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      "label": "The Davies–Levitin lens, for every n",
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      "fullTitle": "A four-element obstruction to birational and piecewise-linear rowmotion periodicity",
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      "fullTitle": "A concavity obstruction and repaired support reductions in a Frankl entropy programme",
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      "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/40"
      ]
    },
    {
      "id": "cluster:bilagrangian-smoothness-fixed-locus-2026-09-12",
      "type": "cluster",
      "label": "Bi-Lagrangian smoothness through a reduced chart and fixed locus",
      "description": "Unrefereed written criterion; classical ingredients, finite producer replay and internal review do not establish external validation, priority, orbit classification or impact.",
      "sharedBoundary": "Unrefereed written criterion; classical ingredients, finite producer replay and internal review do not establish external validation, priority, orbit classification or impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Abilagrangian-smoothness-fixed-locus-2026-09-12",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/1"
      ]
    },
    {
      "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/4"
      ]
    },
    {
      "id": "cluster:bounded-product-reference-gradient-2026-09-08",
      "type": "cluster",
      "label": "All-time reference-gradient comparison for product-weight transpositions",
      "description": "Unrefereed proof candidate for the product-weight branch only. Producer finite checks and internal model-assisted editorial review are not independent reproduction, unaffiliated specialist review or formal verification. No explicit cutoff location, optimal window, limiting profile, nonproduct resolution or historical priority is claimed.",
      "sharedBoundary": "Unrefereed proof candidate for the product-weight branch only. Producer finite checks and internal model-assisted editorial review are not independent reproduction, unaffiliated specialist review or formal verification. No explicit cutoff location, optimal window, limiting profile, nonproduct resolution or historical priority is claimed.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Abounded-product-reference-gradient-2026-09-08",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/58"
      ]
    },
    {
      "id": "cluster:casas-alvero-eight-term",
      "type": "cluster",
      "label": "Degree-twenty sparsity and ramified root-cluster obstructions",
      "description": "Complete centered seven-term support exclusion with written valuation transfer and exact finite checks; no full degree-twenty solution, external assurance or priority promotion.",
      "sharedBoundary": "Complete centered seven-term support exclusion with written valuation transfer and exact finite checks; no full degree-twenty solution, external assurance or priority promotion.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Acasas-alvero-eight-term",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/71"
      ]
    },
    {
      "id": "cluster:catenary-placement-classification",
      "type": "cluster",
      "label": "Placement classification in physical compartment chains",
      "description": "Written all-length identifiability candidate with finite supporting checks; ideal known-gain transfer data; no external validation, formal proof, priority or practical estimation benefit.",
      "sharedBoundary": "Written all-length identifiability candidate with finite supporting checks; ideal known-gain transfer data; no external validation, formal proof, priority or practical estimation benefit.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Acatenary-placement-classification",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/70"
      ]
    },
    {
      "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/11"
      ]
    },
    {
      "id": "cluster:cooper-spencer-temporal-unimodality-2026-09-19",
      "type": "cluster",
      "label": "Parity-sensitive temporal-unimodality counterexample certificates",
      "description": "Unrefereed written proof with exact finite checks; no first priority or external assurance established.",
      "sharedBoundary": "Unrefereed written proof with exact finite checks; no first priority or external assurance established.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Acooper-spencer-temporal-unimodality-2026-09-19",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/63"
      ]
    },
    {
      "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/10"
      ]
    },
    {
      "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/5"
      ]
    },
    {
      "id": "cluster:davies-levitin-lens-conjecture",
      "type": "cluster",
      "label": "The Davies–Levitin lens, for every n",
      "description": "Unrefereed candidate. A written proof with two essential interval certificates; formal verification, external review and unconditional priority are not established.",
      "sharedBoundary": "Unrefereed candidate. A written proof with two essential interval certificates; formal verification, external review and unconditional priority are not established.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Adavies-levitin-lens-conjecture",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/73"
      ]
    },
    {
      "id": "cluster:decision-geometry",
      "type": "cluster",
      "label": "Triangle-network information geometry and boundary certification",
      "description": "Unrefereed model-conditional analytic candidate. Exact rational receipt checks and numerical experiments do not establish universal proof, biological validity, independent reproduction, external review, priority or measured impact.",
      "sharedBoundary": "Unrefereed model-conditional analytic candidate. Exact rational receipt checks and numerical experiments do not establish universal proof, biological validity, independent reproduction, external review, priority or measured impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Adecision-geometry",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/77"
      ]
    },
    {
      "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/47"
      ]
    },
    {
      "id": "cluster:equivariant-tree-torsors-2026-09-08",
      "type": "cluster",
      "label": "Equivariant torsors through restriction kernels and graph symmetries",
      "description": "Unrefereed written proof candidate for explicitly defined minimum equivariance. No unique canonical action, minor-consistent algorithm, efficient general runtime, established priority, external specialist validation or formal verification is claimed.",
      "sharedBoundary": "Unrefereed written proof candidate for explicitly defined minimum equivariance. No unique canonical action, minor-consistent algorithm, efficient general runtime, established priority, external specialist validation or formal verification is claimed.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aequivariant-tree-torsors-2026-09-08",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/54"
      ]
    },
    {
      "id": "cluster:essential-hurwitz-trace-cancellation-2026-09-07",
      "type": "cluster",
      "label": "Essential Hurwitz trace formula and global cancellation",
      "description": "Unrefereed compact formula and uniform written proof candidate. Producer finite replay and internal AI review do not establish unaffiliated whole-proof acceptance, formal verification, historical priority or practical improvement.",
      "sharedBoundary": "Unrefereed compact formula and uniform written proof candidate. Producer finite replay and internal AI review do not establish unaffiliated whole-proof acceptance, formal verification, historical priority or practical improvement.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aessential-hurwitz-trace-cancellation-2026-09-07",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/51"
      ]
    },
    {
      "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/6"
      ]
    },
    {
      "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/35"
      ]
    },
    {
      "id": "cluster:fano-tensor-resultant-geometry-2026-09-19",
      "type": "cluster",
      "label": "Fano tensor resultant and eigenscheme certificates",
      "description": "Unrefereed computational theorem candidate. Default replay does not freshly repeat the complete thirty-prime computation or every finite number-field decomposition. No unaffiliated validation, formal proof, exhaustive priority or impact claim.",
      "sharedBoundary": "Unrefereed computational theorem candidate. Default replay does not freshly repeat the complete thirty-prime computation or every finite number-field decomposition. No unaffiliated validation, formal proof, exhaustive priority or impact claim.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Afano-tensor-resultant-geometry-2026-09-19",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/64"
      ]
    },
    {
      "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/17"
      ]
    },
    {
      "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/19"
      ]
    },
    {
      "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/39"
      ]
    },
    {
      "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/42"
      ]
    },
    {
      "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/32"
      ]
    },
    {
      "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/31"
      ]
    },
    {
      "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/29"
      ]
    },
    {
      "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/16"
      ]
    },
    {
      "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/34"
      ]
    },
    {
      "id": "cluster:free-fermion-frustration-graphs",
      "type": "cluster",
      "label": "Frustration graphs, free spectra and occupation certificates",
      "description": "Faithful graph semantics and complete spectral multiplicities are necessary; numerical selection is not an all-coupling proof.",
      "sharedBoundary": "Faithful graph semantics and complete spectral multiplicities are necessary; numerical selection is not an all-coupling proof.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Afree-fermion-frustration-graphs",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/78"
      ]
    },
    {
      "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/38"
      ]
    },
    {
      "id": "cluster:full-moment-graph-faces-2026-09-09",
      "type": "cluster",
      "label": "Full-moment graph faces and persistent algebraic obstructions",
      "description": "Unrefereed candidate with a complete written argument as both n and d vary. Finite replay is supporting evidence, not universal certification. Fixed-n unboundedness, optimal parameters, historical priority, external review, formal verification and impact are not established.",
      "sharedBoundary": "Unrefereed candidate with a complete written argument as both n and d vary. Finite replay is supporting evidence, not universal certification. Fixed-n unboundedness, optimal parameters, historical priority, external review, formal verification and impact are not established.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Afull-moment-graph-faces-2026-09-09",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/61"
      ]
    },
    {
      "id": "cluster:gk-overlapping-incidence-images-2026-09-20",
      "type": "cluster",
      "label": "Overlapping incidence images and degenerate attachment",
      "description": "Unrefereed written topology proof supported by exact algebraic checks; no external validation or stability claim.",
      "sharedBoundary": "Unrefereed written topology proof supported by exact algebraic checks; no external validation or stability claim.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Agk-overlapping-incidence-images-2026-09-20",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/65"
      ]
    },
    {
      "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/9"
      ]
    },
    {
      "id": "cluster:graph-product-picard-integral-2026-09-08",
      "type": "cluster",
      "label": "Graph-product Picard integral compatibility",
      "description": "Unrefereed uniform written proof candidate under explicit branch-local conventions. Producer exact diagnostics and internal AI review do not establish unaffiliated whole-proof acceptance, formal verification, historical priority or impact.",
      "sharedBoundary": "Unrefereed uniform written proof candidate under explicit branch-local conventions. Producer exact diagnostics and internal AI review do not establish unaffiliated whole-proof acceptance, formal verification, historical priority or impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Agraph-product-picard-integral-2026-09-08",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/53"
      ]
    },
    {
      "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/37"
      ]
    },
    {
      "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/48"
      ]
    },
    {
      "id": "cluster:hilbert-series-matrix-septic-invariants",
      "type": "cluster",
      "label": "Matrix invariants: nine new Hilbert series",
      "description": "Unrefereed candidate. Computer-assisted theorems for nine matrix cases; the septic series proved through degree 760 and conditionally beyond; no formal verification or external review.",
      "sharedBoundary": "Unrefereed candidate. Computer-assisted theorems for nine matrix cases; the septic series proved through degree 760 and conditionally beyond; no formal verification or external review.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Ahilbert-series-matrix-septic-invariants",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/74"
      ]
    },
    {
      "id": "cluster:hilbert-series-ternary-septic-octic-nonic",
      "type": "cluster",
      "label": "Invariants of plane curves of degree 7, 8 and 9",
      "description": "Unrefereed candidate; computer-assisted theorems for d = 7, 8, 9 by known methods; no formal verification or external review.",
      "sharedBoundary": "Unrefereed candidate; computer-assisted theorems for d = 7, 8, 9 by known methods; no formal verification or external review.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Ahilbert-series-ternary-septic-octic-nonic",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/75"
      ]
    },
    {
      "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/7"
      ]
    },
    {
      "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/21"
      ]
    },
    {
      "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/20"
      ]
    },
    {
      "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/18"
      ]
    },
    {
      "id": "cluster:local-minor-ratio-transfer-2026-09-07",
      "type": "cluster",
      "label": "Local minor-ratio sharpness through simultaneous transfer",
      "description": "Unrefereed complete written proof candidate for an explicitly normalized local condition. No independent specialist validation, formal verification, absolute priority clearance, optimal testing complexity or identity with the omitted workshop formula is claimed.",
      "sharedBoundary": "Unrefereed complete written proof candidate for an explicitly normalized local condition. No independent specialist validation, formal verification, absolute priority clearance, optimal testing complexity or identity with the omitted workshop formula is claimed.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Alocal-minor-ratio-transfer-2026-09-07",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/52"
      ]
    },
    {
      "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/25"
      ]
    },
    {
      "id": "cluster:median-radius-integer-separation",
      "type": "cluster",
      "label": "Integer separation and strict graph improvement",
      "description": "Exact dimension-preserving transfer; singleton method illustration, not evidence of research lineage or acceleration.",
      "sharedBoundary": "Exact dimension-preserving transfer; singleton method illustration, not evidence of research lineage or acceleration.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Amedian-radius-integer-separation",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/68"
      ]
    },
    {
      "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/30"
      ]
    },
    {
      "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/45"
      ]
    },
    {
      "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/27"
      ]
    },
    {
      "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/28"
      ]
    },
    {
      "id": "cluster:orthogonal-algebraicity-2026-09-08",
      "type": "cluster",
      "label": "Orthogonal character asymptotics and algebraicity",
      "description": "Unrefereed written classification candidate for fixed nonzero genuine algebraic O(m,C) representations. No arbitrary tca-module classification, virtual-character extension, historical priority, external specialist validation or formal verification is claimed.",
      "sharedBoundary": "Unrefereed written classification candidate for fixed nonzero genuine algebraic O(m,C) representations. No arbitrary tca-module classification, virtual-character extension, historical priority, external specialist validation or formal verification is claimed.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aorthogonal-algebraicity-2026-09-08",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/57"
      ]
    },
    {
      "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/14"
      ]
    },
    {
      "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/13"
      ]
    },
    {
      "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/46"
      ]
    },
    {
      "id": "cluster:ptolemaic-negative-type",
      "type": "cluster",
      "label": "Sharp negative type of finite Ptolemaic metrics",
      "description": "Unrefereed analytic proof candidate for all m >= 6, with complete-split sharpness witnesses. Symbolic checks, finite examples and numerical stress tests are corroboration, not a universal proof certificate. No formal verification, independent reproduction, external specialist review or real-world impact is established.",
      "sharedBoundary": "Unrefereed analytic proof candidate for all m >= 6, with complete-split sharpness witnesses. Symbolic checks, finite examples and numerical stress tests are corroboration, not a universal proof certificate. No formal verification, independent reproduction, external specialist review or real-world impact is established.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aptolemaic-negative-type",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/76"
      ]
    },
    {
      "id": "cluster:ptolemaic-split-stability",
      "type": "cluster",
      "label": "Ptolemaic tangent-cone stability",
      "description": "Exact cone certificates plus a written nonlinear and spectral bridge; global dependency scope remains separate.",
      "sharedBoundary": "Exact cone certificates plus a written nonlinear and spectral bridge; global dependency scope remains separate.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aptolemaic-split-stability",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/79"
      ]
    },
    {
      "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/33"
      ]
    },
    {
      "id": "cluster:quartic-boundary-interlacing-2026-09-12",
      "type": "cluster",
      "label": "Quartic inverse-coefficient boundary interlacing",
      "description": "Uniform written boundary comparison; affine geometry uses external R3. Internal review and finite replay are not external validation.",
      "sharedBoundary": "Uniform written boundary comparison; affine geometry uses external R3. Internal review and finite replay are not external validation.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aquartic-boundary-interlacing-2026-09-12",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/0"
      ]
    },
    {
      "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/44"
      ]
    },
    {
      "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.",
      "sharedBoundary": "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.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Arbm31-channel-convex-cover-radius-2026-09-05",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/43"
      ]
    },
    {
      "id": "cluster:rbm43-eight-point-leakage-obstruction-2026-09-06",
      "type": "cluster",
      "label": "RBM(4,3) finite-selector leakage obstruction",
      "description": "Unrefereed fixed classical real binary RBM(4,3) obstruction; no exact hidden threshold, minimality, sharp error, unaffiliated validation, formal proof, priority or impact claim.",
      "sharedBoundary": "Unrefereed fixed classical real binary RBM(4,3) obstruction; no exact hidden threshold, minimality, sharp error, unaffiliated validation, formal proof, priority or impact claim.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Arbm43-eight-point-leakage-obstruction-2026-09-06",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/3"
      ]
    },
    {
      "id": "cluster:s6-conditional-geometry-and-adjudication",
      "type": "cluster",
      "label": "Conditional geometry and executable adjudication around a claimed complex S6",
      "description": "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.",
      "sharedBoundary": "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.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3As6-conditional-geometry-and-adjudication",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/24"
      ]
    },
    {
      "id": "cluster:sampling-and-optimisation-diagnostics",
      "type": "cluster",
      "label": "Sampling and optimisation diagnostics",
      "description": "Exact quadratic or finite-factor counterexamples do not establish frequency or magnitude in model-scale nonlinear workloads.",
      "sharedBoundary": "Exact quadratic or finite-factor counterexamples do not establish frequency or magnitude in model-scale nonlinear workloads.",
      "memberCount": 2,
      "scopeStatus": "broad-cluster",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Asampling-and-optimisation-diagnostics",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/8"
      ]
    },
    {
      "id": "cluster:seymour-second-neighbourhood-2delta3",
      "type": "cluster",
      "label": "Dense-case structure and certified order bounds for the second neighbourhood conjecture",
      "description": "Written necessary conditions at n = 2δ+3 used as SAT constraints with retained, doubly checked LRAT refutations; exact losing-density counterexamples; no proof of the conjecture or of the case n = 2δ+3, no formal verification of the reduction, external assurance or priority promotion.",
      "sharedBoundary": "Written necessary conditions at n = 2δ+3 used as SAT constraints with retained, doubly checked LRAT refutations; exact losing-density counterexamples; no proof of the conjecture or of the case n = 2δ+3, no formal verification of the reduction, external assurance or priority promotion.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aseymour-second-neighbourhood-2delta3",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/72"
      ]
    },
    {
      "id": "cluster:sharp-four-factor-schubert-surface-obstruction-2026-09-04",
      "type": "cluster",
      "label": "Sharp coordinate Schubert surface deformation obstruction",
      "description": "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.",
      "sharedBoundary": "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.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Asharp-four-factor-schubert-surface-obstruction-2026-09-04",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/41"
      ]
    },
    {
      "id": "cluster:small-world-physical-clocks-2026-09-08",
      "type": "cluster",
      "label": "Small-world random spacing, physical clocks and parity",
      "description": "Unrefereed candidate proof for four fixed-weight clocks. Sparse bounds differ by polylogarithmic factors. No vanishing drift, arbitrary kernel, historical priority, external specialist validation, formal verification or impact claim.",
      "sharedBoundary": "Unrefereed candidate proof for four fixed-weight clocks. Sparse bounds differ by polylogarithmic factors. No vanishing drift, arbitrary kernel, historical priority, external specialist validation, formal verification or impact claim.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Asmall-world-physical-clocks-2026-09-08",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/59"
      ]
    },
    {
      "id": "cluster:stable-power-concavity-boundary-2026-09-08",
      "type": "cluster",
      "label": "Stable density curvature and uniform Gaussian-tail matching",
      "description": "Unrefereed analytic proof candidate with a finite Arb certificate. No optimal fixed-index closed form, weaker CDF-concavity conclusion, historical priority, external specialist review, formal verification or practical impact is claimed.",
      "sharedBoundary": "Unrefereed analytic proof candidate with a finite Arb certificate. No optimal fixed-index closed form, weaker CDF-concavity conclusion, historical priority, external specialist review, formal verification or practical impact is claimed.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Astable-power-concavity-boundary-2026-09-08",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/55"
      ]
    },
    {
      "id": "cluster:subset-profile-obstruction-2026-09-11",
      "type": "cluster",
      "label": "Observable subset events and profile obstructions",
      "description": "Unrefereed candidate; one-sided event bounds and exact finite checks do not supply a replacement profile or external validation.",
      "sharedBoundary": "Unrefereed candidate; one-sided event bounds and exact finite checks do not supply a replacement profile or external validation.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Asubset-profile-obstruction-2026-09-11",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/60"
      ]
    },
    {
      "id": "cluster:symmetric-free-unimodality-moment-endpoints-2026-09-07",
      "type": "cluster",
      "label": "Symmetric free-additive unimodality through moment endpoints",
      "description": "Unrefereed analytic proof candidate. Scoped symbolic identities and internal model review do not establish external whole-proof validation, free strong unimodality, global edge smoothness, priority or impact.",
      "sharedBoundary": "Unrefereed analytic proof candidate. Scoped symbolic identities and internal model review do not establish external whole-proof validation, free strong unimodality, global edge smoothness, priority or impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Asymmetric-free-unimodality-moment-endpoints-2026-09-07",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/50"
      ]
    },
    {
      "id": "cluster:tcell-exact-five-scalar-certificate",
      "type": "cluster",
      "label": "Scalar equilibrium reduction and exact sign counts",
      "description": "Model-specific chain reconstruction and Descartes certificate; singleton method illustration, not a research lineage.",
      "sharedBoundary": "Model-specific chain reconstruction and Descartes certificate; singleton method illustration, not a research lineage.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Atcell-exact-five-scalar-certificate",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/67"
      ]
    },
    {
      "id": "cluster:ternary-rhombus-stability-and-dimensional-boundaries-2026-08-31",
      "type": "cluster",
      "label": "Ternary rhombus stability and higher-dimensional boundary separation",
      "description": "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.",
      "sharedBoundary": "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.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aternary-rhombus-stability-and-dimensional-boundaries-2026-08-31",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/36"
      ]
    },
    {
      "id": "cluster:three-coloured-paths-partial-results-2026-09-08",
      "type": "cluster",
      "label": "Three-coloured path partial theorems and repair obstructions",
      "description": "Unrefereed partial-results dossier; the parent problem remains unresolved. Conditional catalogue coverage, finite exclusions and repair obstructions do not establish arbitrary-order closure, external validation, novelty or impact.",
      "sharedBoundary": "Unrefereed partial-results dossier; the parent problem remains unresolved. Conditional catalogue coverage, finite exclusions and repair obstructions do not establish arbitrary-order closure, external validation, novelty or impact.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Athree-coloured-paths-partial-results-2026-09-08",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/2"
      ]
    },
    {
      "id": "cluster:three-item-jrp-certification-and-logistics-handoff",
      "type": "cluster",
      "label": "Exact three-item replenishment certification and logistics handoff",
      "description": "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.",
      "sharedBoundary": "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.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Athree-item-jrp-certification-and-logistics-handoff",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/22"
      ]
    },
    {
      "id": "cluster:two-class-norm-saturation-2026-09-12",
      "type": "cluster",
      "label": "Two-class moment and full-norm saturation",
      "description": "Internal candidate proof with finite checks; no external validation or impact inference.",
      "sharedBoundary": "Internal candidate proof with finite checks; no external validation or impact inference.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Atwo-class-norm-saturation-2026-09-12",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/62"
      ]
    },
    {
      "id": "cluster:txgraffiti-order48-certificate-successor",
      "type": "cluster",
      "label": "Order-48 cubic counterexample and exhaustive independent-domination certificate",
      "description": "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.",
      "sharedBoundary": "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.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Atxgraffiti-order48-certificate-successor",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/23"
      ]
    },
    {
      "id": "cluster:unlinked-gamma-shape-allocation-2026-09-20",
      "type": "cluster",
      "label": "Gamma shape allocation and finite-cumulant identification",
      "description": "Fixed known positive Gamma dictionary; exact population identification and bounded producer checks, not finite-sample estimation or external validation.",
      "sharedBoundary": "Fixed known positive Gamma dictionary; exact population identification and bounded producer checks, not finite-sample estimation or external validation.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Aunlinked-gamma-shape-allocation-2026-09-20",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/66"
      ]
    },
    {
      "id": "cluster:wales-policy-attribution-identification",
      "type": "cluster",
      "label": "Wales policy-attribution identification audit",
      "description": "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.",
      "sharedBoundary": "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.",
      "memberCount": 1,
      "scopeStatus": "cluster-seed",
      "active": true,
      "effectiveDate": null,
      "supersedes": null,
      "supersededBy": null,
      "url": "https://evidencepress.org/atlas/?node=cluster%3Awales-policy-attribution-identification",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/12"
      ]
    },
    {
      "id": "cluster:wishart-reachable-noise-classification",
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      "id": "edge:cff1bfbd4621d25033d9"
    },
    {
      "source": "release:bilateral-deficiency-regular-dim",
      "target": "cluster:exact-combinatorial-certificates",
      "predicate": "member-of-cluster",
      "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/6"
      ],
      "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/4"
      ],
      "id": "edge:59358bbb220c0148e788"
    },
    {
      "source": "release:bounded-product-transposition-cutoff",
      "target": "cluster:bounded-product-reference-gradient-2026-09-08",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists bounded-product-transposition-cutoff as a member of All-time reference-gradient comparison for product-weight transpositions.",
      "inferenceLimit": "Unrefereed proof candidate for the product-weight branch only. Producer finite checks and internal model-assisted editorial review are not independent reproduction, unaffiliated specialist review or formal verification. No explicit cutoff location, optimal window, limiting profile, nonproduct resolution or historical priority is claimed.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/58"
      ],
      "id": "edge:a38941ddfbb15abdf350"
    },
    {
      "source": "release:casas-alvero-eight-term",
      "target": "cluster:casas-alvero-eight-term",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists casas-alvero-eight-term as a member of Degree-twenty sparsity and ramified root-cluster obstructions.",
      "inferenceLimit": "Complete centered seven-term support exclusion with written valuation transfer and exact finite checks; no full degree-twenty solution, external assurance or priority promotion.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/71"
      ],
      "id": "edge:3a1daba808a1c6947492"
    },
    {
      "source": "release:catenary-placement-classification",
      "target": "cluster:catenary-placement-classification",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists catenary-placement-classification as a member of Placement classification in physical compartment chains.",
      "inferenceLimit": "Written all-length identifiability candidate with finite supporting checks; ideal known-gain transfer data; no external validation, formal proof, priority or practical estimation benefit.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/70"
      ],
      "id": "edge:202e3f4fc26508531d5a"
    },
    {
      "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/7"
      ],
      "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/22"
      ],
      "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/7"
      ],
      "id": "edge:fe9d84720d78ef4ef5fa"
    },
    {
      "source": "release:cooper-spencer-temporal-unimodality",
      "target": "cluster:cooper-spencer-temporal-unimodality-2026-09-19",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists cooper-spencer-temporal-unimodality as a member of Parity-sensitive temporal-unimodality counterexample certificates.",
      "inferenceLimit": "Unrefereed written proof with exact finite checks; no first priority or external assurance established.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/63"
      ],
      "id": "edge:c5b663ea6b0e5506fc0d"
    },
    {
      "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/5"
      ],
      "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/5"
      ],
      "id": "edge:fdca7d05911aa27c3d90"
    },
    {
      "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/21"
      ],
      "id": "edge:e849155088bdae228c94"
    },
    {
      "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/20"
      ],
      "id": "edge:6c1b664e7d0006c95531"
    },
    {
      "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/18"
      ],
      "id": "edge:c6dd26d48da7601e8af9"
    },
    {
      "source": "release:davies-levitin-lens-conjecture",
      "target": "cluster:davies-levitin-lens-conjecture",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists davies-levitin-lens-conjecture as a member of The Davies–Levitin lens, for every n.",
      "inferenceLimit": "Unrefereed candidate. A written proof with two essential interval certificates; formal verification, external review and unconditional priority are not established.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/73"
      ],
      "id": "edge:23d55d5090b15b43a07c"
    },
    {
      "source": "release:decision-geometry",
      "target": "cluster:decision-geometry",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists decision-geometry as a member of Triangle-network information geometry and boundary certification.",
      "inferenceLimit": "Unrefereed model-conditional analytic candidate. Exact rational receipt checks and numerical experiments do not establish universal proof, biological validity, independent reproduction, external review, priority or measured impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/77"
      ],
      "id": "edge:e2cdba91ffcdbe0858e9"
    },
    {
      "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/4"
      ],
      "id": "edge:3c3ba6d95d4e4008b1ae"
    },
    {
      "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/36"
      ],
      "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/47"
      ],
      "id": "edge:f38884a06b1d5c0dd157"
    },
    {
      "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/6"
      ],
      "id": "edge:c5ec8acd4451ed6f29d7"
    },
    {
      "source": "release:essential-hurwitz-trace-formula",
      "target": "cluster:essential-hurwitz-trace-cancellation-2026-09-07",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists essential-hurwitz-trace-formula as a member of Essential Hurwitz trace formula and global cancellation.",
      "inferenceLimit": "Unrefereed compact formula and uniform written proof candidate. Producer finite replay and internal AI review do not establish unaffiliated whole-proof acceptance, formal verification, historical priority or practical improvement.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/51"
      ],
      "id": "edge:d96e7fda6d377df1dcda"
    },
    {
      "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/8"
      ],
      "id": "edge:c0ea2d834233642d720f"
    },
    {
      "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/4"
      ],
      "id": "edge:e86fde2e0e5db65e747b"
    },
    {
      "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/4"
      ],
      "id": "edge:6445762089a4bac6abf4"
    },
    {
      "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/29"
      ],
      "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/35"
      ],
      "id": "edge:c0f8e6d8aa4c327dd753"
    },
    {
      "source": "release:fano-plane-spectrum",
      "target": "cluster:fano-tensor-resultant-geometry-2026-09-19",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists fano-plane-spectrum as a member of Fano tensor resultant and eigenscheme certificates.",
      "inferenceLimit": "Unrefereed computational theorem candidate. Default replay does not freshly repeat the complete thirty-prime computation or every finite number-field decomposition. No unaffiliated validation, formal proof, exhaustive priority or impact claim.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/64"
      ],
      "id": "edge:6fee17e888eccc7d8eb5"
    },
    {
      "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/19"
      ],
      "id": "edge:ac9f3e02eb66fb8acc1f"
    },
    {
      "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/39"
      ],
      "id": "edge:f6bae105e61905a6f87a"
    },
    {
      "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/42"
      ],
      "id": "edge:4e2e5b35d8e1f348b109"
    },
    {
      "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/32"
      ],
      "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/31"
      ],
      "id": "edge:8b19ad8f0237e99a59dd"
    },
    {
      "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/16"
      ],
      "id": "edge:28d3a19e3220485d4bc4"
    },
    {
      "source": "release:free-fermion-frustration-graphs",
      "target": "cluster:free-fermion-frustration-graphs",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists free-fermion-frustration-graphs as a member of Frustration graphs, free spectra and occupation certificates.",
      "inferenceLimit": "Faithful graph semantics and complete spectral multiplicities are necessary; numerical selection is not an all-coupling proof.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/78"
      ],
      "id": "edge:1d1b49f898ce3d78677f"
    },
    {
      "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/13"
      ],
      "id": "edge:44bc813c8a3b98302919"
    },
    {
      "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/14"
      ],
      "id": "edge:cff39385534d8476b698"
    },
    {
      "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/17"
      ],
      "id": "edge:e853d32fe368f4149db4"
    },
    {
      "source": "release:gk-shared-phosphatase-connectedness",
      "target": "cluster:gk-overlapping-incidence-images-2026-09-20",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists gk-shared-phosphatase-connectedness as a member of Overlapping incidence images and degenerate attachment.",
      "inferenceLimit": "Unrefereed written topology proof supported by exact algebraic checks; no external validation or stability claim.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/65"
      ],
      "id": "edge:55fc1484e89d44c3d148"
    },
    {
      "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/5"
      ],
      "id": "edge:d69a61ea92bf2832c50f"
    },
    {
      "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/37"
      ],
      "id": "edge:057089354dcf01b076be"
    },
    {
      "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/48"
      ],
      "id": "edge:51995649f6dc66baf410"
    },
    {
      "source": "release:hilbert-series-matrix-septic-invariants",
      "target": "cluster:hilbert-series-matrix-septic-invariants",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists hilbert-series-matrix-septic-invariants as a member of Matrix invariants: nine new Hilbert series.",
      "inferenceLimit": "Unrefereed candidate. Computer-assisted theorems for nine matrix cases; the septic series proved through degree 760 and conditionally beyond; no formal verification or external review.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/74"
      ],
      "id": "edge:ddc17aa88035c4910b38"
    },
    {
      "source": "release:hilbert-series-ternary-septic-octic-nonic",
      "target": "cluster:hilbert-series-ternary-septic-octic-nonic",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists hilbert-series-ternary-septic-octic-nonic as a member of Invariants of plane curves of degree 7, 8 and 9.",
      "inferenceLimit": "Unrefereed candidate; computer-assisted theorems for d = 7, 8, 9 by known methods; no formal verification or external review.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/75"
      ],
      "id": "edge:6ac6ca3c01cae5b0a96e"
    },
    {
      "source": "release:irreducible-pushforwards-quartic-transitions",
      "target": "cluster:grand-problem-salvage",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists irreducible-pushforwards-quartic-transitions as a member of Grand-problem salvage.",
      "inferenceLimit": "The extracted modules may be useful while the parent conjecture remains explicitly unresolved.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/9"
      ],
      "id": "edge:780bc3c8010047c5b5f9"
    },
    {
      "source": "release:linear-nonbacktracking-jordan-growth",
      "target": "cluster:nonbacktracking-jordan-valuation-realization",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists linear-nonbacktracking-jordan-growth as a member of Non-backtracking Jordan valuation and graph realization.",
      "inferenceLimit": "Written arbitrary-parameter valuation and graph embedding, with finite producer controls; no independent validation, exact extremum, optimal constants, priority or impact established.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/45"
      ],
      "id": "edge:9581d1caa48e54512e79"
    },
    {
      "source": "release:lps-structural-reductions",
      "target": "cluster:lps-fixed-width-structural-and-padic-programme",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists lps-structural-reductions as a member of Fixed-width LPS reductions, quartic gauge repair and p-adic signals.",
      "inferenceLimit": "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.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/25"
      ],
      "id": "edge:9f39bb35a626c551e6f0"
    },
    {
      "source": "release:median-radius-obstructions",
      "target": "cluster:median-radius-integer-separation",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists median-radius-obstructions as a member of Integer separation and strict graph improvement.",
      "inferenceLimit": "Exact dimension-preserving transfer; singleton method illustration, not evidence of research lineage or acceleration.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/68"
      ],
      "id": "edge:8220f27d28aaf1e3a59d"
    },
    {
      "source": "release:moment-ideals-unbounded-generator-degrees",
      "target": "cluster:full-moment-graph-faces-2026-09-09",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists moment-ideals-unbounded-generator-degrees as a member of Full-moment graph faces and persistent algebraic obstructions.",
      "inferenceLimit": "Unrefereed candidate with a complete written argument as both n and d vary. Finite replay is supporting evidence, not universal certification. Fixed-n unboundedness, optimal parameters, historical priority, external review, formal verification and impact are not established.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/61"
      ],
      "id": "edge:d6de97060cfe5d787178"
    },
    {
      "source": "release:negative-square-energy-five-vertex-valley",
      "target": "cluster:negative-square-energy-ordered-valley-2026-08-30",
      "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/30"
      ],
      "id": "edge:86724535cc69e6a8b588"
    },
    {
      "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/27"
      ],
      "id": "edge:688f0480050db300c16c"
    },
    {
      "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/28"
      ],
      "id": "edge:a8142c42b4b9b61ae706"
    },
    {
      "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/38"
      ],
      "id": "edge:7fd4eb7a29e0a905c926"
    },
    {
      "source": "release:potts-censoring-counterexample",
      "target": "cluster:potts-finite-word-censoring-obstruction-2026-09-06",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "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.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/46"
      ],
      "id": "edge:2dfaf65092908638620c"
    },
    {
      "source": "release:ptolemaic-negative-type",
      "target": "cluster:ptolemaic-negative-type",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists ptolemaic-negative-type as a member of Sharp negative type of finite Ptolemaic metrics.",
      "inferenceLimit": "Unrefereed analytic proof candidate for all m >= 6, with complete-split sharpness witnesses. Symbolic checks, finite examples and numerical stress tests are corroboration, not a universal proof certificate. No formal verification, independent reproduction, external specialist review or real-world impact is established.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/76"
      ],
      "id": "edge:c4a72c3a6c55d438a3de"
    },
    {
      "source": "release:ptolemaic-split-stability",
      "target": "cluster:ptolemaic-split-stability",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists ptolemaic-split-stability as a member of Ptolemaic tangent-cone stability.",
      "inferenceLimit": "Exact cone certificates plus a written nonlinear and spectral bridge; global dependency scope remains separate.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/79"
      ],
      "id": "edge:bbc44166b3f62dd41ed6"
    },
    {
      "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/33"
      ],
      "id": "edge:72acc58d82d8eb7ddf55"
    },
    {
      "source": "release:quartic-inverse-coefficients",
      "target": "cluster:quartic-boundary-interlacing-2026-09-12",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists quartic-inverse-coefficients as a member of Quartic inverse-coefficient boundary interlacing.",
      "inferenceLimit": "Uniform written boundary comparison; affine geometry uses external R3. Internal review and finite replay are not external validation.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/0"
      ],
      "id": "edge:5c6379c4ca2bb5b99726"
    },
    {
      "source": "release:random-reshuffling-baseline-policy",
      "target": "cluster:sampling-and-optimisation-diagnostics",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "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/8"
      ],
      "id": "edge:876414f7175255c6f431"
    },
    {
      "source": "release:rbm31-exact-kl-radius",
      "target": "cluster:rbm31-channel-convex-cover-radius-2026-09-05",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "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": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/43"
      ],
      "id": "edge:fc118c0aaf41fe5f7e40"
    },
    {
      "source": "release:rbm43-eight-point-obstruction",
      "target": "cluster:rbm43-eight-point-leakage-obstruction-2026-09-06",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "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": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/3"
      ],
      "id": "edge:af4d271b240b89693102"
    },
    {
      "source": "release:reducible-incidence-divisors",
      "target": "cluster:binary-form-jacobian-and-obstruction",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "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/4"
      ],
      "id": "edge:4ea3587ddab47eb2ec2f"
    },
    {
      "source": "release:s6-extension-results-candidate",
      "target": "cluster:s6-conditional-geometry-and-adjudication",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "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/24"
      ],
      "id": "edge:828503b0b6dfb150ce87"
    },
    {
      "source": "release:seymour-second-neighbourhood-2delta3",
      "target": "cluster:seymour-second-neighbourhood-2delta3",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists seymour-second-neighbourhood-2delta3 as a member of Dense-case structure and certified order bounds for the second neighbourhood conjecture.",
      "inferenceLimit": "Written necessary conditions at n = 2δ+3 used as SAT constraints with retained, doubly checked LRAT refutations; exact losing-density counterexamples; no proof of the conjecture or of the case n = 2δ+3, no formal verification of the reduction, external assurance or priority promotion.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/72"
      ],
      "id": "edge:fa0e283c46b5407fccb4"
    },
    {
      "source": "release:sfs-identifiability-audit",
      "target": "cluster:certified-demographic-identifiability",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "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/11"
      ],
      "id": "edge:f93cee06125e4a55c8c6"
    },
    {
      "source": "release:sharp-bilagrangian-smoothness",
      "target": "cluster:bilagrangian-smoothness-fixed-locus-2026-09-12",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists sharp-bilagrangian-smoothness as a member of Bi-Lagrangian smoothness through a reduced chart and fixed locus.",
      "inferenceLimit": "Unrefereed written criterion; classical ingredients, finite producer replay and internal review do not establish external validation, priority, orbit classification or impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/1"
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      "id": "edge:c481f867987cccb234cc"
    },
    {
      "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",
      "construction": "generated-from-source-record",
      "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": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/41"
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      "id": "edge:c3e54648bdf577f4cdb4"
    },
    {
      "source": "release:sharp-local-minor-ratios",
      "target": "cluster:local-minor-ratio-transfer-2026-09-07",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists sharp-local-minor-ratios as a member of Local minor-ratio sharpness through simultaneous transfer.",
      "inferenceLimit": "Unrefereed complete written proof candidate for an explicitly normalized local condition. No independent specialist validation, formal verification, absolute priority clearance, optimal testing complexity or identity with the omitted workshop formula is claimed.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/52"
      ],
      "id": "edge:5194a9a7a99ec6319049"
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    {
      "source": "release:sharp-quartic-hadamard-powers",
      "target": "cluster:quartic-coefficient-power-boundary-2026-09-05",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "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": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/44"
      ],
      "id": "edge:7ca4cb65193204569b67"
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    {
      "source": "release:six-dimensional-zonoid-counterexample",
      "target": "cluster:zonoid-signed-sum-certificates-2026-09-08",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists six-dimensional-zonoid-counterexample as a member of Universal zonoid bounds from rational signed-sum certificates.",
      "inferenceLimit": "Unrefereed computer-assisted candidate. Exact producer replay and five internal model-assisted editorial reports are not unaffiliated specialist review, independent reproduction or formal verification. Historical priority, least counterexample dimension and global dimension-six extremality are not established.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/56"
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      "id": "edge:93a3e7df1450bd631e57"
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    {
      "source": "release:smooth-point-certificates-polydegree-containments",
      "target": "cluster:binary-form-jacobian-and-obstruction",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists smooth-point-certificates-polydegree-containments 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/4"
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      "id": "edge:6ba265f8ef640600905f"
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    {
      "source": "release:stable-power-concavity-gaussian-boundary",
      "target": "cluster:stable-power-concavity-boundary-2026-09-08",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists stable-power-concavity-gaussian-boundary as a member of Stable density curvature and uniform Gaussian-tail matching.",
      "inferenceLimit": "Unrefereed analytic proof candidate with a finite Arb certificate. No optimal fixed-index closed form, weaker CDF-concavity conclusion, historical priority, external specialist review, formal verification or practical impact is claimed.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/55"
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      "id": "edge:a16a948592abac9db4c5"
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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.",
      "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/7"
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      "id": "edge:b4baae4004919805d4dc"
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    {
      "source": "release:symmetric-determinantal-hilbert-threshold",
      "target": "cluster:orthogonal-algebraicity-2026-09-08",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists symmetric-determinantal-hilbert-threshold as a member of Orthogonal character asymptotics and algebraicity.",
      "inferenceLimit": "Unrefereed written classification candidate for fixed nonzero genuine algebraic O(m,C) representations. No arbitrary tca-module classification, virtual-character extension, historical priority, external specialist validation or formal verification is claimed.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/57"
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      "id": "edge:acaa3bbe87c4a3e28cae"
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    {
      "source": "release:symmetric-unimodality-free-convolution",
      "target": "cluster:symmetric-free-unimodality-moment-endpoints-2026-09-07",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists symmetric-unimodality-free-convolution as a member of Symmetric free-additive unimodality through moment endpoints.",
      "inferenceLimit": "Unrefereed analytic proof candidate. Scoped symbolic identities and internal model review do not establish external whole-proof validation, free strong unimodality, global edge smoothness, priority or impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/50"
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      "id": "edge:77eb08013b31e799029b"
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    {
      "source": "release:symmetry-respecting-tree-torsors",
      "target": "cluster:equivariant-tree-torsors-2026-09-08",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists symmetry-respecting-tree-torsors as a member of Equivariant torsors through restriction kernels and graph symmetries.",
      "inferenceLimit": "Unrefereed written proof candidate for explicitly defined minimum equivariance. No unique canonical action, minor-consistent algorithm, efficient general runtime, established priority, external specialist validation or formal verification is claimed.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/54"
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      "id": "edge:d3d2032d6b82a6f04c45"
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    {
      "source": "release:tcell-exactly-five",
      "target": "cluster:tcell-exact-five-scalar-certificate",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists tcell-exactly-five as a member of Scalar equilibrium reduction and exact sign counts.",
      "inferenceLimit": "Model-specific chain reconstruction and Descartes certificate; singleton method illustration, not a research lineage.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/67"
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      "id": "edge:594bd4c2195bc1d44e54"
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    {
      "source": "release:three-coloured-paths-partial-results",
      "target": "cluster:three-coloured-paths-partial-results-2026-09-08",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists three-coloured-paths-partial-results as a member of Three-coloured path partial theorems and repair obstructions.",
      "inferenceLimit": "Unrefereed partial-results dossier; the parent problem remains unresolved. Conditional catalogue coverage, finite exclusions and repair obstructions do not establish arbitrary-order closure, external validation, novelty or impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/2"
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      "id": "edge:7c44b95d370fe95d78de"
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    {
      "source": "release:triangulated-graph-product-picard",
      "target": "cluster:graph-product-picard-integral-2026-09-08",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists triangulated-graph-product-picard as a member of Graph-product Picard integral compatibility.",
      "inferenceLimit": "Unrefereed uniform written proof candidate under explicit branch-local conventions. Producer exact diagnostics and internal AI review do not establish unaffiliated whole-proof acceptance, formal verification, historical priority or impact.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/53"
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      "id": "edge:f3c9025eecda0febd5e2"
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    {
      "source": "release:two-class-transposition-profiles",
      "target": "cluster:two-class-norm-saturation-2026-09-12",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists two-class-transposition-profiles as a member of Two-class moment and full-norm saturation.",
      "inferenceLimit": "Internal candidate proof with finite checks; no external validation or impact inference.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/62"
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      "id": "edge:6a64bdc3240bbee64704"
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    {
      "source": "release:txgraffiti-c3-resolution",
      "target": "cluster:exact-combinatorial-certificates",
      "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/6"
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      "id": "edge:7f39bf8f65206444b6ec"
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    {
      "source": "release:txgraffiti-order48-successor",
      "target": "cluster:txgraffiti-order48-certificate-successor",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists txgraffiti-order48-successor as a member of Order-48 cubic counterexample and exhaustive independent-domination certificate.",
      "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": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/23"
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      "id": "edge:76126c9930f75e98f231"
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    {
      "source": "release:unbounded-bns-component-orbits",
      "target": "cluster:free-by-cyclic-bns-component-orbit-obstruction-2026-08-31",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "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": [
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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",
      "construction": "generated-from-source-record",
      "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/10"
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      "id": "edge:a9bdb414541bbd386ac2"
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    {
      "source": "release:unlinked-gamma-regression",
      "target": "cluster:unlinked-gamma-shape-allocation-2026-09-20",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists unlinked-gamma-regression as a member of Gamma shape allocation and finite-cumulant identification.",
      "inferenceLimit": "Fixed known positive Gamma dictionary; exact population identification and bounded producer checks, not finite-sample estimation or external validation.",
      "sourceRefs": [
        "https://evidencepress.org/api/method-registry.json#/methodClusters/66"
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      "id": "edge:7efce3746ba371911120"
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    {
      "source": "release:vr2-k4-equals-20",
      "target": "cluster:exact-combinatorial-certificates",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "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/6"
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      "id": "edge:84cf3198d2326b29f575"
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    {
      "source": "release:wales-20mph-casualty-attribution",
      "target": "cluster:wales-policy-attribution-identification",
      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "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/12"
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      "id": "edge:bbebc662491ed6d981cf"
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    {
      "source": "release:wishart-reachable-noise",
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      "predicate": "member-of-cluster",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "The method registry lists wishart-reachable-noise as a member of Reachable-noise and singular-scale Wishart classification.",
      "inferenceLimit": "Written infinite-dimensional candidate proof with finite symbolic supporting checks; no external validation, formal proof, priority or empirical pricing benefit.",
      "sourceRefs": [
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      "id": "edge:dddc5c5320521720734d"
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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.",
      "inferenceLimit": "Certificate replay establishes encoded bounded claims; source-to-encoding correctness and independent reconstruction remain separate.",
      "sourceRefs": [
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      "id": "edge:bcf77083ee91b7f84169"
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      "source": "release:affine-diversification-fibres",
      "target": "lineage:affine-diversification-programme",
      "predicate": "member-of-lineage",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "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.",
      "inferenceLimit": "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.",
      "sourceRefs": [
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      "id": "edge:851632085c00e79b9824"
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      "source": "release:amplitude-modules-fused-support-bautin-bound",
      "target": "lineage:cyclicity-programme",
      "predicate": "member-of-lineage",
      "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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      "id": "edge:7ca8220c0955a4ae4811"
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      "source": "release:bordered-jacobian-foundations",
      "target": "lineage:binary-form-programme",
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      "knowledgeStatus": "asserted",
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      "basis": "Each member explicitly identifies another member as foundational, parent, child, companion or continuation work in the published release metadata.",
      "inferenceLimit": "Dependency and reuse within this programme are not independent confirmation; a shared semantic or mathematical defect can propagate across the lineage.",
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      "id": "edge:87dc189426f3fbd94b06"
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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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      "source": "release:cyclicity-loci-exponential-periods",
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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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      "source": "release:cyclicity-root-span-low-rank",
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      "source": "release:cyclicity-support-fusion-atlas",
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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:degree-difference-affine-slices",
      "target": "lineage:binary-form-programme",
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      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "Each member explicitly identifies another member as foundational, parent, child, companion or continuation work in the published release metadata.",
      "inferenceLimit": "Dependency and reuse within this programme are not independent confirmation; a shared semantic or mathematical defect can propagate across the lineage.",
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      "source": "release:exact-smith-invariants-affine-determinant-lines",
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      "knowledgeStatus": "asserted",
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      "source": "release:exotic-affine-three-spheres",
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      "predicate": "member-of-lineage",
      "knowledgeStatus": "asserted",
      "construction": "generated-from-source-record",
      "basis": "Each member explicitly identifies another member as foundational, parent, child, companion or continuation work in the published release metadata.",
      "inferenceLimit": "Dependency and reuse within this programme are not independent confirmation; a shared semantic or mathematical defect can propagate across the lineage.",
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      "source": "release:finite-sample-affine-diversification",
      "target": "lineage:affine-diversification-programme",
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      "knowledgeStatus": "asserted",
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