proceeds via a mechanism structurally identical to spontaneous symmetry breaking in established field theory. We give the resolved output its correct group-theoretic form, showing that chirality must enter as an orientation reversal rather than as a sign factor, and that the resulting output space is O(2) rather than U(1). The specific outcome of that resolution — a chosen chirality and phase — is shown to follow from a deterministic but chaotically sensitive process, admitting genuine variation across independent instantiations without requiring any element of true physical indeterminism.\n\nThe foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). The author directed this process, evaluated and selected among proposed derivations, and takes full responsibility for the accuracy and originality of the final work."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.22726807","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":2,"versionOfCount":0,"created":"2026-09-12T14:44:28Z","registered":"2026-09-12T14:44:28Z","published":null,"updated":"2026-09-19T17:50:17Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.22848311","type":"dois","attributes":{"doi":"10.5281/zenodo.22848311","identifiers":[{"identifier":"oai:zenodo.org:22848311","identifierType":"oai"}],"creators":[{"nameType":"Personal","affiliation":[{"affiliationIdentifier":"https://ror.org/02k3smh20","name":"University of Kentucky","affiliationIdentifierScheme":"ROR"}],"familyName":"Paul Rodgers","name":"Paul Rodgers","nameIdentifiers":[]}],"titles":[{"title":"The 2D Boundary: Lattice Formation, Dual Descriptions, Defects, and Global Geometry"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-09-19","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.22726853","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 manuscript provides a unified account of the two-dimensional boundary substrate underlying this framework. 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We derive the boundary’s coordination geometry from a wave-interference energy-minimization principle; establish explicitly that the substrate admits two dual descriptions — a honeycomb lattice and its triangular dual — and specify which structural results belong to which, correcting an earlier formulation that conflated them; show that the bipartite two-sublattice structure belongs to the honeycomb description specifically; characterize the local coordination defects the lattice admits; establish the boundary’s global shape as a flat, non-compact expanding disk, correcting an earlier closed-surface formulation; state the growth law and its cosmological consequence, correcting an earlier characterization of the nucleosynthesis conflict as a contradiction with observation rather than with the standard account; and identify Euler’s polyhedron relation as a single invariant governing the local coordination structure.\n\nThe foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. 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