{ "schemaVersion": "1.6", "slug": "primitive-su-primitivity", "title": "Primitivity of the SU(2n)₂ₙ superconducting series", "shortTitle": "Two obstructions to splitting a superconductor", "url": "https://evidencepress.org/releases/primitive-su-primitivity/", "oneLine": "A uniform written proof excludes two ways of separating an existing family of topological superconductors into simpler factors.", "abstract": "For every even N≥4, the neutral resolved rank in the charge-one SU(N)_N construction exceeds every nonzero-sector rank by at least N/2, and each nonzero sector contains an electron-exchanged pair. Lemma 4 turns these facts into the two obstructions to the permitted electron-compatible invertible-vortex factors, including Abelian dressing. The proof uses established cyclic-resolution and charge-counting machinery; it is not a new physical construction or experimental demonstration.", "datePublished": "2026-10-11", "dateModified": "2026-10-11", "version": "1.1.0-candidate", "doi": "10.5281/zenodo.23299598", "doiUrl": "https://doi.org/10.5281/zenodo.23299598", "conceptDoi": "10.5281/zenodo.23299597", "pdfUrl": "https://zenodo.org/records/23299598/files/primitive-su-primitivity-v1.1.0-candidate.pdf", "altPdfUrl": "https://github.com/ipitchford/primitive-su-primitivity/releases/download/v1.1.0-candidate/primitive-su-primitivity-v1.1.0-candidate.pdf", "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/23299598", "repoUrl": "https://github.com/ipitchford/primitive-su-primitivity", "releaseUrl": "https://github.com/ipitchford/primitive-su-primitivity/releases/tag/v1.1.0-candidate", "markdownUrl": "https://evidencepress.org/releases/primitive-su-primitivity/index.md", "bibtexUrl": "https://evidencepress.org/releases/primitive-su-primitivity/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/primitive-su-primitivity.mp3", "imageUrl": "https://evidencepress.org/assets/og/primitive-su-primitivity.png?v=4386b22df1", "coverArtUrl": "https://evidencepress.org/assets/art/primitive-su-primitivity.svg?v=73501d418a", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/primitive-su-primitivity.mp3", "name": "Audio briefing — Two obstructions to splitting a superconductor", "description": "Synthetic explanation, not additional scientific evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/primitive-su-primitivity.txt" } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Unrefereed written-proof candidate with fresh internal finite-code checks. No formal verification, unaffiliated reproduction, external peer review, microscopic realisation or experimental validation is established." }, "assurance": [ { "dimension": "availability", "label": "Availability and archiving", "question": "Is the evidence package publicly retrievable from an archive under a persistent identifier?", "state": "passed", "evidenceUrl": "https://zenodo.org/records/23299598", "note": "The immutable research archive and release assets were confirmed public and byte-identical; availability does not establish correctness." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "passed", "note": "Seven explicit tests passed in normal and optimized Python; direct H-enumeration, an independently implemented dynamic programme, exact rank checks through N=100 and five semantic negative controls passed. These coordinated internal checks do not prove the universal categorical argument.", "evidenceUrl": "https://github.com/ipitchford/primitive-su-primitivity/blob/v1.1.0-candidate/REPLAY_RECEIPT.md" }, { "dimension": "independentRerun", "label": "Independent rerun", "question": "Has someone else run the supplied implementation and obtained the stated result?", "state": "not-assessed", "note": "This assurance dimension is not established by the coordinated internal checks or reserved DOI identity." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "This assurance dimension is not established by the coordinated internal checks or reserved DOI identity." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "This assurance dimension is not established by the coordinated internal checks or reserved DOI identity." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "This assurance dimension is not established by the coordinated internal checks or reserved DOI identity." }, { "dimension": "editorialPeerReview", "label": "Editorial peer review", "question": "Has a journal or venue run peer review to a decision?", "state": "not-assessed", "note": "This assurance dimension is not established by the coordinated internal checks or reserved DOI identity." }, { "dimension": "dataEnvironmentReproducibility", "label": "Data and environment reproducibility", "question": "Are data and computational environment pinned well enough to rebuild?", "state": "partial", "evidenceUrl": "https://github.com/ipitchford/primitive-su-primitivity/blob/v1.1.0-candidate/ENVIRONMENT.txt", "note": "Standard-library code, retained inputs, exact outputs and environment details support replay; no unaffiliated reproduction is established." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "OpenAI Codex: review action, internal checking and publication preparation" ], "humanRole": "Publication authority only; no human research contribution asserted.", "reviewStatus": "Unrefereed written-proof candidate with fresh internal finite-code checks. No formal verification, unaffiliated reproduction, external peer review, microscopic realisation or experimental validation is established." }, "attributionBoundary": null, "problem": { "name": "Uniform primitivity of the even-rank equal-level superconducting family", "url": "https://arxiv.org/abs/2610.10679v1" }, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "canonical-theorem", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "Supplied research and review, revised attribution and categorical bridge, exact finite internal checks. No historical research clocks reconstructed.", "grandfatheredAtSchemaVersion": null, "keywords": [ "topological superconductivity", "SU(N)_N", "primitivity", "simple currents", "cyclic stabilizers", "Ramanujan sums" ], "keyResults": [ "Neutral-sector rank exceeds every nonzero-sector rank by at least N/2 for every even N≥4.", "Lemma 4 combines rank mismatch and an electron-moved object to exclude both permitted vortex factors, including Abelian dressing.", "The N=2 boundary passes the rank test but fails the pair test: both obstructions are necessary." ], "reviews": [], "evidencePackage": "Universal written argument; seven finite tests passed in normal and optimized Python, with direct H-enumeration through N=10, independent dynamic-programme and rank checks through N=100, and five semantic negative controls.", "openProblems": [], "mathObjects": [], "relatedWorks": [ { "citation": "Gao et al. (2026), SC♯: Superconductivity intertwined with topological order, v1, §§IV.5 and VII.4: construction, definition and proposed all-parameter primitivity.", "url": "https://arxiv.org/abs/2610.10679v1", "doi": "10.48550/arXiv.2610.10679" }, { "citation": "Gao, Wang, Yang and Wu (2026), Topological charge-2ne superconductors, v4: the originating family and corrected fixed-point convention.", "url": "https://arxiv.org/abs/2512.21325v4", "doi": "10.48550/arXiv.2512.21325" }, { "citation": "Elashvili, Jibladze and Pataraia (1999), Combinatorics of necklaces and Hermite reciprocity: exact charge-counting predecessors.", "url": "https://rmi.tsu.ge/~jib/pubs/elajipa.pdf", "doi": null }, { "citation": "Fuchs, Runkel and Schweigert (2004), TFT construction of RCFT correlators III: Simple currents, Lemma 4.6 and Proposition 4.7.", "url": "https://arxiv.org/abs/hep-th/0403157", "doi": null }, { "citation": "Closset, Furrer and Khlaif (2025), One-form symmetries and the 3d N=2 A-model: related quotient-counting machinery, not an identified fine-sector primitivity proof.", "url": "https://arxiv.org/abs/2405.18141v4", "doi": "10.48550/arXiv.2405.18141" } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:primitive-su-primitivity", "attemptIds": [ "ep-attempt:primitive-su-primitivity-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "evidence-assessment", "communication" ], "lineageId": null, "accelerationPrimitives": [ "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "decisionObject": { "type": "obstruction", "description": "Exclude both prescribed electron-compatible vortex factors in every nonzero flux sector.", "scope": "Charge-one SU(N)_N construction, even N≥4, retained physical electron and full flux grading." }, "bottleneckTargeted": [ "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "Induction identifies the charge-preserving resolved object sets with all even-subgroup modules; object count and electron action supply separate obstructions.", "remainingRisks": [ "Written categorical argument is not formally verified.", "Finite rank checks cannot certify the physical interpretation.", "No microscopic realisation or experimental validation." ] }, "humanJudgmentGates": [ "External mathematical-physics scrutiny of the stated construction and factorisation convention remains open." ], "parentLinks": [], "assuranceTarget": { "dimensions": [ "independentRerun", "specialistReview" ], "nextAction": "Audit the categorical bridge and reproduce the exact diagnostics outside the producer workflow.", "claimCeiling": "Unrefereed written-proof candidate with fresh internal finite-code checks. 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