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        "Ewens sampling formula",
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      "fullTitle": "Structural reductions toward the quartic Hessian conjecture in dimension four",
      "description": "Exact certificates narrow a degree-five repeated-factor boundary of full HC4—the all-degree Hessian Conjecture in four variables—without proving secant closure, full HC4 or JC2.",
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      "fullTitle": "Reducedness of the Hilbert scheme of eight points in affine four-space",
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      "fullTitle": "LPS structural reductions: duality, quartic obstruction, and p-adic certificates",
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      "directInterReleaseDegree": 0
    },
    {
      "id": "release:vr2-k4-equals-20",
      "type": "release",
      "label": "VR2(K4) = 20",
      "fullTitle": "VR2(K4) = 20: twenty vertices force two vertex-disjoint monochromatic K4s",
      "description": "Colour every edge among 20 points red or blue and you cannot avoid two completely separate single-colour foursomes — while a carefully built 19-point colouring can. A companion result to z(20) = 6.",
      "statementFingerprint": "sha256:accc3eb504617737229e63d7da18cb7fdc320b8991f5eb88c70eb9845498d3bc",
      "url": "https://evidencepress.org/releases/vr2-k4-equals-20/",
      "datePublished": "2026-07-28",
      "dateModified": "2026-07-28",
      "status": "unrefereed-candidate",
      "doi": "10.5281/zenodo.21647654",
      "keywords": [
        "Ramsey theory",
        "vertex-disjoint monochromatic subgraphs",
        "VR2(K4)",
        "K4",
        "R(4,4)",
        "Paley graph",
        "SAT certificates",
        "LRAT",
        "cake_lpr",
        "computer-assisted proof",
        "AI-generated mathematics"
      ],
      "sourceRefs": [
        "https://evidencepress.org/releases/vr2-k4-equals-20/paper.json"
      ],
      "directInterReleaseDegree": 2
    },
    {
      "id": "release:wales-20mph-casualty-attribution",
      "type": "release",
      "label": "Wales 20 mph casualty attribution",
      "fullTitle": "Wales 20 mph Casualty Attribution Audit: A Constructive Non-Identification Result",
      "description": "The first-year casualty decline is descriptively reproducible, but the frozen aggregate evidence identifies neither the point value nor the sign of the policy effect on affected roads.",
      "statementFingerprint": "sha256:17fd521120f526d22408d476bc8677cfbe3bd647c8bbaf14f1265272857e64e8",
      "url": "https://evidencepress.org/releases/wales-20mph-casualty-attribution/",
      "datePublished": "2026-08-11",
      "dateModified": "2026-08-22",
      "status": "unrefereed-candidate",
      "doi": "10.5281/zenodo.21894035",
      "keywords": [
        "Wales",
        "20 mph",
        "road casualties",
        "policy identification",
        "causal inference",
        "non-identification",
        "constructive counterexample",
        "treatment misclassification",
        "official statistics",
        "reproducible policy analysis"
      ],
      "sourceRefs": [
        "https://evidencepress.org/releases/wales-20mph-casualty-attribution/paper.json"
      ],
      "directInterReleaseDegree": 2
    },
    {
      "id": "release:z20-equals-6",
      "type": "release",
      "label": "z(20) = 6 (Erdős problem 758)",
      "fullTitle": "z(20) = 6: resolving the first open case of Erdős problem 758",
      "description": "Every graph on 20 vertices can be split into six parts, each a clique or an independent set — and 6 is best possible. A computer-assisted proof, released with its full certificate chain, settles the first open case of an Erdős–Gimbel problem.",
      "statementFingerprint": "sha256:691cf65936d1c6b417d3b4fecb0a6a04ce2ff5f442837154b33ebc62aaa8964a",
      "url": "https://evidencepress.org/releases/z20-equals-6/",
      "datePublished": "2026-07-28",
      "dateModified": "2026-07-28",
      "status": "unrefereed-candidate",
      "doi": "10.5281/zenodo.21647645",
      "keywords": [
        "cochromatic number",
        "Erdős problem 758",
        "Erdős–Gimbel",
        "Ramsey theory",
        "R(4,4)",
        "Paley graph",
        "SAT certificates",
        "DRUP",
        "LRAT",
        "cake_lpr",
        "computer-assisted proof",
        "AI-generated mathematics"
      ],
      "sourceRefs": [
        "https://evidencepress.org/releases/z20-equals-6/paper.json"
      ],
      "directInterReleaseDegree": 2
    },
    {
      "id": "lineage:affine-diversification-programme",
      "type": "lineage",
      "label": "Affine diversification partial-identification programme",
      "description": "The finite-sample successor explicitly extends the predecessor's affine cumulative-loss fibre, fixed-signal sharp bounds and endpoint-sampling diagnostic by adding signal uncertainty, three-valued decisions and a frozen CRABS comparison.",
      "basis": "The finite-sample successor explicitly extends the predecessor's affine cumulative-loss fibre, fixed-signal sharp bounds and endpoint-sampling diagnostic by adding signal uncertainty, three-valued decisions and a frozen CRABS comparison.",
      "sharedBoundary": "The successor reuses the predecessor's mathematical and software framework and therefore does not independently confirm it. A shared error in the affine coordinate, probability bridge or encoding can propagate across the lineage.",
      "rootReleaseSlug": "affine-diversification-fibres",
      "memberCount": 2,
      "url": "https://evidencepress.org/atlas/?node=lineage%3Aaffine-diversification-programme",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/lineages/2"
      ]
    },
    {
      "id": "lineage:binary-form-programme",
      "type": "lineage",
      "label": "Binary-form factorisation programme",
      "description": "Each member explicitly identifies another member as foundational, parent, child, companion or continuation work in the published release metadata.",
      "basis": "Each member explicitly identifies another member as foundational, parent, child, companion or continuation work in the published release metadata.",
      "sharedBoundary": "Dependency and reuse within this programme are not independent confirmation; a shared semantic or mathematical defect can propagate across the lineage.",
      "rootReleaseSlug": "degree-difference-affine-slices",
      "memberCount": 5,
      "url": "https://evidencepress.org/atlas/?node=lineage%3Abinary-form-programme",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/lineages/0"
      ]
    },
    {
      "id": "lineage:cyclicity-programme",
      "type": "lineage",
      "label": "Fixed-seed cyclicity programme",
      "description": "The root-span release explicitly cites the cyclicity-loci release as its predecessor and extends the same fixed-seed cyclicity programme.",
      "basis": "The root-span release explicitly cites the cyclicity-loci release as its predecessor and extends the same fixed-seed cyclicity programme.",
      "sharedBoundary": "The child release reuses the fixed-seed framework and therefore does not independently confirm the parent release or its analytic bridge.",
      "rootReleaseSlug": "cyclicity-loci-exponential-periods",
      "memberCount": 4,
      "url": "https://evidencepress.org/atlas/?node=lineage%3Acyclicity-programme",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/lineages/1"
      ]
    },
    {
      "id": "lineage:joint-replenishment-exact-certification-programme",
      "type": "lineage",
      "label": "Exact joint-replenishment certification programme",
      "description": "The three-item successor explicitly extends the parent's common-origin model, independent-cap reduction boundary, exact two-item interval and certificate-first conventions with a distinct primitive-triple tail architecture and logistics evaluation handoff.",
      "basis": "The three-item successor explicitly extends the parent's common-origin model, independent-cap reduction boundary, exact two-item interval and certificate-first conventions with a distinct primitive-triple tail architecture and logistics evaluation handoff.",
      "sharedBoundary": "The successor reuses parent assumptions, code patterns and producer coordination. This lineage is dependency evidence, not independent confirmation, and a shared semantic, algebraic or implementation defect may propagate across both releases.",
      "rootReleaseSlug": "certified-two-item-jrp",
      "memberCount": 2,
      "url": "https://evidencepress.org/atlas/?node=lineage%3Ajoint-replenishment-exact-certification-programme",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/lineages/3"
      ]
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    {
      "id": "lineage:txgraffiti-counterexample-order-programme",
      "type": "lineage",
      "label": "TxGraffiti cubic-counterexample order programme",
      "description": "The order-48 successor explicitly identifies the public 50-vertex release as its parent, supplies a different smaller graph and resolves the parent's open below-50 search direction by construction without retracting the parent or inheriting its separate restricted-class theorems.",
      "basis": "The order-48 successor explicitly identifies the public 50-vertex release as its parent, supplies a different smaller graph and resolves the parent's open below-50 search direction by construction without retracting the parent or inheriting its separate restricted-class theorems.",
      "sharedBoundary": "The successor reuses problem framing, provenance and certificate architecture from the parent. This lineage is dependency evidence, not independent confirmation, and a shared source-to-semantics or implementation defect may propagate across both releases.",
      "rootReleaseSlug": "txgraffiti-c3-resolution",
      "memberCount": 2,
      "url": "https://evidencepress.org/atlas/?node=lineage%3Atxgraffiti-counterexample-order-programme",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/lineages/4"
      ]
    },
    {
      "id": "cluster:aggregation-licence-and-target-sufficiency",
      "type": "cluster",
      "label": "Aggregation licences and target sufficiency",
      "description": "A common fibre-factorisation diagnostic can expose missing decision-relevant information across fields without establishing that their scientific mechanisms are identical, that the admissible sets and targets are empirically valid, or that the proposed reporting licence improves research or policy decisions.",
      "sharedBoundary": "A common fibre-factorisation diagnostic can expose missing decision-relevant information across fields without establishing that their scientific mechanisms are identical, that the admissible sets and targets are empirically valid, or that the proposed reporting licence improves research or policy decisions.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aaggregation-licence-and-target-sufficiency",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/12"
      ]
    },
    {
      "id": "cluster:amplitude-modules-fused-support-bautin-2026-08-28",
      "type": "cluster",
      "label": "Amplitude modules, fused inverse support and an ordinary coefficient-Bautin cutoff",
      "description": "The written classifications, exact producer replay and model-mediated editorial repair support an anonymous unrefereed theorem candidate only. They do not establish independent reconstruction, formal verification, external specialist or editorial peer review, identity with alternative Bautin conventions, absolute priority, three historically posed open problems solved, a real planar limit-cycle bound or research impact.",
      "sharedBoundary": "The written classifications, exact producer replay and model-mediated editorial repair support an anonymous unrefereed theorem candidate only. They do not establish independent reconstruction, formal verification, external specialist or editorial peer review, identity with alternative Bautin conventions, absolute priority, three historically posed open problems solved, a real planar limit-cycle bound or research impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aamplitude-modules-fused-support-bautin-2026-08-28",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/23"
      ]
    },
    {
      "id": "cluster:ap4-ramsey-diameter-36-finite-certificate-2026-09-03",
      "type": "cluster",
      "label": "Finite four-term-AP Ramsey diameter certificate",
      "description": "The written source-to-CNF bridge, exact 26-point lower refutation, separately certified Graham 27-point upper witness, semantic reconstruction, small oracle and hostile controls support an anonymous unrefereed finite theorem candidate for v_{2,4}([37]) = 27. They do not establish W*(4) = 27, control primitive diameter above 36, answer the AIM asymptotic questions, supply unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, exhaustive novelty, absolute priority or workflow impact.",
      "sharedBoundary": "The written source-to-CNF bridge, exact 26-point lower refutation, separately certified Graham 27-point upper witness, semantic reconstruction, small oracle and hostile controls support an anonymous unrefereed finite theorem candidate for v_{2,4}([37]) = 27. They do not establish W*(4) = 27, control primitive diameter above 36, answer the AIM asymptotic questions, supply unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, exhaustive novelty, absolute priority or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aap4-ramsey-diameter-36-finite-certificate-2026-09-03",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/37"
      ]
    },
    {
      "id": "cluster:binary-form-jacobian-and-obstruction",
      "type": "cluster",
      "label": "Binary-form Jacobian, determinant and obstruction toolkit",
      "description": "Related internal releases can reuse identities and methods but do not independently validate their shared mathematical or semantic premises.",
      "sharedBoundary": "Related internal releases can reuse identities and methods but do not independently validate their shared mathematical or semantic premises.",
      "memberCount": 6,
      "scopeStatus": "broad-cluster",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Abinary-form-jacobian-and-obstruction",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/1"
      ]
    },
    {
      "id": "cluster:certified-demographic-identifiability",
      "type": "cluster",
      "label": "Certified demographic identifiability auditing",
      "description": "Certified identified-set bounds and pre-registered audits expose what declared error models concede without establishing that any declared model is scientifically correct, that the underlying spectra are artefact-free, or that a setting-conditional verdict settles the biological dispute.",
      "sharedBoundary": "Certified identified-set bounds and pre-registered audits expose what declared error models concede without establishing that any declared model is scientifically correct, that the underlying spectra are artefact-free, or that a setting-conditional verdict settles the biological dispute.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Acertified-demographic-identifiability",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/8"
      ]
    },
    {
      "id": "cluster:cross-field-identification-and-selector-provenance",
      "type": "cluster",
      "label": "Cross-field identification and selector provenance",
      "description": "A common Selector Ledger can expose assumption-supported narrowing across fields without establishing that their observation maps share one exact symmetry, that the field mappings are independently validated, or that the reporting instrument improves practice.",
      "sharedBoundary": "A common Selector Ledger can expose assumption-supported narrowing across fields without establishing that their observation maps share one exact symmetry, that the field mappings are independently validated, or that the reporting instrument improves practice.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Across-field-identification-and-selector-provenance",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/7"
      ]
    },
    {
      "id": "cluster:cyclicity-and-spectral-compression",
      "type": "cluster",
      "label": "Cyclicity and spectral compression",
      "description": "Exact algebraic or representation-theoretic compression does not discharge every analytic bridge or establish application-level impact.",
      "sharedBoundary": "Exact algebraic or representation-theoretic compression does not discharge every analytic bridge or establish application-level impact.",
      "memberCount": 3,
      "scopeStatus": "broad-cluster",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Acyclicity-and-spectral-compression",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/2"
      ]
    },
    {
      "id": "cluster:dyck-two-cut-entropy-2026-09-06",
      "type": "cluster",
      "label": "Two-cut entropy for the original Dyck rejection walk",
      "description": "Unrefereed analytic proof candidate for the original length-2n ordered independent-coordinate Dyck rejection walk. No cutoff, sharp upper constant, numerical burn-in guarantee, computational-runtime bound, sampler optimality, external peer review, formal verification or priority clearance.",
      "sharedBoundary": "Unrefereed analytic proof candidate for the original length-2n ordered independent-coordinate Dyck rejection walk. No cutoff, sharp upper constant, numerical burn-in guarantee, computational-runtime bound, sampler optimality, external peer review, formal verification or priority clearance.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Adyck-two-cut-entropy-2026-09-06",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/44"
      ]
    },
    {
      "id": "cluster:exact-combinatorial-certificates",
      "type": "cluster",
      "label": "Exact combinatorial certificate architecture",
      "description": "Certificate replay establishes encoded bounded claims; source-to-encoding correctness and independent reconstruction remain separate.",
      "sharedBoundary": "Certificate replay establishes encoded bounded claims; source-to-encoding correctness and independent reconstruction remain separate.",
      "memberCount": 5,
      "scopeStatus": "broad-cluster",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aexact-combinatorial-certificates",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/3"
      ]
    },
    {
      "id": "cluster:factorial-spike-componentwise-fi-noetherianity-separation-2026-08-31",
      "type": "cluster",
      "label": "Factorial-spike componentwise versus FI-Noetherianity separation",
      "description": "The universal monomial proof, exact native-width factorisation criterion, strict FI-ideal witnesses, four hostile controls and producer replay support an anonymous unrefereed characteristic-free separation of componentwise Noetherianity from FI-Noetherianity. They do not make the sub-FI-algebra finitely generated, produce a non-free module or a module counterexample over the ambient polynomial FI-algebra, establish historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact.",
      "sharedBoundary": "The universal monomial proof, exact native-width factorisation criterion, strict FI-ideal witnesses, four hostile controls and producer replay support an anonymous unrefereed characteristic-free separation of componentwise Noetherianity from FI-Noetherianity. They do not make the sub-FI-algebra finitely generated, produce a non-free module or a module counterexample over the ambient polynomial FI-algebra, establish historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Afactorial-spike-componentwise-fi-noetherianity-separation-2026-08-31",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/32"
      ]
    },
    {
      "id": "cluster:finite-polynomial-rigidity-certificates",
      "type": "cluster",
      "label": "Finite polynomial-rigidity certificates and executable frontier",
      "description": "Exact finite-field certificates plus properness establish only the stated finite R(3,n) instances. They do not supply an all-degree theorem, independent reconstruction, a proof of the unrestricted Strong Factorial Conjecture or the general Polydegree Conjecture, or evidence of research-workflow impact.",
      "sharedBoundary": "Exact finite-field certificates plus properness establish only the stated finite R(3,n) instances. They do not supply an all-degree theorem, independent reconstruction, a proof of the unrestricted Strong Factorial Conjecture or the general Polydegree Conjecture, or evidence of research-workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Afinite-polynomial-rigidity-certificates",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/14"
      ]
    },
    {
      "id": "cluster:finite-sample-affine-signal-to-decision",
      "type": "cluster",
      "label": "Finite-sample affine signal-to-decision workflows",
      "description": "The exact fixed-stem signal band and affine decision rule are conditional on the declared homogeneous model and observation boundary. Producer replay and a finite CRABS benchmark do not establish biological validity, broad comparative utility, independent reconstruction, specialist review, priority or field impact.",
      "sharedBoundary": "The exact fixed-stem signal band and affine decision rule are conditional on the declared homogeneous model and observation boundary. Producer replay and a finite CRABS benchmark do not establish biological validity, broad comparative utility, independent reconstruction, specialist review, priority or field impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Afinite-sample-affine-signal-to-decision",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/16"
      ]
    },
    {
      "id": "cluster:fisk-toeplitz-deletion-interlacing-finite-certificate-2026-09-01",
      "type": "cluster",
      "label": "Finite Fisk Toeplitz-minor deletion-interlacing certificate",
      "description": "The written Bezout-interlacing proof, complete 61,192-term degree-five certificate, lower-degree exact recomputation, semantic mutations and producer replay support an anonymous unrefereed finite theorem candidate through five positive alphabet entries. They do not establish degree six beyond the first three minors, zero-boundary cases, Fisk's all-degree conjecture, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, exhaustive novelty, absolute priority or workflow impact.",
      "sharedBoundary": "The written Bezout-interlacing proof, complete 61,192-term degree-five certificate, lower-degree exact recomputation, semantic mutations and producer replay support an anonymous unrefereed finite theorem candidate through five positive alphabet entries. They do not establish degree six beyond the first three minors, zero-boundary cases, Fisk's all-degree conjecture, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, exhaustive novelty, absolute priority or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Afisk-toeplitz-deletion-interlacing-finite-certificate-2026-09-01",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/36"
      ]
    },
    {
      "id": "cluster:fixed-d-fi-d-toeplitz-kernel-obstruction-2026-09-04",
      "type": "cluster",
      "label": "Fixed-d FI_d Toeplitz kernel obstruction",
      "description": "The explicit countable two-colour construction, bidiagonal Toeplitz blocks, symmetric-group coinvariant calculation, Yoneda kernel obstruction, hostile mutations and producer replay support an anonymous unrefereed theorem candidate showing that finitely presented FI_d-modules are not abelian for each fixed finite d at least two over characteristic-zero fields. They do not settle positive characteristic, d=1, related noetherianity categories, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, exhaustive novelty, absolute priority or workflow impact.",
      "sharedBoundary": "The explicit countable two-colour construction, bidiagonal Toeplitz blocks, symmetric-group coinvariant calculation, Yoneda kernel obstruction, hostile mutations and producer replay support an anonymous unrefereed theorem candidate showing that finitely presented FI_d-modules are not abelian for each fixed finite d at least two over characteristic-zero fields. They do not settle positive characteristic, d=1, related noetherianity categories, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, exhaustive novelty, absolute priority or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Afixed-d-fi-d-toeplitz-kernel-obstruction-2026-09-04",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/39"
      ]
    },
    {
      "id": "cluster:four-element-rowmotion-obstruction-2026-08-30",
      "type": "cluster",
      "label": "Four-element birational and piecewise-linear rowmotion obstruction",
      "description": "The two exact fixed-point derivative obstructions, exhaustive enumeration and period calculation for every finite poset through size three, five semantic corruptions and producer replay support an anonymous unrefereed theorem candidate. They do not classify d-complete posets, rooted trees or fences, make the four-element Hasse shape new, establish historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact.",
      "sharedBoundary": "The two exact fixed-point derivative obstructions, exhaustive enumeration and period calculation for every finite poset through size three, five semantic corruptions and producer replay support an anonymous unrefereed theorem candidate. They do not classify d-complete posets, rooted trees or fences, make the four-element Hasse shape new, establish historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Afour-element-rowmotion-obstruction-2026-08-30",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/29"
      ]
    },
    {
      "id": "cluster:four-point-inductive-cubical-excision-counterexample-2026-08-30",
      "type": "cluster",
      "label": "Four-point directed inductive-cubical excision counterexample",
      "description": "The explicit four-point interior cover, integral relative-chain calculation, matrix certificate, producer-side concordance checks and clean-environment replay support an anonymous unrefereed candidate only for normalized (J_+, inductive-product) cubical singular homology. They do not decide the J_1 or I inductive theories, symmetric graph closures, historical priority, unaffiliated reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact.",
      "sharedBoundary": "The explicit four-point interior cover, integral relative-chain calculation, matrix certificate, producer-side concordance checks and clean-environment replay support an anonymous unrefereed candidate only for normalized (J_+, inductive-product) cubical singular homology. They do not decide the J_1 or I inductive theories, symmetric graph closures, historical priority, unaffiliated reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Afour-point-inductive-cubical-excision-counterexample-2026-08-30",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/28"
      ]
    },
    {
      "id": "cluster:four-state-monotone-row-diameter-counterexample-2026-08-29",
      "type": "cluster",
      "label": "Four-state monotone row-diameter counterexample and two-spin classification",
      "description": "The exact four-state witness, all-time two-spin classification, cardinality-minimality proof, bounded zero-field screen and producer replay support an anonymous unrefereed candidate. They do not settle the all-graph zero-field Ising question or AIM diagnostics 1.6(2-3), and do not establish exhaustive novelty, absolute priority, independent reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact.",
      "sharedBoundary": "The exact four-state witness, all-time two-spin classification, cardinality-minimality proof, bounded zero-field screen and producer replay support an anonymous unrefereed candidate. They do not settle the all-graph zero-field Ising question or AIM diagnostics 1.6(2-3), and do not establish exhaustive novelty, absolute priority, independent reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Afour-state-monotone-row-diameter-counterexample-2026-08-29",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/26"
      ]
    },
    {
      "id": "cluster:frankl-entropy-obstruction-and-repair",
      "type": "cluster",
      "label": "Frankl entropy obstruction and repaired reductions",
      "description": "The source-specific counterdirection and repaired support reductions do not prove the global candidate inequality, establish a new Frankl bound, validate the uninspected CISS text, or convert producer-side exact and directed-rounding checks into independent mathematical review.",
      "sharedBoundary": "The source-specific counterdirection and repaired support reductions do not prove the global candidate inequality, establish a new Frankl bound, validate the uninspected CISS text, or convert producer-side exact and directed-rounding checks into independent mathematical review.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Afrankl-entropy-obstruction-and-repair",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/13"
      ]
    },
    {
      "id": "cluster:free-by-cyclic-bns-component-orbit-obstruction-2026-08-31",
      "type": "cluster",
      "label": "Free-by-cyclic BNS component-orbit obstruction",
      "description": "The written all-m proof, exact 2m+2 BNS component count conditional on Cashen-Levitt Corollary 2.10, componentwise kernel-rank minima, at-least-m+1 outer-orbit obstruction, eight claim-boundary controls and producer replay support an anonymous unrefereed theorem candidate. They do not compute the exact orbit count or Out(G_m), replace the imported BNS theorem, establish historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact.",
      "sharedBoundary": "The written all-m proof, exact 2m+2 BNS component count conditional on Cashen-Levitt Corollary 2.10, componentwise kernel-rank minima, at-least-m+1 outer-orbit obstruction, eight claim-boundary controls and producer replay support an anonymous unrefereed theorem candidate. They do not compute the exact orbit count or Out(G_m), replace the imported BNS theorem, establish historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Afree-by-cyclic-bns-component-orbit-obstruction-2026-08-31",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/31"
      ]
    },
    {
      "id": "cluster:free-normal-cover-all-fuchsian-pinching-2026-09-01",
      "type": "cluster",
      "label": "Free normal cover and all-Fuchsian pinching construction",
      "description": "The fixed-kernel construction, explicit reduced-surface and all-Fuchsian group-space bridge, imported-theorem hypothesis maps, fixed-width collar estimate, hostile controls and producer replay support an anonymous unrefereed all-Fuchsian strengthening candidate. They do not establish a first solution under the broad group-deformation reading, monotonicity, an exact exponent formula, global deformation-space identification, historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review or workflow impact.",
      "sharedBoundary": "The fixed-kernel construction, explicit reduced-surface and all-Fuchsian group-space bridge, imported-theorem hypothesis maps, fixed-width collar estimate, hostile controls and producer replay support an anonymous unrefereed all-Fuchsian strengthening candidate. They do not establish a first solution under the broad group-deformation reading, monotonicity, an exact exponent formula, global deformation-space identification, historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Afree-normal-cover-all-fuchsian-pinching-2026-09-01",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/35"
      ]
    },
    {
      "id": "cluster:grand-problem-salvage",
      "type": "cluster",
      "label": "Grand-problem salvage",
      "description": "The extracted modules may be useful while the parent conjecture remains explicitly unresolved.",
      "sharedBoundary": "The extracted modules may be useful while the parent conjecture remains explicitly unresolved.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Agrand-problem-salvage",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/6"
      ]
    },
    {
      "id": "cluster:hc4-binary-decimic-normal-layer-structural-reductions-2026-09-01",
      "type": "cluster",
      "label": "HC4 binary-decimic normal-layer structural reductions",
      "description": "The exact five-support certificates, all-31-generator tangent radical containment, three rational secant colon elements, fail-closed fourth-target recovery and prospectively frozen 16-column rational source-kernel theorem support an anonymous unrefereed computer-assisted structural-reductions candidate. They do not prove inhomogeneous fourth-target membership, colon equality, saturation, secant-orbit closure, full normal-layer or polynomial-level closure, HC4, JC2, unaffiliated reconstruction, formal verification, external specialist review, editorial peer review, absolute priority or workflow impact.",
      "sharedBoundary": "The exact five-support certificates, all-31-generator tangent radical containment, three rational secant colon elements, fail-closed fourth-target recovery and prospectively frozen 16-column rational source-kernel theorem support an anonymous unrefereed computer-assisted structural-reductions candidate. They do not prove inhomogeneous fourth-target membership, colon equality, saturation, secant-orbit closure, full normal-layer or polynomial-level closure, HC4, JC2, unaffiliated reconstruction, formal verification, external specialist review, editorial peer review, absolute priority or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Ahc4-binary-decimic-normal-layer-structural-reductions-2026-09-01",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/34"
      ]
    },
    {
      "id": "cluster:hilb8-local-reducedness-2026-09-07",
      "type": "cluster",
      "label": "Hilbert-scheme local reducedness and mixed-prime finite-module comparison",
      "description": "Source-specific unrefereed characteristic-zero proof candidate; finite arithmetic and internal replay do not establish external validation or transfer to other Hilbert schemes.",
      "sharedBoundary": "Source-specific unrefereed characteristic-zero proof candidate; finite arithmetic and internal replay do not establish external validation or transfer to other Hilbert schemes.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Ahilb8-local-reducedness-2026-09-07",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/45"
      ]
    },
    {
      "id": "cluster:identification-and-robust-operations",
      "type": "cluster",
      "label": "Identification and robust operations",
      "description": "Identified sets, exact bounds and decision margins are conditional on the declared observation map and model; real-world decision effects are unmeasured.",
      "sharedBoundary": "Identified sets, exact bounds and decision margins are conditional on the declared observation map and model; real-world decision effects are unmeasured.",
      "memberCount": 4,
      "scopeStatus": "broad-cluster",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aidentification-and-robust-operations",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/4"
      ]
    },
    {
      "id": "cluster:inverse-root-amplitude-laurent-moments-2026-08-21",
      "type": "cluster",
      "label": "Inverse-root amplitude, endpoint-moment and Laurent-channel calculus",
      "description": "The combined fixed-seed, polynomial-amplitude, specified-zero-cycle and Laurent local-channel theorems are unrefereed producer-workflow claims. The all-degree fixed-seed and endpoint classifications remain relative to named imported monodromy, finite-projective-group, Ritt and polynomial-moment results. Exact replay, partial Lean controls, same-programme CAS implementations, finite regressions and internal model-assisted review do not establish correctness of the imported results, a finite all-Laurent atlas, independent reconstruction, external specialist review, priority or field impact.",
      "sharedBoundary": "The combined fixed-seed, polynomial-amplitude, specified-zero-cycle and Laurent local-channel theorems are unrefereed producer-workflow claims. The all-degree fixed-seed and endpoint classifications remain relative to named imported monodromy, finite-projective-group, Ritt and polynomial-moment results. Exact replay, partial Lean controls, same-programme CAS implementations, finite regressions and internal model-assisted review do not establish correctness of the imported results, a finite all-Laurent atlas, independent reconstruction, external specialist review, priority or field impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": "2026-08-21",
      "supersedes": "cluster:inverse-root-support-fusion-all-degree-2026-08-21",
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Ainverse-root-amplitude-laurent-moments-2026-08-21",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/18"
      ]
    },
    {
      "id": "cluster:inverse-root-support-fusion-all-degree-2026-08-21",
      "type": "cluster",
      "label": "All-degree inverse-root classification and rank-preserving extension oracles",
      "description": "The all-degree low-rank coefficient classification and extension oracle are unrefereed producer-workflow claims relative to named primitive-monodromy and finite-projective-group classifications. Written proof, partial Lean controls, separate same-programme CAS implementations, finite regressions and internal model-assisted re-audits do not establish correctness of imported results, independent reconstruction, external specialist review, priority or field impact.",
      "sharedBoundary": "The all-degree low-rank coefficient classification and extension oracle are unrefereed producer-workflow claims relative to named primitive-monodromy and finite-projective-group classifications. Written proof, partial Lean controls, separate same-programme CAS implementations, finite regressions and internal model-assisted re-audits do not establish correctness of imported results, independent reconstruction, external specialist review, priority or field impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": false,
      "effectiveDate": "2026-08-21",
      "supersedes": "cluster:inverse-root-support-fusion-atlas",
      "supersededBy": "cluster:inverse-root-amplitude-laurent-moments-2026-08-21",
      "url": "https://evidencepress.org/atlas/?node=cluster%3Ainverse-root-support-fusion-all-degree-2026-08-21",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/17"
      ]
    },
    {
      "id": "cluster:inverse-root-support-fusion-atlas",
      "type": "cluster",
      "label": "Inverse-root support, Fourier fusion and bounded coefficient atlases",
      "description": "The universal written support and fusion theorems and the exact degree-twenty atlas remain unrefereed producer-workflow claims. Finite atlas replay does not establish the all-degree coefficient conjecture, independent reconstruction, specialist review, priority or field impact.",
      "sharedBoundary": "The universal written support and fusion theorems and the exact degree-twenty atlas remain unrefereed producer-workflow claims. Finite atlas replay does not establish the all-degree coefficient conjecture, independent reconstruction, specialist review, priority or field impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": false,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": "cluster:inverse-root-support-fusion-all-degree-2026-08-21",
      "url": "https://evidencepress.org/atlas/?node=cluster%3Ainverse-root-support-fusion-atlas",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/15"
      ]
    },
    {
      "id": "cluster:lps-fixed-width-structural-and-padic-programme",
      "type": "cluster",
      "label": "Fixed-width LPS reductions, quartic gauge repair and p-adic signals",
      "description": "The determinant duality, fixed-width adjacent-flag reduction, localized quartic gauge bridge, bounded exact checks and p-adic certificates expose a smaller research target. They do not establish the missing uniform radical membership, any of the five target conjectures, independent reconstruction, formal verification, external specialist review, priority or workflow impact.",
      "sharedBoundary": "The determinant duality, fixed-width adjacent-flag reduction, localized quartic gauge bridge, bounded exact checks and p-adic certificates expose a smaller research target. They do not establish the missing uniform radical membership, any of the five target conjectures, independent reconstruction, formal verification, external specialist review, priority or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Alps-fixed-width-structural-and-padic-programme",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/22"
      ]
    },
    {
      "id": "cluster:negative-square-energy-ordered-valley-2026-08-30",
      "type": "cluster",
      "label": "Negative square-energy ordered valley and five-vertex classification",
      "description": "The exact five-vertex prescribed-order valley, structural minimality through four vertices, exhaustive five-vertex census, favourable-order boundary witness and producer replay support an anonymous unrefereed candidate. They refute only universal prescribed-order peak-unimodality and do not settle either favourable-order existential formulation or establish exhaustive novelty, absolute priority, unaffiliated reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact.",
      "sharedBoundary": "The exact five-vertex prescribed-order valley, structural minimality through four vertices, exhaustive five-vertex census, favourable-order boundary witness and producer replay support an anonymous unrefereed candidate. They refute only universal prescribed-order peak-unimodality and do not settle either favourable-order existential formulation or establish exhaustive novelty, absolute priority, unaffiliated reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Anegative-square-energy-ordered-valley-2026-08-30",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/27"
      ]
    },
    {
      "id": "cluster:nonbacktracking-jordan-valuation-realization",
      "type": "cluster",
      "label": "Non-backtracking Jordan valuation and graph realization",
      "description": "Written arbitrary-parameter valuation and graph embedding, with finite producer controls; no independent validation, exact extremum, optimal constants, priority or impact established.",
      "sharedBoundary": "Written arbitrary-parameter valuation and graph embedding, with finite producer controls; no independent validation, exact extremum, optimal constants, priority or impact established.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Anonbacktracking-jordan-valuation-realization",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/42"
      ]
    },
    {
      "id": "cluster:o01d0-hermite-boundary-and-falsification-2026-08-28",
      "type": "cluster",
      "label": "O-01d0 polar-fibre, Hermite-boundary, and falsification reductions",
      "description": "The fixed-index properness criterion, Hermite incidence and boundary lemmas, exact architecture failures, and bounded pair-content scans expose four executable gates. They do not establish uniform O-01d0, AF5 transversality, any linked conjecture, independent reconstruction, formal verification, external specialist review, priority, or workflow impact.",
      "sharedBoundary": "The fixed-index properness criterion, Hermite incidence and boundary lemmas, exact architecture failures, and bounded pair-content scans expose four executable gates. They do not establish uniform O-01d0, AF5 transversality, any linked conjecture, independent reconstruction, formal verification, external specialist review, priority, or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Ao01d0-hermite-boundary-and-falsification-2026-08-28",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/24"
      ]
    },
    {
      "id": "cluster:odd-order-popular-difference-counterexample-2026-08-29",
      "type": "cluster",
      "label": "Three-layer popular-difference counterexample and endpoint obstruction",
      "description": "The exact C21 witness, elementary three-layer count, below-2/5 odd-cyclic obstruction, producer replay and targeted source audit support an anonymous unrefereed candidate. They do not establish sufficiency or sharpness at 2/5, witness minimality, exhaustive novelty, absolute priority, independent reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact.",
      "sharedBoundary": "The exact C21 witness, elementary three-layer count, below-2/5 odd-cyclic obstruction, producer replay and targeted source audit support an anonymous unrefereed candidate. They do not establish sufficiency or sharpness at 2/5, witness minimality, exhaustive novelty, absolute priority, independent reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aodd-order-popular-difference-counterexample-2026-08-29",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/25"
      ]
    },
    {
      "id": "cluster:polydegree-e4-fourier-formal-boundary-bundle",
      "type": "cluster",
      "label": "Effective e=4 Polydegree persistence and scoped companion assurance",
      "description": "The all-degree e=4 candidate depends on the published specialization criterion, the stated smooth-zero and Fourier-persistence bridges, a producer-side finite Arb ledger and an analytic tail. The scoped Lean companion and conditional boundary theorem do not independently confirm the Polydegree argument or establish Furter's R(3), JC2, HC4, priority or workflow impact.",
      "sharedBoundary": "The all-degree e=4 candidate depends on the published specialization criterion, the stated smooth-zero and Fourier-persistence bridges, a producer-side finite Arb ledger and an analytic tail. The scoped Lean companion and conditional boundary theorem do not independently confirm the Polydegree argument or establish Furter's R(3), JC2, HC4, priority or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Apolydegree-e4-fourier-formal-boundary-bundle",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/11"
      ]
    },
    {
      "id": "cluster:polydegree-fourier-persistence-certificates",
      "type": "cluster",
      "label": "Polydegree smooth-point and Fourier-persistence certificates",
      "description": "The all-degree conclusion depends jointly on the stated Jacobian smooth-point reduction, asymptotic Fourier limit, exact eventual envelope and finite Arb bridge. Producer-side replay and reuse of the earlier smooth-point package do not constitute independent theorem reconstruction, specialist review or evidence for the conjectural fixed-e programme.",
      "sharedBoundary": "The all-degree conclusion depends jointly on the stated Jacobian smooth-point reduction, asymptotic Fourier limit, exact eventual envelope and finite Arb bridge. Producer-side replay and reuse of the earlier smooth-point package do not constitute independent theorem reconstruction, specialist review or evidence for the conjectural fixed-e programme.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Apolydegree-fourier-persistence-certificates",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/10"
      ]
    },
    {
      "id": "cluster:potts-finite-word-censoring-obstruction-2026-09-06",
      "type": "cluster",
      "label": "Exact finite-word ferromagnetic Potts censoring obstruction",
      "description": "Unrefereed exact finite-horizon q=3 counterexample candidate. No mixing-time, random-scan, every-q, minimality, practical speed-up, exhaustive novelty, priority, unaffiliated validation, formal proof or impact claim.",
      "sharedBoundary": "Unrefereed exact finite-horizon q=3 counterexample candidate. No mixing-time, random-scan, every-q, minimality, practical speed-up, exhaustive novelty, priority, unaffiliated validation, formal proof or impact claim.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Apotts-finite-word-censoring-obstruction-2026-09-06",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/43"
      ]
    },
    {
      "id": "cluster:pure-tensor-analytic-rank-normalization-obstruction-2026-08-30",
      "type": "cluster",
      "label": "Pure-tensor analytic-rank normalization obstruction",
      "description": "The exact pure-tensor and diagonal-bias formulas, all-power written proof, direct coefficient enumeration, seven semantic controls and producer replay support an anonymous unrefereed conditional counterexample to one literal unnormalised analytic-rank comparator. They do not reconstruct historical intention, refute normalized or powered-identity formulations, settle partition rank, establish novelty or priority, or provide unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact.",
      "sharedBoundary": "The exact pure-tensor and diagonal-bias formulas, all-power written proof, direct coefficient enumeration, seven semantic controls and producer replay support an anonymous unrefereed conditional counterexample to one literal unnormalised analytic-rank comparator. They do not reconstruct historical intention, refute normalized or powered-identity formulations, settle partition rank, establish novelty or priority, or provide unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Apure-tensor-analytic-rank-normalization-obstruction-2026-08-30",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/30"
      ]
    },
    {
      "id": "cluster:quartic-coefficient-power-boundary-2026-09-05",
      "type": "cluster",
      "label": "Quartic coefficient-power boundary classification",
      "description": "Unrefereed quartic theorem candidate with exact auxiliary checks; no external validation, formal proof, full AIM solution, all-degree classification, historical priority, four-star grade or impact established.",
      "sharedBoundary": "Unrefereed quartic theorem candidate with exact auxiliary checks; no external validation, formal proof, full AIM solution, all-degree classification, historical priority, four-star grade or impact established.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aquartic-coefficient-power-boundary-2026-09-05",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/41"
      ]
    },
    {
      "id": "cluster:rbm31-channel-convex-cover-radius-2026-09-05",
      "type": "cluster",
      "label": "Reverse-channel and exact convex-cover KL radius certificate",
      "description": "Anonymous AI-assisted unrefereed computer-assisted theorem candidate for the exact three-bit two-product-mixture KL radius, with a constructive rational interface and a non-sharp conditioning corollary. Not unaffiliated verification, formal proof, authenticated specialist review, journal peer review, exhaustive novelty, priority, a four-star rating or demonstrated impact.",
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        "policy",
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        "productivity"
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        "an endpoint or transition region is uncovered",
        "normalisations differ across regimes",
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      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists bilateral-deficiency-regular-dim as a member of Exact combinatorial certificate architecture.",
      "inferenceLimit": "Certificate replay establishes encoded bounded claims; source-to-encoding correctness and independent reconstruction remain separate.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/3"
      ],
      "id": "edge:ce312ce5f3908d057ed7"
    },
    {
      "source": "release:bordered-jacobian-foundations",
      "target": "cluster:binary-form-jacobian-and-obstruction",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists bordered-jacobian-foundations as a member of Binary-form Jacobian, determinant and obstruction toolkit.",
      "inferenceLimit": "Related internal releases can reuse identities and methods but do not independently validate their shared mathematical or semantic premises.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/1"
      ],
      "id": "edge:59358bbb220c0148e788"
    },
    {
      "source": "release:certified-commitment-horizons",
      "target": "cluster:identification-and-robust-operations",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists certified-commitment-horizons as a member of Identification and robust operations.",
      "inferenceLimit": "Identified sets, exact bounds and decision margins are conditional on the declared observation map and model; real-world decision effects are unmeasured.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/4"
      ],
      "id": "edge:bee7f85d60f97ecbbefe"
    },
    {
      "source": "release:certified-three-item-jrp-gap",
      "target": "cluster:three-item-jrp-certification-and-logistics-handoff",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists certified-three-item-jrp-gap as a member of Exact three-item replenishment certification and logistics handoff.",
      "inferenceLimit": "The exact rational witness, finite primitive-plus-boundary closure, producer-side verifier and staged logistics protocol support a scoped unrefereed candidate only. They do not establish the exact global constant, independent reconstruction, formal verification, external specialist or editorial peer review, operational validation, savings or field impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/19"
      ],
      "id": "edge:86e4eae9aae61a4e96b8"
    },
    {
      "source": "release:certified-two-item-jrp",
      "target": "cluster:identification-and-robust-operations",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists certified-two-item-jrp as a member of Identification and robust operations.",
      "inferenceLimit": "Identified sets, exact bounds and decision margins are conditional on the declared observation map and model; real-world decision effects are unmeasured.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/4"
      ],
      "id": "edge:fe9d84720d78ef4ef5fa"
    },
    {
      "source": "release:cyclicity-loci-exponential-periods",
      "target": "cluster:cyclicity-and-spectral-compression",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists cyclicity-loci-exponential-periods as a member of Cyclicity and spectral compression.",
      "inferenceLimit": "Exact algebraic or representation-theoretic compression does not discharge every analytic bridge or establish application-level impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/2"
      ],
      "id": "edge:bc70fb75b6222317a85b"
    },
    {
      "source": "release:cyclicity-root-span-low-rank",
      "target": "cluster:cyclicity-and-spectral-compression",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists cyclicity-root-span-low-rank as a member of Cyclicity and spectral compression.",
      "inferenceLimit": "Exact algebraic or representation-theoretic compression does not discharge every analytic bridge or establish application-level impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/2"
      ],
      "id": "edge:fdca7d05911aa27c3d90"
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    {
      "source": "release:cyclicity-support-fusion-atlas",
      "target": "cluster:inverse-root-amplitude-laurent-moments-2026-08-21",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists cyclicity-support-fusion-atlas in the dated successor cluster Inverse-root amplitude, endpoint-moment and Laurent-channel calculus, which supersedes inverse-root-support-fusion-all-degree-2026-08-21.",
      "inferenceLimit": "The combined fixed-seed, polynomial-amplitude, specified-zero-cycle and Laurent local-channel theorems are unrefereed producer-workflow claims. The all-degree fixed-seed and endpoint classifications remain relative to named imported monodromy, finite-projective-group, Ritt and polynomial-moment results. Exact replay, partial Lean controls, same-programme CAS implementations, finite regressions and internal model-assisted review do not establish correctness of the imported results, a finite all-Laurent atlas, independent reconstruction, external specialist review, priority or field impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/18"
      ],
      "id": "edge:e849155088bdae228c94"
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    {
      "source": "release:cyclicity-support-fusion-atlas",
      "target": "cluster:inverse-root-support-fusion-all-degree-2026-08-21",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists cyclicity-support-fusion-atlas in the dated successor cluster All-degree inverse-root classification and rank-preserving extension oracles, which supersedes inverse-root-support-fusion-atlas.",
      "inferenceLimit": "The all-degree low-rank coefficient classification and extension oracle are unrefereed producer-workflow claims relative to named primitive-monodromy and finite-projective-group classifications. Written proof, partial Lean controls, separate same-programme CAS implementations, finite regressions and internal model-assisted re-audits do not establish correctness of imported results, independent reconstruction, external specialist review, priority or field impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/17"
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      "id": "edge:6c1b664e7d0006c95531"
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    {
      "source": "release:cyclicity-support-fusion-atlas",
      "target": "cluster:inverse-root-support-fusion-atlas",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry retains cyclicity-support-fusion-atlas in the historical cluster Inverse-root support, Fourier fusion and bounded coefficient atlases, superseded by inverse-root-support-fusion-all-degree-2026-08-21.",
      "inferenceLimit": "The universal written support and fusion theorems and the exact degree-twenty atlas remain unrefereed producer-workflow claims. Finite atlas replay does not establish the all-degree coefficient conjecture, independent reconstruction, specialist review, priority or field impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/15"
      ],
      "id": "edge:c6dd26d48da7601e8af9"
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    {
      "source": "release:degree-difference-affine-slices",
      "target": "cluster:binary-form-jacobian-and-obstruction",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists degree-difference-affine-slices as a member of Binary-form Jacobian, determinant and obstruction toolkit.",
      "inferenceLimit": "Related internal releases can reuse identities and methods but do not independently validate their shared mathematical or semantic premises.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/1"
      ],
      "id": "edge:3c3ba6d95d4e4008b1ae"
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    {
      "source": "release:degree-independent-rhombus-criterion",
      "target": "cluster:ternary-rhombus-stability-and-dimensional-boundaries-2026-08-31",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists degree-independent-rhombus-criterion as a member of Ternary rhombus stability and higher-dimensional boundary separation.",
      "inferenceLimit": "The written factor-3 ternary proof, explicit coordinate-face quadratic family, strict-exchange impossibility, prior-art-Fano-derived normalized obstruction, hostile controls and deterministic producer replay support an anonymous unrefereed partial theorem candidate. They do not classify the normalized m=4,5,6 cases, prove the factor 3 optimal, exclude every higher-dimensional quantitative criterion, establish historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/33"
      ],
      "id": "edge:999b5f9aadc631f2056e"
    },
    {
      "source": "release:dyck-transpositions-n-log-n",
      "target": "cluster:dyck-two-cut-entropy-2026-09-06",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists dyck-transpositions-n-log-n as a member of Two-cut entropy for the original Dyck rejection walk.",
      "inferenceLimit": "Unrefereed analytic proof candidate for the original length-2n ordered independent-coordinate Dyck rejection walk. No cutoff, sharp upper constant, numerical burn-in guarantee, computational-runtime bound, sampler optimality, external peer review, formal verification or priority clearance.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/44"
      ],
      "id": "edge:f38884a06b1d5c0dd157"
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    {
      "source": "release:erdos-848-all-n",
      "target": "cluster:exact-combinatorial-certificates",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists erdos-848-all-n as a member of Exact combinatorial certificate architecture.",
      "inferenceLimit": "Certificate replay establishes encoded bounded claims; source-to-encoding correctness and independent reconstruction remain separate.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/3"
      ],
      "id": "edge:c5ec8acd4451ed6f29d7"
    },
    {
      "source": "release:exact-low-length-recht-re-inequalities",
      "target": "cluster:sampling-and-optimisation-diagnostics",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists exact-low-length-recht-re-inequalities as a member of Sampling and optimisation diagnostics.",
      "inferenceLimit": "Exact quadratic or finite-factor counterexamples do not establish frequency or magnitude in model-scale nonlinear workloads.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/5"
      ],
      "id": "edge:c0ea2d834233642d720f"
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    {
      "source": "release:exact-smith-invariants-affine-determinant-lines",
      "target": "cluster:binary-form-jacobian-and-obstruction",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists exact-smith-invariants-affine-determinant-lines as a member of Binary-form Jacobian, determinant and obstruction toolkit.",
      "inferenceLimit": "Related internal releases can reuse identities and methods but do not independently validate their shared mathematical or semantic premises.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/1"
      ],
      "id": "edge:e86fde2e0e5db65e747b"
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    {
      "source": "release:exotic-affine-three-spheres",
      "target": "cluster:binary-form-jacobian-and-obstruction",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists exotic-affine-three-spheres as a member of Binary-form Jacobian, determinant and obstruction toolkit.",
      "inferenceLimit": "Related internal releases can reuse identities and methods but do not independently validate their shared mathematical or semantic premises.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/1"
      ],
      "id": "edge:6445762089a4bac6abf4"
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    {
      "source": "release:extremes-do-not-always-maximise",
      "target": "cluster:four-state-monotone-row-diameter-counterexample-2026-08-29",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists extremes-do-not-always-maximise as a member of Four-state monotone row-diameter counterexample and two-spin classification.",
      "inferenceLimit": "The exact four-state witness, all-time two-spin classification, cardinality-minimality proof, bounded zero-field screen and producer replay support an anonymous unrefereed candidate. They do not settle the all-graph zero-field Ising question or AIM diagnostics 1.6(2-3), and do not establish exhaustive novelty, absolute priority, independent reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/26"
      ],
      "id": "edge:6bfed9a64250da520c73"
    },
    {
      "source": "release:factorial-spikes-fi-noetherianity",
      "target": "cluster:factorial-spike-componentwise-fi-noetherianity-separation-2026-08-31",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists factorial-spikes-fi-noetherianity as a member of Factorial-spike componentwise versus FI-Noetherianity separation.",
      "inferenceLimit": "The universal monomial proof, exact native-width factorisation criterion, strict FI-ideal witnesses, four hostile controls and producer replay support an anonymous unrefereed characteristic-free separation of componentwise Noetherianity from FI-Noetherianity. They do not make the sub-FI-algebra finitely generated, produce a non-free module or a module counterexample over the ambient polynomial FI-algebra, establish historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/32"
      ],
      "id": "edge:c0f8e6d8aa4c327dd753"
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    {
      "source": "release:finite-sample-affine-diversification",
      "target": "cluster:finite-sample-affine-signal-to-decision",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists finite-sample-affine-diversification as a member of Finite-sample affine signal-to-decision workflows.",
      "inferenceLimit": "The exact fixed-stem signal band and affine decision rule are conditional on the declared homogeneous model and observation boundary. Producer replay and a finite CRABS benchmark do not establish biological validity, broad comparative utility, independent reconstruction, specialist review, priority or field impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/16"
      ],
      "id": "edge:ac9f3e02eb66fb8acc1f"
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    {
      "source": "release:fisk-toeplitz-deletion-interlacing-through-five",
      "target": "cluster:fisk-toeplitz-deletion-interlacing-finite-certificate-2026-09-01",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists fisk-toeplitz-deletion-interlacing-through-five as a member of Finite Fisk Toeplitz-minor deletion-interlacing certificate.",
      "inferenceLimit": "The written Bezout-interlacing proof, complete 61,192-term degree-five certificate, lower-degree exact recomputation, semantic mutations and producer replay support an anonymous unrefereed finite theorem candidate through five positive alphabet entries. They do not establish degree six beyond the first three minors, zero-boundary cases, Fisk's all-degree conjecture, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, exhaustive novelty, absolute priority or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/36"
      ],
      "id": "edge:f6bae105e61905a6f87a"
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    {
      "source": "release:fixed-d-toeplitz-obstruction",
      "target": "cluster:fixed-d-fi-d-toeplitz-kernel-obstruction-2026-09-04",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists fixed-d-toeplitz-obstruction as a member of Fixed-d FI_d Toeplitz kernel obstruction.",
      "inferenceLimit": "The explicit countable two-colour construction, bidiagonal Toeplitz blocks, symmetric-group coinvariant calculation, Yoneda kernel obstruction, hostile mutations and producer replay support an anonymous unrefereed theorem candidate showing that finitely presented FI_d-modules are not abelian for each fixed finite d at least two over characteristic-zero fields. They do not settle positive characteristic, d=1, related noetherianity categories, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, exhaustive novelty, absolute priority or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/39"
      ],
      "id": "edge:4e2e5b35d8e1f348b109"
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    {
      "source": "release:four-element-rowmotion-periodicity",
      "target": "cluster:four-element-rowmotion-obstruction-2026-08-30",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists four-element-rowmotion-periodicity as a member of Four-element birational and piecewise-linear rowmotion obstruction.",
      "inferenceLimit": "The two exact fixed-point derivative obstructions, exhaustive enumeration and period calculation for every finite poset through size three, five semantic corruptions and producer replay support an anonymous unrefereed theorem candidate. They do not classify d-complete posets, rooted trees or fences, make the four-element Hasse shape new, establish historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/29"
      ],
      "id": "edge:05a74e632c888e237b5b"
    },
    {
      "source": "release:four-point-inductive-cubical-excision",
      "target": "cluster:four-point-inductive-cubical-excision-counterexample-2026-08-30",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists four-point-inductive-cubical-excision as a member of Four-point directed inductive-cubical excision counterexample.",
      "inferenceLimit": "The explicit four-point interior cover, integral relative-chain calculation, matrix certificate, producer-side concordance checks and clean-environment replay support an anonymous unrefereed candidate only for normalized (J_+, inductive-product) cubical singular homology. They do not decide the J_1 or I inductive theories, symmetric graph closures, historical priority, unaffiliated reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/28"
      ],
      "id": "edge:8b19ad8f0237e99a59dd"
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    {
      "source": "release:frankl-concavity-obstruction",
      "target": "cluster:frankl-entropy-obstruction-and-repair",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists frankl-concavity-obstruction as a member of Frankl entropy obstruction and repaired reductions.",
      "inferenceLimit": "The source-specific counterdirection and repaired support reductions do not prove the global candidate inequality, establish a new Frankl bound, validate the uninspected CISS text, or convert producer-side exact and directed-rounding checks into independent mathematical review.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/13"
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      "id": "edge:28d3a19e3220485d4bc4"
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    {
      "source": "release:full-e3-column-polydegree-conjecture",
      "target": "cluster:polydegree-fourier-persistence-certificates",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists full-e3-column-polydegree-conjecture as a member of Polydegree smooth-point and Fourier-persistence certificates.",
      "inferenceLimit": "The all-degree conclusion depends jointly on the stated Jacobian smooth-point reduction, asymptotic Fourier limit, exact eventual envelope and finite Arb bridge. Producer-side replay and reuse of the earlier smooth-point package do not constitute independent theorem reconstruction, specialist review or evidence for the conjectural fixed-e programme.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/10"
      ],
      "id": "edge:44bc813c8a3b98302919"
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    {
      "source": "release:full-e4-polydegree-column",
      "target": "cluster:polydegree-e4-fourier-formal-boundary-bundle",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists full-e4-polydegree-column as a member of Effective e=4 Polydegree persistence and scoped companion assurance.",
      "inferenceLimit": "The all-degree e=4 candidate depends on the published specialization criterion, the stated smooth-zero and Fourier-persistence bridges, a producer-side finite Arb ledger and an analytic tail. The scoped Lean companion and conditional boundary theorem do not independently confirm the Polydegree argument or establish Furter's R(3), JC2, HC4, priority or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/11"
      ],
      "id": "edge:cff39385534d8476b698"
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    {
      "source": "release:furter-r3-through-299",
      "target": "cluster:finite-polynomial-rigidity-certificates",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists furter-r3-through-299 as a member of Finite polynomial-rigidity certificates and executable frontier.",
      "inferenceLimit": "Exact finite-field certificates plus properness establish only the stated finite R(3,n) instances. They do not supply an all-degree theorem, independent reconstruction, a proof of the unrestricted Strong Factorial Conjecture or the general Polydegree Conjecture, or evidence of research-workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/14"
      ],
      "id": "edge:e853d32fe368f4149db4"
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    {
      "source": "release:hahn-ewens-mixing-theorem",
      "target": "cluster:cyclicity-and-spectral-compression",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists hahn-ewens-mixing-theorem as a member of Cyclicity and spectral compression.",
      "inferenceLimit": "Exact algebraic or representation-theoretic compression does not discharge every analytic bridge or establish application-level impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/2"
      ],
      "id": "edge:d69a61ea92bf2832c50f"
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    {
      "source": "release:hc4-five-support-structural-reductions",
      "target": "cluster:hc4-binary-decimic-normal-layer-structural-reductions-2026-09-01",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists hc4-five-support-structural-reductions as a member of HC4 binary-decimic normal-layer structural reductions.",
      "inferenceLimit": "The exact five-support certificates, all-31-generator tangent radical containment, three rational secant colon elements, fail-closed fourth-target recovery and prospectively frozen 16-column rational source-kernel theorem support an anonymous unrefereed computer-assisted structural-reductions candidate. They do not prove inhomogeneous fourth-target membership, colon equality, saturation, secant-orbit closure, full normal-layer or polynomial-level closure, HC4, JC2, unaffiliated reconstruction, formal verification, external specialist review, editorial peer review, absolute priority or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/34"
      ],
      "id": "edge:057089354dcf01b076be"
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    {
      "source": "release:hilbert-eight-points-reducedness",
      "target": "cluster:hilb8-local-reducedness-2026-09-07",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists hilbert-eight-points-reducedness as a member of Hilbert-scheme local reducedness and mixed-prime finite-module comparison.",
      "inferenceLimit": "Source-specific unrefereed characteristic-zero proof candidate; finite arithmetic and internal replay do not establish external validation or transfer to other Hilbert schemes.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/45"
      ],
      "id": "edge:51995649f6dc66baf410"
    },
    {
      "source": "release:irreducible-pushforwards-quartic-transitions",
      "target": "cluster:grand-problem-salvage",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists irreducible-pushforwards-quartic-transitions as a member of Grand-problem salvage.",
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        "https://evidencepress.org/api/method-registry.json#/methodClusters/6"
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      "basis": "The method registry lists linear-nonbacktracking-jordan-growth as a member of Non-backtracking Jordan valuation and graph realization.",
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        "https://evidencepress.org/api/method-registry.json#/methodClusters/42"
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      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists lps-structural-reductions as a member of Fixed-width LPS reductions, quartic gauge repair and p-adic signals.",
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      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists negative-square-energy-five-vertex-valley as a member of Negative square-energy ordered valley and five-vertex classification.",
      "inferenceLimit": "The exact five-vertex prescribed-order valley, structural minimality through four vertices, exhaustive five-vertex census, favourable-order boundary witness and producer replay support an anonymous unrefereed candidate. They refute only universal prescribed-order peak-unimodality and do not settle either favourable-order existential formulation or establish exhaustive novelty, absolute priority, unaffiliated reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/27"
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      "id": "edge:86724535cc69e6a8b588"
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    {
      "source": "release:o01d0-polar-fibre-structural-reductions",
      "target": "cluster:o01d0-hermite-boundary-and-falsification-2026-08-28",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists o01d0-polar-fibre-structural-reductions as a member of O-01d0 polar-fibre, Hermite-boundary, and falsification reductions.",
      "inferenceLimit": "The fixed-index properness criterion, Hermite incidence and boundary lemmas, exact architecture failures, and bounded pair-content scans expose four executable gates. They do not establish uniform O-01d0, AF5 transversality, any linked conjecture, independent reconstruction, formal verification, external specialist review, priority, or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/24"
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      "id": "edge:688f0480050db300c16c"
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      "source": "release:odd-order-one-third-popular-differences",
      "target": "cluster:odd-order-popular-difference-counterexample-2026-08-29",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists odd-order-one-third-popular-differences as a member of Three-layer popular-difference counterexample and endpoint obstruction.",
      "inferenceLimit": "The exact C21 witness, elementary three-layer count, below-2/5 odd-cyclic obstruction, producer replay and targeted source audit support an anonymous unrefereed candidate. They do not establish sufficiency or sharpness at 2/5, witness minimality, exhaustive novelty, absolute priority, independent reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/25"
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      "id": "edge:a8142c42b4b9b61ae706"
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    {
      "source": "release:pinching-free-normal-cover",
      "target": "cluster:free-normal-cover-all-fuchsian-pinching-2026-09-01",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists pinching-free-normal-cover as a member of Free normal cover and all-Fuchsian pinching construction.",
      "inferenceLimit": "The fixed-kernel construction, explicit reduced-surface and all-Fuchsian group-space bridge, imported-theorem hypothesis maps, fixed-width collar estimate, hostile controls and producer replay support an anonymous unrefereed all-Fuchsian strengthening candidate. They do not establish a first solution under the broad group-deformation reading, monotonicity, an exact exponent formula, global deformation-space identification, historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/35"
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      "id": "edge:7fd4eb7a29e0a905c926"
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    {
      "source": "release:potts-censoring-counterexample",
      "target": "cluster:potts-finite-word-censoring-obstruction-2026-09-06",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists potts-censoring-counterexample as a member of Exact finite-word ferromagnetic Potts censoring obstruction.",
      "inferenceLimit": "Unrefereed exact finite-horizon q=3 counterexample candidate. No mixing-time, random-scan, every-q, minimality, practical speed-up, exhaustive novelty, priority, unaffiliated validation, formal proof or impact claim.",
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      "source": "release:pure-tensor-analytic-rank-counterexample",
      "target": "cluster:pure-tensor-analytic-rank-normalization-obstruction-2026-08-30",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists pure-tensor-analytic-rank-counterexample as a member of Pure-tensor analytic-rank normalization obstruction.",
      "inferenceLimit": "The exact pure-tensor and diagonal-bias formulas, all-power written proof, direct coefficient enumeration, seven semantic controls and producer replay support an anonymous unrefereed conditional counterexample to one literal unnormalised analytic-rank comparator. They do not reconstruct historical intention, refute normalized or powered-identity formulations, settle partition rank, establish novelty or priority, or provide unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/30"
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      "id": "edge:72acc58d82d8eb7ddf55"
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      "source": "release:random-reshuffling-baseline-policy",
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      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists random-reshuffling-baseline-policy as a member of Sampling and optimisation diagnostics.",
      "inferenceLimit": "Exact quadratic or finite-factor counterexamples do not establish frequency or magnitude in model-scale nonlinear workloads.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/5"
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      "id": "edge:876414f7175255c6f431"
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      "source": "release:rbm31-exact-kl-radius",
      "target": "cluster:rbm31-channel-convex-cover-radius-2026-09-05",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists rbm31-exact-kl-radius as a member of Reverse-channel and exact convex-cover KL radius certificate.",
      "inferenceLimit": "Anonymous AI-assisted unrefereed computer-assisted theorem candidate for the exact three-bit two-product-mixture KL radius, with a constructive rational interface and a non-sharp conditioning corollary. Not unaffiliated verification, formal proof, authenticated specialist review, journal peer review, exhaustive novelty, priority, a four-star rating or demonstrated impact.",
      "sourceRefs": [
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      "id": "edge:fc118c0aaf41fe5f7e40"
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    {
      "source": "release:rbm43-eight-point-obstruction",
      "target": "cluster:rbm43-eight-point-leakage-obstruction-2026-09-06",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists rbm43-eight-point-obstruction as a member of RBM(4,3) finite-selector leakage obstruction.",
      "inferenceLimit": "Unrefereed fixed classical real binary RBM(4,3) obstruction; no exact hidden threshold, minimality, sharp error, unaffiliated validation, formal proof, priority or impact claim.",
      "sourceRefs": [
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      "id": "edge:af4d271b240b89693102"
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    {
      "source": "release:reducible-incidence-divisors",
      "target": "cluster:binary-form-jacobian-and-obstruction",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists reducible-incidence-divisors as a member of Binary-form Jacobian, determinant and obstruction toolkit.",
      "inferenceLimit": "Related internal releases can reuse identities and methods but do not independently validate their shared mathematical or semantic premises.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/1"
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      "id": "edge:4ea3587ddab47eb2ec2f"
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      "source": "release:s6-extension-results-candidate",
      "target": "cluster:s6-conditional-geometry-and-adjudication",
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      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists s6-extension-results-candidate as a member of Conditional geometry and executable adjudication around a claimed complex S6.",
      "inferenceLimit": "Exact arithmetic, symbolic replay and written arguments under explicit hypotheses do not establish the source manuscript's compact complex threefold, smoothness, S6 topology, independent reconstruction, external specialist review, priority or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/21"
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      "id": "edge:828503b0b6dfb150ce87"
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      "source": "release:sfs-identifiability-audit",
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      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists sfs-identifiability-audit as a member of Certified demographic identifiability auditing.",
      "inferenceLimit": "Certified identified-set bounds and pre-registered audits expose what declared error models concede without establishing that any declared model is scientifically correct, that the underlying spectra are artefact-free, or that a setting-conditional verdict settles the biological dispute.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/8"
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      "id": "edge:f93cee06125e4a55c8c6"
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    {
      "source": "release:sharp-four-factor-cohen-macaulay-obstruction",
      "target": "cluster:sharp-four-factor-schubert-surface-obstruction-2026-09-04",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists sharp-four-factor-cohen-macaulay-obstruction as a member of Sharp coordinate Schubert surface deformation obstruction.",
      "inferenceLimit": "The Stanley–Reisner connectivity criterion, multidegree-to-rank-two-matroid obstruction, complete-multipartite realization, scheme-theoretic degeneration bridge, sharp path and exact finite replay support an anonymous unrefereed classification candidate for coordinate Schubert surface unions in (P1)^n. They do not classify higher-dimensional Schubert unions or arbitrary flag varieties, supply unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, exhaustive novelty, absolute priority or workflow impact.",
      "sourceRefs": [
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      "id": "edge:c3e54648bdf577f4cdb4"
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      "source": "release:sharp-quartic-hadamard-powers",
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      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists sharp-quartic-hadamard-powers as a member of Quartic coefficient-power boundary classification.",
      "inferenceLimit": "Unrefereed quartic theorem candidate with exact auxiliary checks; no external validation, formal proof, full AIM solution, all-degree classification, historical priority, four-star grade or impact established.",
      "sourceRefs": [
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      "id": "edge:7ca4cb65193204569b67"
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    {
      "source": "release:smooth-point-certificates-polydegree-containments",
      "target": "cluster:binary-form-jacobian-and-obstruction",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists smooth-point-certificates-polydegree-containments as a member of Binary-form Jacobian, determinant and obstruction toolkit.",
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      "sourceRefs": [
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      "id": "edge:6ba265f8ef640600905f"
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    {
      "source": "release:stocks-are-not-flows",
      "target": "cluster:identification-and-robust-operations",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists stocks-are-not-flows as a member of Identification and robust operations.",
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      "sourceRefs": [
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      "source": "release:txgraffiti-c3-resolution",
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      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists txgraffiti-c3-resolution as a member of Exact combinatorial certificate architecture.",
      "inferenceLimit": "Certificate replay establishes encoded bounded claims; source-to-encoding correctness and independent reconstruction remain separate.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/3"
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      "id": "edge:7f39bf8f65206444b6ec"
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      "source": "release:txgraffiti-order48-successor",
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      "knowledgeStatus": "asserted",
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      "inferenceLimit": "The explicit graph, witnesses and proof-tree replay establish only the stated order-48 object theorem and counterexample-order upper bound. They do not establish global minimality, uniqueness, independent reconstruction, formal verification, specialist review, priority or workflow impact.",
      "sourceRefs": [
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      "id": "edge:76126c9930f75e98f231"
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      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists unbounded-bns-component-orbits as a member of Free-by-cyclic BNS component-orbit obstruction.",
      "inferenceLimit": "The written all-m proof, exact 2m+2 BNS component count conditional on Cashen-Levitt Corollary 2.10, componentwise kernel-rank minima, at-least-m+1 outer-orbit obstruction, eight claim-boundary controls and producer replay support an anonymous unrefereed theorem candidate. They do not compute the exact orbit count or Out(G_m), replace the imported BNS theorem, establish historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/31"
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      "id": "edge:d0d4a1e4f2c128702711"
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    {
      "source": "release:unique-answer-not-identified",
      "target": "cluster:cross-field-identification-and-selector-provenance",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists unique-answer-not-identified as a member of Cross-field identification and selector provenance.",
      "inferenceLimit": "A common Selector Ledger can expose assumption-supported narrowing across fields without establishing that their observation maps share one exact symmetry, that the field mappings are independently validated, or that the reporting instrument improves practice.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/7"
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      "id": "edge:a9bdb414541bbd386ac2"
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    {
      "source": "release:vr2-k4-equals-20",
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      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists vr2-k4-equals-20 as a member of Exact combinatorial certificate architecture.",
      "inferenceLimit": "Certificate replay establishes encoded bounded claims; source-to-encoding correctness and independent reconstruction remain separate.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/3"
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      "id": "edge:84cf3198d2326b29f575"
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      "source": "release:wales-20mph-casualty-attribution",
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      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
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      "basis": "The method registry lists wales-20mph-casualty-attribution as a member of Wales policy-attribution identification audit.",
      "inferenceLimit": "The constructive witness establishes non-identification only for the registered aggregate corpus, affected-road estimand and admitted rival class; it does not estimate the policy effect, settle policy merit or establish workflow impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/9"
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      "id": "edge:bbebc662491ed6d981cf"
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    {
      "source": "release:z20-equals-6",
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      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists z20-equals-6 as a member of Exact combinatorial certificate architecture.",
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      "sourceRefs": [
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      "id": "edge:bcf77083ee91b7f84169"
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      "source": "release:affine-diversification-fibres",
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      "knowledgeStatus": "asserted",
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      "basis": "The finite-sample successor explicitly extends the predecessor's affine cumulative-loss fibre, fixed-signal sharp bounds and endpoint-sampling diagnostic by adding signal uncertainty, three-valued decisions and a frozen CRABS comparison.",
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      "sourceRefs": [
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      "source": "release:amplitude-modules-fused-support-bautin-bound",
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      "basis": "The root-span release explicitly cites the cyclicity-loci release as its predecessor and extends the same fixed-seed cyclicity programme.",
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      "sourceRefs": [
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      "source": "release:bordered-jacobian-foundations",
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      "source": "release:certified-three-item-jrp-gap",
      "target": "lineage:joint-replenishment-exact-certification-programme",
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      "knowledgeStatus": "asserted",
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      "basis": "The three-item successor explicitly extends the parent's common-origin model, independent-cap reduction boundary, exact two-item interval and certificate-first conventions with a distinct primitive-triple tail architecture and logistics evaluation handoff.",
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      "sourceRefs": [
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      "source": "release:certified-two-item-jrp",
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      "knowledgeStatus": "asserted",
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      "sourceRefs": [
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      "knowledgeStatus": "asserted",
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      "basis": "The root-span release explicitly cites the cyclicity-loci release as its predecessor and extends the same fixed-seed cyclicity programme.",
      "inferenceLimit": "The child release reuses the fixed-seed framework and therefore does not independently confirm the parent release or its analytic bridge.",
      "sourceRefs": [
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      "source": "release:cyclicity-root-span-low-rank",
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      "knowledgeStatus": "asserted",
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      "sourceRefs": [
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      "source": "release:cyclicity-support-fusion-atlas",
      "target": "lineage:cyclicity-programme",
      "predicate": "member-of-lineage",
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