{
  "schemaVersion": "1.6",
  "slug": "szollosi-mub-exclusion",
  "title": "One continuous route to four quantum bases is ruled out",
  "shortTitle": "Szöllősi-family MUB exclusion",
  "url": "https://evidencepress.org/releases/szollosi-mub-exclusion/",
  "oneLine": "A certificate-backed candidate excludes a whole two-parameter family, including its boundary, without claiming to settle the six-dimensional problem.",
  "abstract": "The candidate excludes MUB quadruplets containing the standard basis and a member of the closed two-circulant Szöllősi family in complex dimension six. An untrusted hull generator is separated from an interval-arithmetic and graph checker. Canonical half-open parameter ownership handles boundary cells, and content-bound clean replay prevents stale receipts from certifying changed inputs. The Fourier-family result re-proves an existing theorem. The unrestricted three-basis maximum remains conditional on a separate conjecture.",
  "datePublished": "2026-09-30",
  "dateModified": "2026-09-30",
  "version": "3.0-candidate",
  "doi": "10.5281/zenodo.23051062",
  "doiUrl": "https://doi.org/10.5281/zenodo.23051062",
  "conceptDoi": "10.5281/zenodo.23051061",
  "pdfUrl": "https://github.com/ipitchford/szollosi-mub-exclusion/releases/download/v3.0-candidate/paper.pdf",
  "altPdfUrl": "https://zenodo.org/records/23051062/files/paper.pdf?download=1",
  "altPdfLabel": null,
  "zenodoUrl": "https://zenodo.org/records/23051062",
  "repoUrl": "https://github.com/ipitchford/szollosi-mub-exclusion",
  "releaseUrl": "https://github.com/ipitchford/szollosi-mub-exclusion/releases/tag/v3.0-candidate",
  "markdownUrl": "https://evidencepress.org/releases/szollosi-mub-exclusion/index.md",
  "bibtexUrl": "https://evidencepress.org/releases/szollosi-mub-exclusion/cite.bib",
  "audioUrl": "https://evidencepress.org/assets/audio/szollosi-mub-exclusion.mp3",
  "imageUrl": "https://evidencepress.org/assets/og/szollosi-mub-exclusion.png?v=0ac26fb304",
  "coverArtUrl": "https://evidencepress.org/assets/art/szollosi-mub-exclusion.svg?v=46d9063b9e",
  "media": [
    {
      "type": "audio",
      "url": "https://evidencepress.org/assets/audio/szollosi-mub-exclusion.mp3",
      "name": "Plain-English audio briefing",
      "description": "Synthetic explanation, not additional scientific evidence.",
      "transcriptUrl": "https://evidencepress.org/assets/audio/szollosi-mub-exclusion.txt"
    }
  ],
  "authors": [
    "Anonymous"
  ],
  "license": "CC0-1.0",
  "status": "unrefereed-candidate",
  "verification": {
    "peerReviewed": false,
    "independentlyReproduced": false,
    "formallyVerified": false,
    "internallyReplayed": true,
    "detail": "Unrefereed candidate with complete fresh local replay. Not end-to-end formally verified or externally peer reviewed. The full dimension-six MUB problem remains open."
  },
  "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/23051062",
      "note": "All six public GitHub and Zenodo assets fully downloaded and hash-matched to the frozen local inventory."
    },
    {
      "dimension": "internalReplay",
      "label": "Internal replay",
      "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?",
      "state": "passed",
      "note": "Both complete covers passed fresh local replay: 14,658 Szollosi and 1,935 Fourier boxes, with 75 boundary parents subdivided afresh.",
      "evidenceUrl": "https://github.com/ipitchford/szollosi-mub-exclusion/blob/v3.0-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": "No unaffiliated complete replay established."
    },
    {
      "dimension": "independentReimplementation",
      "label": "Independent reimplementation",
      "question": "Has someone else reached the result from an independent implementation?",
      "state": "not-assessed",
      "note": "Generator/checker implementation separation is not unaffiliated reproduction."
    },
    {
      "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": "Supplied review preserved; external identity and independence not authenticated."
    },
    {
      "dimension": "editorialPeerReview",
      "label": "Editorial peer review",
      "question": "Has a journal or venue run peer review to a decision?",
      "state": "not-assessed",
      "note": "No external editorial peer review."
    },
    {
      "dimension": "dataEnvironmentReproducibility",
      "label": "Data and environment reproducibility",
      "question": "Are data and computational environment pinned well enough to rebuild?",
      "state": "partial",
      "note": "Full content-bound local replay, fresh-extraction tests and pinned Linux CI passed. Linux CI does not rerun the full phase-space computation. Compiler/hardware and written semantic bridge remain trusted.",
      "evidenceUrl": "https://github.com/ipitchford/szollosi-mub-exclusion/actions/runs/36679180874"
    }
  ],
  "provenance": {
    "aiGenerated": true,
    "aiAssisted": true,
    "generatedBy": [
      "Supplied AI-assisted research and review; source identities are repository-reported, not authenticated",
      "Codex revision and publication checks"
    ],
    "humanRole": "Publication authorisation and supplied materials only; no human scientific contribution is inferred. Scholarly creator Anonymous.",
    "disclosure": "Producer-coordinated checking is not unaffiliated reproduction or external peer review."
  },
  "attributionBoundary": null,
  "problem": {
    "name": "MMVW Conjecture 3: Szöllősi-family MUB quadruplet exclusion",
    "url": "https://doi.org/10.1007/s10801-026-01506-x"
  },
  "orderedProductAverage": null,
  "corrections": [],
  "publicCorrections": [],
  "publicCorrectionIndexes": null,
  "pageStructureVersion": "2.0",
  "pageStructureVariant": "canonical-theorem",
  "pageStructureWaivers": [],
  "recordMaturity": "current",
  "metadataProvenance": "Supplied v2 manuscript and 30 September reviewer audit. Revision 3 repairs ownership, receipt binding and unsupported assurance. Complete fresh producer-side replay is retained in the versioned package.",
  "grandfatheredAtSchemaVersion": null,
  "keywords": [
    "mutually unbiased bases",
    "complex Hadamard matrices",
    "dimension six",
    "Szöllősi family",
    "interval arithmetic",
    "computer-assisted proof"
  ],
  "keyResults": [
    "Exclusion for the entire specified closed two-circulant Szöllősi family, including degenerate parameters.",
    "Hull coverage and graph obstruction avoid requiring an exact isolated-root count.",
    "Fourier exclusion is a checked re-proof of prior work.",
    "The unrestricted dimension-six maximum remains conditional on MMVW Conjecture 2."
  ],
  "reviews": [],
  "evidencePackage": "Fresh interval/graph replay of 14,658 Szöllősi and 1,935 Fourier boxes, including 75 boundary subdivisions; exact symmetry identities; boundary and stale-cache regressions.",
  "openProblems": [
    "MMVW Conjecture 2 remains unproved here.",
    "Larger algebraic families need explicit encodings, capacity checks and branch coverage."
  ],
  "mathObjects": [],
  "relatedWorks": [
    {
      "citation": "Matolcsi, Matszangosz, Varga and Weiner (2026), Triplets of mutually unbiased bases: Conjecture 3 and the conditional reduction in Proposition 4.2.",
      "url": "https://doi.org/10.1007/s10801-026-01506-x",
      "doi": "10.1007/s10801-026-01506-x"
    },
    {
      "citation": "Jaming et al. (2009), A generalized Pauli problem and an infinite family of MUB-triplets in dimension 6: the prior Fourier exclusion.",
      "url": "https://doi.org/10.1088/1751-8113/42/24/245305",
      "doi": "10.1088/1751-8113/42/24/245305"
    },
    {
      "citation": "Szöllősi (2010), A two-parameter family of complex Hadamard matrices of order 6 induced by hypocycloids.",
      "url": "https://doi.org/10.1090/S0002-9939-09-10102-8",
      "doi": "10.1090/S0002-9939-09-10102-8"
    },
    {
      "citation": "McNulty and Weigert (2025), correction identifying a failed earlier argument; not a disproof of the target theorem.",
      "url": "https://arxiv.org/abs/2504.13067",
      "doi": "10.48550/arXiv.2504.13067"
    }
  ],
  "claimAssurance": null,
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    "lineageId": null,
    "accelerationPrimitives": [
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      "agent-readable-research-object"
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    "decisionObject": {
      "type": "certificate",
      "description": "Closed-family MUB exclusion by interval coverage and graph obstruction.",
      "scope": "Specified Szollosi two-circulant family in dimension six; Fourier re-proof; general maximum conditional."
    },
    "bottleneckTargeted": [
      "assurance",
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    "semanticBridge": {
      "state": "explicit",
      "description": "Symmetry reduction, canonical half-open ownership, closed interval enclosures, vector hull coverage, self-separation and exclusion of two compatible six-cliques.",
      "remainingRisks": [
        "Written bridge and interval kernel are not formally verified.",
        "Producer-side full replay does not establish unaffiliated reproduction.",
        "The result does not cover all order-six Hadamard matrices."
      ]
    },
    "humanJudgmentGates": [
      "Publication authorisation only; no human scientific contribution or additional review stage is inferred."
    ],
    "parentLinks": [
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        "relation": "depends-on-claim",
        "workId": null,
        "legacyReleaseSlug": null,
        "externalUrl": "https://doi.org/10.1007/s10801-026-01506-x",
        "inheritedClaim": "Conditional reduction of the dimension-six maximum to Conjectures 2 and 3.",
        "inheritedAssuranceCeiling": "Published conditional mathematical reduction; Conjecture 2 remains an unproved input."
      }
    ],
    "assuranceTarget": {
      "dimensions": [
        "independentRerun",
        "formalVerification",
        "specialistReview",
        "semanticValidation",
        "noveltyAssessment",
        "priorityAssessment"
      ],
      "nextAction": "Audit the ownership and interval-to-graph bridge and independently replay the complete cover.",
      "claimCeiling": "Unrefereed candidate; producer-side checking."
    },
    "impactClaims": [
      {
        "id": "szollosi-mub-exclusion-no-impact",
        "aim": "science",
        "outcome": "Inspectable exclusion of a continuous Hadamard family",
        "setting": "Producer-coordinated publication",
        "status": "NO_IMPACT_EVIDENCE",
        "designClass": "none",
        "comparator": "None.",
        "estimand": "No impact effect estimated.",
        "evidenceRefs": [],
        "registeredDesignRef": null,
        "independentAssessment": null
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    "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:szollosi-mub-exclusion-publication",
        "status": "active",
        "resultClass": "pending",
        "metrics": {
          "schemaVersion": "1.0",
          "measurementScope": "publication-only",
          "scopeBoundary": "Remaining replay monitoring, final packaging and publication. Prior repairs are left-censored here, not reconstructed.",
          "forecast": {
            "frozenAt": "2026-09-30T04:09:34.069Z",
            "procedureClass": "remaining-mathematical-candidate-publication",
            "targetOutcome": "Passed complete replay, public identical archives and canonical site readback.",
            "expectedActiveMinutes": 90,
            "plausibleLowMinutes": 60,
            "plausibleHighMinutes": 150,
            "expectedUnattendedWaitMinutes": 240,
            "referenceClass": {
              "label": "Remaining-task decomposition",
              "sampleSize": 0,
              "basis": "Judgment forecast; current four-worker full replay dominates elapsed time."
            },
            "fermiComponents": [
              {
                "component": "Final evidence, archive and providers",
                "count": 1,
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                "centralMinutesPerUnit": 45,
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                "basis": "Replay completion and package freeze pending."
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                "component": "Site QA, CI and guarded publication",
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                "basis": "Two new-slug publication cycles."
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            "probabilityPositiveSignal": 0.9,
            "probabilityTargetClosure": 0.8,
            "probabilityHorizonMinutes": 480,
            "assumptions": [
              "Full replay completes without a fatal defect.",
              "Providers remain available."
            ],
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              "Replay or provider failure.",
              "Material semantic or rights defect."
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            "stopRule": "No workflow cap; continue required gates. Hold publication for unresolved fatal defects."
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}