{ "schemaVersion": "1.6", "slug": "three-copy-werner-undistillability", "title": "Three copies, the same distillation boundary", "shortTitle": "Three-copy qutrit Werner undistillability", "url": "https://evidencepress.org/releases/three-copy-werner-undistillability/", "oneLine": "An exact certificate supports the three-copy qutrit Werner threshold: distillation is possible precisely below α = −1/2.", "abstract": "This candidate establishes nonnegativity of the three-copy partial-transpose form for every complex 27 × 27 matrix of rank at most two at the boundary qutrit Werner state (2I − F)/15. A portable exact certificate checks 716 positive semidefinite multipliers and a 2,374-coordinate identity. A parameter argument gives three-copy distillability exactly for α < −1/2 in the physical Werner family. The claim is restricted to dimension three and three copies; the arbitrary-copy problem remains open.", "datePublished": "2026-10-04", "dateModified": "2026-10-04", "version": "1.1.0-candidate", "doi": "10.5281/zenodo.23134454", "doiUrl": "https://doi.org/10.5281/zenodo.23134454", "conceptDoi": "10.5281/zenodo.23134453", "pdfUrl": "https://github.com/ipitchford/three-copy-werner-undistillability/releases/download/v1.1.0-candidate/paper.pdf", "altPdfUrl": "https://zenodo.org/records/23134454/files/paper.pdf?download=1", "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/23134454", "repoUrl": "https://github.com/ipitchford/three-copy-werner-undistillability", "releaseUrl": "https://github.com/ipitchford/three-copy-werner-undistillability/releases/tag/v1.1.0-candidate", "markdownUrl": "https://evidencepress.org/releases/three-copy-werner-undistillability/index.md", "bibtexUrl": "https://evidencepress.org/releases/three-copy-werner-undistillability/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/three-copy-werner-undistillability.mp3?v=020b1a1da5", "imageUrl": "https://evidencepress.org/assets/og/three-copy-werner-undistillability.png?v=4cc394ab74", "coverArtUrl": "https://evidencepress.org/assets/art/three-copy-werner-undistillability.svg?v=bd05764cba", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/three-copy-werner-undistillability.mp3?v=020b1a1da5", "name": "Plain-English audio briefing", "description": "Communication aid; not additional research evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/three-copy-werner-undistillability.txt" } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Computer-assisted mathematical candidate with exact producer replay and a supplied alternative audit. No authenticated external specialist or editorial peer review; no proof-assistant formalisation." }, "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/23134454", "note": "All four assets checked against public provider checksums and full downloads from GitHub and Zenodo on 4 October 2026." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "passed", "note": "Fresh final-archive normal and optimized Python replays, all 716 multipliers and 2,374 equations, semantic corruption controls, 716 supplied congruence checks, and hosted CI at 66cd2f931abb1a2f24e18e1b86e280401be9a5e8 passed. Producer checking only." }, { "dimension": "independentRerun", "label": "Independent rerun", "question": "Has someone else run the supplied implementation and obtained the stated result?", "state": "not-assessed", "note": "The supplied audit retains author coordinate and foundation logic; unaffiliated reproduction is not authenticated." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "Alternative exact arithmetic checks and congruence witnesses are disclosed; a wholly independent implementation is not established." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "No end-to-end proof-assistant verification." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "The supplied report has no authenticated human specialist identity or institution." }, { "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 editorial acceptance is established." }, { "dimension": "dataEnvironmentReproducibility", "label": "Data and environment reproducibility", "question": "Are data and computational environment pinned well enough to rebuild?", "state": "partial", "note": "Pinned Python dependencies passed on local macOS and hosted Linux in both Python modes. Unaffiliated reproduction is not established; optional historical construction claims are excluded." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "Codex mathematical construction and exact verification", "Supplied referee report and alternative arithmetic audit; authorship unauthenticated", "Codex scoped revision and publication" ], "humanRole": "Publication authorised by the user; no human scientific contribution inferred.", "disclosure": "Anonymous is the scholarly creator and Evidence Press the publisher. Supplied review and producer checking are not authenticated external peer review." }, "attributionBoundary": null, "problem": { "name": "Can three copies distil entanglement from the boundary qutrit Werner state?", "url": "https://doi.org/10.1007/s11005-025-01935-y" }, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "canonical-theorem", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "Original exact package revised against the supplied report of 4 October 2026. All 719 mathematical data files are unchanged. Report authorship and human specialist credentials are not authenticated.", "grandfatheredAtSchemaVersion": null, "keywords": [ "Werner states", "quantum entanglement", "distillability", "qutrits", "three copies", "exact semidefinite certificate" ], "keyResults": [ "Nonnegative three-copy form for every complex rank-at-most-two 27 × 27 coefficient matrix at the qutrit boundary.", "Three-copy distillability exactly for α < −1/2 throughout the physical qutrit Werner parameter range.", "Portable exact certificate; no normality, Hermitian or common-plane support restriction." ], "reviews": [], "evidencePackage": "716 exact Gram multipliers, 2,374 zero residual coordinates, fresh normal and optimized Python replays, semantic corruption controls and exact rechecking of 716 supplied congruence witnesses.", "openProblems": [], "mathObjects": [], "relatedWorks": [ { "citation": "Costa Rico (2025). Partial-trace formulations of Werner-state distillability; an inherited reduction used in the manuscript.", "url": "https://doi.org/10.1007/s11005-025-01935-y", "doi": "10.1007/s11005-025-01935-y" }, { "citation": "Fu, Gao and Park (2026), arXiv:2607.21367v2. A two-copy result; its copy quantifier differs from this three-copy certificate.", "url": "https://arxiv.org/abs/2607.21367v2", "doi": "10.48550/arXiv.2607.21367" }, { "citation": "Fraser, Huber, Pozsgay and Vona (2026), arXiv:2607.24309v1. Concurrent two-copy partial-trace inequalities.", "url": "https://arxiv.org/abs/2607.24309v1", "doi": "10.48550/arXiv.2607.24309" }, { "citation": "Bharti, Gajjala and Haug (2026), arXiv:2607.24479v1. Two-copy analysis and restricted marginal results; no general three-copy induction.", "url": "https://arxiv.org/abs/2607.24479v1", "doi": "10.48550/arXiv.2607.24479" }, { "citation": "Wu and Zou (2026), arXiv:2608.02647v1. Normal and common-plane three-copy sectors and crossed-Gram formulations.", "url": "https://arxiv.org/abs/2608.02647v1", "doi": "10.48550/arXiv.2608.02647" }, { "citation": "Vianna and Doherty (2006), quant-ph/0608095. Semidefinite optimisation as an antecedent method for distillability.", "url": "https://arxiv.org/abs/quant-ph/0608095", "doi": null } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:three-copy-werner-undistillability", "attemptIds": [ "ep-attempt:three-copy-werner-undistillability-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "evidence-assessment" ], "lineageId": null, "accelerationPrimitives": [ "certificate-first", "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "decisionObject": { "type": "certificate", "description": "Exact nonnegativity of the boundary three-copy qutrit rank-two form.", "scope": "Every complex 27 × 27 matrix of rank at most two; dimension three and three copies only." }, "bottleneckTargeted": [ "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "The paper maps the physical partial-transpose distillation test to partial traces, rank-two coordinates and an exact PSD dual identity.", "remainingRisks": [ "The written encoding and representation arguments are not proof-assistant formalised.", "All-copy and higher-dimensional cases are outside scope.", "Bounded literature checking does not establish priority." ] }, "humanJudgmentGates": [ "User authorised publication; no human research or referee role inferred.", "Qualified specialists can assess the physical encoding and representation-theoretic proof chain." ], "parentLinks": [ { "relation": "reuses-evidence", "workId": null, "legacyReleaseSlug": null, "externalUrl": "https://doi.org/10.1007/s11005-025-01935-y", "inheritedClaim": "Partial-trace formulation of the Werner-state distillation criterion.", "inheritedAssuranceCeiling": "Published methodological antecedent; not validation of this certificate." } ], "assuranceTarget": { "dimensions": [ "independentRerun", "independentReimplementation", "formalVerification", "specialistReview", "noveltyAssessment", "priorityAssessment" ], "nextAction": "Unaffiliated replay and specialist checking of the physical-to-algebraic bridge and exact module basis.", "claimCeiling": "Computer-assisted candidate with exact producer replay; no authenticated peer review." }, "impactClaims": [ { "id": "three-copy-werner-undistillability-no-impact", "aim": "science", "outcome": "An exact three-copy qutrit threshold and reusable certificate", "setting": "AI-assisted mathematical research and publication", "status": "NO_IMPACT_EVIDENCE", "designClass": "none", "comparator": "No matched-assurance research or workflow comparator is registered.", "estimand": "No discovery-speed, publication-speed, scientific-adoption or real-world impact effect is 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:three-copy-werner-undistillability-publication", "status": "result-ready", "resultClass": "positive", "metrics": { "schemaVersion": "1.0", "measurementScope": "assurance-through-publication", "scopeBoundary": "Revision and publication from this registration; prior discovery and initial source reading are excluded.", "forecast": { "frozenAt": "2026-10-04T09:18:42.929Z", "procedureClass": "referee-revision-and-full-publication", "targetOutcome": "Exact-version public research archive and canonical Evidence Press release with standard media.", "expectedActiveMinutes": 150, "plausibleLowMinutes": 120, "plausibleHighMinutes": 210, "expectedUnattendedWaitMinutes": 30, "referenceClass": { "label": "Full candidate publication with an existing exact certificate", "sampleSize": 0, "basis": "Prospective route estimate, not an empirical speed claim." }, "fermiComponents": [ { "component": "Revision, literature comparison, replay and paper QA", "count": 1, "lowMinutesPerUnit": 45, "centralMinutesPerUnit": 60, "highMinutesPerUnit": 90, "basis": "Core certificate already exists; comments are bounded." }, { "component": "Archival publication, standard media and two site deployment cycles", "count": 1, "lowMinutesPerUnit": 75, "centralMinutesPerUnit": 90, "highMinutesPerUnit": 120, "basis": "Required public identities and guarded new-slug workflow." } ], "probabilityPositiveSignal": 0.9, "probabilityTargetClosure": 0.9, "probabilityHorizonMinutes": 300, "assumptions": [ "Supplied principal proof chains need no redesign.", "Required providers remain accessible." ], "reforecastTriggers": [ "A replay failure or an integrity defect in the frozen archive.", "Provider outage, credential expiry or integrity failure." ], "stopRule": "Timing is telemetry, not a cap; continue unless integrity, rights or provider access blocks publication." }, "outcome": null }, "missingnessReason": null } ] } }