{ "schemaVersion": "1.6", "slug": "free-fermion-frustration-graphs", "title": "Which frustration graphs give free fermions?", "shortTitle": "When interacting spins have a free spectrum", "url": "https://evidencepress.org/releases/free-fermion-frustration-graphs/", "oneLine": "A graph criterion characterises whole-spectrum freeness at every coupling under faithful Pauli realisation; exact sector certificates reveal a larger, carefully distinguished class.", "abstract": "This unrefereed mathematical-physics candidate proves a converse to the even-hole, claw-free theorem for faithful Pauli realisations. Outside that graph class, whole-spectrum free couplings form a proper algebraic exceptional set. It also gives exact four-block formulas for periodic Fendley chains of lengths eight and nine, a central-coefficient certification criterion, and heredity of a weaker prescribed-mode property. A revised trace-projector argument proves parity-pattern completeness for a three-mode subclass. Exact checks cover 107 graphs; another 1,621 examples remain numerical candidates. The work does not provide a general sector classification or new fermionic ladder operators.", "datePublished": "2026-09-27", "dateModified": "2026-09-27", "version": "1.0.0-candidate", "doi": "10.5281/zenodo.22994980", "doiUrl": "https://doi.org/10.5281/zenodo.22994980", "conceptDoi": "10.5281/zenodo.22994979", "pdfUrl": "https://github.com/ipitchford/free-fermion-frustration-graphs/releases/download/v1.0.0-candidate/free_fermion_frustration_graphs.pdf", "altPdfUrl": "https://zenodo.org/records/22994980/files/free_fermion_frustration_graphs.pdf?download=1", "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/22994980", "repoUrl": "https://github.com/ipitchford/free-fermion-frustration-graphs", "releaseUrl": "https://github.com/ipitchford/free-fermion-frustration-graphs/releases/tag/v1.0.0-candidate", "markdownUrl": "https://evidencepress.org/releases/free-fermion-frustration-graphs/index.md", "bibtexUrl": "https://evidencepress.org/releases/free-fermion-frustration-graphs/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/free-fermion-frustration-graphs.mp3?v=d37798706a", "imageUrl": "https://evidencepress.org/assets/og/free-fermion-frustration-graphs.png?v=a4004d64f6", "coverArtUrl": "https://evidencepress.org/assets/art/free-fermion-frustration-graphs.svg?v=63f32f6717", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/free-fermion-frustration-graphs.mp3", "name": "Plain-English audio briefing", "description": "OpenAI synthetic voice; communication only.", "transcriptUrl": "https://evidencepress.org/assets/audio/free-fermion-frustration-graphs.txt" } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Unrefereed candidate with producer-coordinated model review and local checks. The separately implemented exact checker passed all 107 graphs. The slower original FLINT route was partially replayed, not completed. Numerical rechecks cover 1,728 positives, 1,201 negatives and 64 additional samples. No formal proof, unaffiliated reproduction, external peer review or exhaustive novelty clearance is claimed." }, "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/22994980", "note": "All six assets downloaded from GitHub and Zenodo and SHA-256 matched against the final local release. Availability is not mathematical validation." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "passed", "note": "All 107 graphs passed the separately implemented exact route; partial original FLINT replay is labelled separately. Hardened numerical selections and rejection controls passed." }, { "dimension": "independentRerun", "label": "Independent rerun", "question": "Has someone else run the supplied implementation and obtained the stated result?", "state": "not-assessed", "note": "No unaffiliated rerun is evidenced; coordinated agents and supplied replay records do not establish independence." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "A separately implemented review checker was replayed, but coordinated model-based work is not evidence of unaffiliated reproduction." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "No proof-assistant verification of the analytic claims." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "The supplied favourable review is retained as a document, not an authenticated external specialist endorsement." }, { "dimension": "editorialPeerReview", "label": "Editorial peer review", "question": "Has a journal or venue run peer review to a decision?", "state": "not-assessed", "note": "No journal or external venue peer review is claimed." }, { "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/free-fermion-frustration-graphs/actions/runs/36312894887", "note": "Linux CI passed normal and optimized default replay at tagged commit28ca7d4b75a3fb8cc5c8c7b959c566d907f64377. Local clean-extraction replay also passed. Original FLINT is partial63/107; full graph catalogue not regenerated; PDF build not hermetic." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "AI-assisted mathematical research and manuscript preparation; exact originating model identities are not asserted", "Producer-side Python exact, symbolic and numerical checks", "Codex publication intake and authoring" ], "humanRole": "Publication authority and supplied materials only; no human scientific contribution is inferred. Scholarly creator remains Anonymous.", "disclosure": "Received reviews, internal replay and publication checks are producer-coordinated evidence, not authenticated external review or independent reproduction." }, "attributionBoundary": null, "problem": { "name": "Whole-spectrum and sector-wise free-fermion spectra", "url": "https://arxiv.org/abs/2012.07857v2" }, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "canonical-theorem", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "Supplied v3 draft and model-review audit were checked at intake. The public edition repairs the auxiliary completeness argument, corrects the literature boundary, hardens the numerical checks and preserves historical data. Publication availability is assessed separately from mathematical validity. Published GitHub v1.0.0-candidate and Zenodo22994980 have six fully downloaded, hash-matched assets, checked27September2026.", "grandfatheredAtSchemaVersion": null, "keywords": [ "free fermions", "frustration graphs", "quantum spin chains", "graph Clifford algebra", "even-hole claw-free graphs", "spectral multiplicity", "exact certificates", "Fendley chain" ], "keyResults": [ "Faithful Pauli whole-spectrum freeness for every independent real coupling is equivalent to the graph being even-hole- and claw-free.", "Outside that class, whole-spectrum free couplings form a proper real algebraic exceptional set.", "Four explicit invariant free blocks at all couplings for periodic Fendley lengths 8 and 9; merged coefficient sectors need not be free at exceptional couplings.", "Weak prescribed-mode heredity and a three-mode parity-completeness proposition; strict Z-heredity remains open.", "107 exact graph certificates; 1,621 further sampled-coupling candidates are not exact classifications." ], "reviews": [], "evidencePackage": "Written mathematical arguments, two exact implementations, 107 graph identities spanning 792 coefficient-label classes and 1,404 central characters, numerical replays and rejection controls, physical-spin checks, source comparisons and a point-by-point review response.", "openProblems": [], "mathObjects": [], "relatedWorks": [ { "citation": "Elman, Chapman and Flammia (2021), Free fermions behind the disguise: even-hole, claw-free sufficiency, the baseline for the faithful converse.", "url": "https://doi.org/10.1007/s00220-021-04220-w", "doi": "10.1007/s00220-021-04220-w" }, { "citation": "Chapman, Elman and Mann (2023), A unified graph-theoretic framework for free-fermion solvability, v1: symmetry-sector ladder operators; identification with the present coefficient sectors requires an explicit bridge.", "url": "https://arxiv.org/abs/2305.15625v1", "doi": "10.48550/arXiv.2305.15625" }, { "citation": "Ruh and Elman (2026), Expanding the class of free fermions via twin-collapse methods: reductions and Proposition 14 on induced-subgraph heredity.", "url": "https://doi.org/10.1103/svfv-vdh5", "doi": "10.1103/svfv-vdh5" }, { "citation": "Zheng, Pozsgay and Chen (2026), Exact solutions of hidden free fermion models, v1: arbitrary-length periodic transfer relations, not superseded by the present two-length formulas.", "url": "https://arxiv.org/abs/2609.14134v1", "doi": "10.48550/arXiv.2609.14134" }, { "citation": "Fukai, Vona and Pozsgay (2026), A free fermions in disguise model with claws: constrained physical families illustrate why faithfulness and independent couplings matter.", "url": "https://doi.org/10.21468/SciPostPhys.21.1.011", "doi": "10.21468/SciPostPhys.21.1.011" }, { "citation": "Fendley and Pozsgay (2024), Free fermions beyond Jordan and Wigner: transfer-polynomial support and the separate question of spectral occupation.", "url": "https://doi.org/10.21468/SciPostPhys.16.4.102", "doi": "10.21468/SciPostPhys.16.4.102" } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:free-fermion-frustration-graphs", "attemptIds": [ "ep-attempt:free-fermion-frustration-graphs-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "evidence-assessment" ], "lineageId": null, "accelerationPrimitives": [ "structural-compression", "certificate-first", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "decisionObject": { "type": "certificate", "description": "Faithful whole-spectrum graph classification and bounded exact sector certificates.", "scope": "Independent real couplings; faithful Pauli realisations; fixed-block conclusions separated from merged coefficient sectors." }, "bottleneckTargeted": [ "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "Graph Clifford relations encode the faithful Pauli Hamiltonian. Characteristic identities establish complete energy multisets, rather than merely spectral support.", "remainingRisks": [ "Universal proofs are not formalised.", "The 1,621 uncertified candidates are supported only at sampled couplings.", "Special-coupling merged sectors can fail power-of-two replication." ] }, "humanJudgmentGates": [ "Publication authorisation only; no human scientific contribution or additional review stage is inferred." ], "parentLinks": [ { "relation": "depends-on-claim", "workId": null, "legacyReleaseSlug": null, "externalUrl": "https://arxiv.org/abs/2012.07857v2", "inheritedClaim": "Even-hole, claw-free sufficiency for free spectra.", "inheritedAssuranceCeiling": "Imported published mathematical result; not independently reproved here." } ], "assuranceTarget": { "dimensions": [ "independentRerun", "formalVerification", "specialistReview", "semanticValidation", "noveltyAssessment", "priorityAssessment" ], "nextAction": "Unaffiliated reconstruction of the faithful converse and parity-completeness proof, followed by independent certificate replay.", "claimCeiling": "Unrefereed proof candidate with exact and numerical producer checks." }, "impactClaims": [ { "id": "free-fermion-frustration-graphs-no-impact", "aim": "science", "outcome": "Inspectable spectral classification and exact examples", "setting": "Producer-coordinated publication", "status": "NO_IMPACT_EVIDENCE", "designClass": "none", "comparator": "No matched comparator.", "estimand": "No impact effect estimated.", "evidenceRefs": [], "registeredDesignRef": null, "independentAssessment": null } ] }, "researchMetrics": { "schemaVersion": "1.0", "policyUrl": "https://evidencepress.org/api/research-metrics-policy.json", "workLedgerUrl": "https://evidencepress.org/api/work-ledger.json", "claimCeiling": "These records describe scoped workflow inputs and outcomes. They support calibration and reference-class construction, but do not by themselves establish research acceleration, theorem correctness, novelty, independent assurance or impact.", "attempts": [ { "attemptId": "ep-attempt:free-fermion-frustration-graphs-publication", "status": "active", "resultClass": "pending", "metrics": { "schemaVersion": "1.0", "measurementScope": "assurance-through-publication", "scopeBoundary": "Only work after this registration is measured. Earlier research, supplied reviews, intake and initial targeted checking are left-censored. No comparative acceleration or discovery-time claim.", "forecast": { "frozenAt": "2026-09-27T10:09:07.917Z", "procedureClass": "review-repair-and-full-candidate-publication", "targetOutcome": "Revised unrefereed candidate, exact replay and scoped numerical controls, identical public archives, conforming page and media with canonical readback.", "expectedActiveMinutes": 70, "plausibleLowMinutes": 50, "plausibleHighMinutes": 110, "expectedUnattendedWaitMinutes": 20, "referenceClass": { "label": "Remaining-task decomposition", "sampleSize": 0, "basis": "Prospective judgment, not an empirical timing benchmark; private workflow forecast was made earlier and retained unchanged." }, "fermiComponents": [ { "component": "Revision and scoped proof checks", "count": 1, "lowMinutesPerUnit": 20, "centralMinutesPerUnit": 30, "highMinutesPerUnit": 50, "basis": "Remaining authorised work; elapsed execution and unattended waits recorded separately." }, { "component": "Archive, GitHub and Zenodo", "count": 1, "lowMinutesPerUnit": 10, "centralMinutesPerUnit": 15, "highMinutesPerUnit": 20, "basis": "Remaining authorised work; elapsed execution and unattended waits recorded separately." }, { "component": "Page and informative media", "count": 1, "lowMinutesPerUnit": 12, "centralMinutesPerUnit": 15, "highMinutesPerUnit": 22, "basis": "Remaining authorised work; elapsed execution and unattended waits recorded separately." }, { "component": "Deploy and canonical readback", "count": 1, "lowMinutesPerUnit": 8, "centralMinutesPerUnit": 10, "highMinutesPerUnit": 18, "basis": "Remaining authorised work; elapsed execution and unattended waits recorded separately." } ], "probabilityPositiveSignal": 0.85, "probabilityTargetClosure": 0.8, "probabilityHorizonMinutes": 120, "assumptions": [ "No fatal proof, integrity or rights defect is found in the affected final checks.", "The authorised providers remain accessible, and existing automation can publish the final candidate assets.", "All claimed assurance remains unrefereed and producer-side unless separately evidenced." ], "reforecastTriggers": [ "A provider or credential failure blocks the relevant publication path.", "A load-bearing defect requires substantive repair beyond packaging.", "Final asset identity or deployment readback fails." ], "stopRule": "A forecast is not a cap. Continue mandatory publication work after an overrun; stop propagation for a fatal integrity or rights defect, and record real provider blocks without claiming completion." }, "outcome": null }, "missingnessReason": null } ] } }