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  "site": "Evidence Press",
  "baseUrl": "https://evidencepress.org",
  "description": "Exact searchable mathematical objects transcribed from release metadata. Inclusion preserves the release claim and assurance boundary; it does not independently verify the object.",
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      "releaseSlug": "furter-r3-through-299",
      "releaseTitle": "Exact finite rigidity for Furter's R(3): all windows through n=299",
      "releaseUrl": "https://evidencepress.org/releases/furter-r3-through-299/",
      "releaseDoi": "10.5281/zenodo.21939362",
      "releaseVersion": "0.1.0",
      "releaseStatus": "unrefereed-candidate",
      "id": "ep-math:furter-r3-through-299:furter-r3-finite-window",
      "kind": "statement",
      "label": "Furter R(3) finite window",
      "plainText": "R(3,n) holds for every integer n with 1 <= n <= 299",
      "latex": "R(3,n)\\text{ holds for every }1\\le n\\le299",
      "status": "claimed-result",
      "scope": "Exact finite principal statement of this anonymous unrefereed candidate; it does not establish universal R(3).",
      "sequenceTerms": [],
      "oeisId": null
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      "schemaVersion": "1.0",
      "releaseSlug": "furter-r3-through-299",
      "releaseTitle": "Exact finite rigidity for Furter's R(3): all windows through n=299",
      "releaseUrl": "https://evidencepress.org/releases/furter-r3-through-299/",
      "releaseDoi": "10.5281/zenodo.21939362",
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      "releaseStatus": "unrefereed-candidate",
      "id": "ep-math:furter-r3-through-299:inverse-coefficient-radical-window",
      "kind": "statement",
      "label": "Inverse-coefficient radical window",
      "plainText": "radical((g_(d,3), g_(d+1,3), g_(d+2,3)) Q[x_1,x_2,x_3]) = (x_1,x_2,x_3) for 2 <= d <= 300",
      "latex": "\\sqrt{(g_{d,3},g_{d+1,3},g_{d+2,3})\\mathbf Q[x_1,x_2,x_3]}=(x_1,x_2,x_3)\\quad(2\\le d\\le300)",
      "status": "claimed-result",
      "scope": "Equivalent finite radical formulation used by the release; producer-side exact certificates are reported for the stated range only.",
      "sequenceTerms": [],
      "oeisId": null
    },
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      "schemaVersion": "1.0",
      "releaseSlug": "full-e3-column-polydegree-conjecture",
      "releaseTitle": "A Jacobian smooth-point criterion and the full e=3 column of the Polydegree Conjecture",
      "releaseUrl": "https://evidencepress.org/releases/full-e3-column-polydegree-conjecture/",
      "releaseDoi": "10.5281/zenodo.21909085",
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      "id": "ep-math:full-e3-column-polydegree-conjecture:full-e3-polydegree-containment",
      "kind": "statement",
      "label": "Full e=3 Polydegree containment",
      "plainText": "G_(d+3) is contained in closure(G_(d,4)) for every integer d >= 2",
      "latex": "\\mathcal G_{(d+3)}\\subseteq\\overline{\\mathcal G_{(d,4)}}\\quad(d\\ge2)",
      "status": "claimed-result",
      "scope": "All-degree principal statement of this anonymous unrefereed candidate; the release reports producer-side exact algebra and finite Arb certificates but no unaffiliated rerun or specialist review.",
      "sequenceTerms": [],
      "oeisId": null
    },
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      "schemaVersion": "1.0",
      "releaseSlug": "exact-smith-invariants-affine-determinant-lines",
      "releaseTitle": "Exact Smith Invariants and Affine Determinant Lines of Binary-Form Factorisation",
      "releaseUrl": "https://evidencepress.org/releases/exact-smith-invariants-affine-determinant-lines/",
      "releaseDoi": "10.5281/zenodo.21861347",
      "releaseVersion": "0.1.0-candidate",
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      "id": "ep-math:exact-smith-invariants-affine-determinant-lines:all-factor-bordered-jacobian",
      "kind": "identity",
      "label": "All-factor bordered Jacobian determinant",
      "plainText": "det D(m_d,g_1,...,g_(k-1)) = +/- Delta_d det(delta_b g_a)",
      "latex": "\\det D(m_{\\mathbf d},g_1,\\ldots,g_{k-1})=\\pm\\Delta_{\\mathbf d}\\det(\\delta_b g_a)",
      "status": "claimed-result",
      "scope": "Universal multi-border determinant identity asserted by the anonymous unrefereed candidate; exact replay checks examples and structural consequences but does not replace independent proof review.",
      "sequenceTerms": [],
      "oeisId": null
    },
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      "schemaVersion": "1.0",
      "releaseSlug": "exact-smith-invariants-affine-determinant-lines",
      "releaseTitle": "Exact Smith Invariants and Affine Determinant Lines of Binary-Form Factorisation",
      "releaseUrl": "https://evidencepress.org/releases/exact-smith-invariants-affine-determinant-lines/",
      "releaseDoi": "10.5281/zenodo.21861347",
      "releaseVersion": "0.1.0-candidate",
      "releaseStatus": "unrefereed-candidate",
      "id": "ep-math:exact-smith-invariants-affine-determinant-lines:root-partition-degree",
      "kind": "formula",
      "label": "Labelled root-partition degree",
      "plainText": "nu = D! / product_i(d_i!) where D = sum_i d_i",
      "latex": "\\nu=\\frac{D!}{\\prod_i d_i!},\\qquad D=\\sum_i d_i",
      "status": "supporting-result",
      "scope": "Multinomial root-partition factor in the release's finite-locally-free degree formula, under its stated generic and normalisation hypotheses.",
      "sequenceTerms": [],
      "oeisId": null
    },
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      "schemaVersion": "1.0",
      "releaseSlug": "hahn-ewens-mixing-theorem",
      "releaseTitle": "A stabiliser--Ewens deformation: full Hahn spectrum and a sharp stationary-average chi-square transition",
      "releaseUrl": "https://evidencepress.org/releases/hahn-ewens-mixing-theorem/",
      "releaseDoi": "10.5281/zenodo.21864287",
      "releaseVersion": "0.1.0-candidate",
      "releaseStatus": "unrefereed-candidate",
      "id": "ep-math:hahn-ewens-mixing-theorem:stationary-average-chi-square-threshold",
      "kind": "bound",
      "label": "Stationary-average chi-square transition scale",
      "plainText": "t_N = (log(2)/(2 delta)) N/log(N), where delta = min(2c, alpha+beta-2c)",
      "latex": "t_N=\\frac{\\log 2}{2\\delta}\\frac{N}{\\log N},\\qquad\\delta=\\min(2c,\\alpha+\\beta-2c)",
      "status": "claimed-result",
      "scope": "Open-region stationary-weighted average conditional point-start chi-square transition claimed by the anonymous unrefereed candidate; no critical-point, fixed-start, worst-case or total-variation result is asserted.",
      "sequenceTerms": [],
      "oeisId": null
    },
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      "schemaVersion": "1.0",
      "releaseSlug": "smooth-point-certificates-polydegree-containments",
      "releaseTitle": "Smooth-Point Certificates for Polydegree Containments: A Jacobian Interpretation of the Lewis-Perry-Straub Determinant",
      "releaseUrl": "https://evidencepress.org/releases/smooth-point-certificates-polydegree-containments/",
      "releaseDoi": "10.5281/zenodo.21864574",
      "releaseVersion": "0.4.1-candidate",
      "releaseStatus": "unrefereed-candidate",
      "id": "ep-math:smooth-point-certificates-polydegree-containments:e3-affine-intersection-length",
      "kind": "sequence",
      "label": "Computed e=3 affine intersection lengths",
      "plainText": "a(d) = floor(d(d+1)/6) for 2 <= d <= 20",
      "latex": "a(d)=\\left\\lfloor\\frac{d(d+1)}6\\right\\rfloor\\quad(2\\le d\\le20)",
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        "35",
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        "51",
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      ],
      "status": "computed-finite",
      "scope": "Exact rational and Singular computation for d=2 through d=20; this parent release explicitly leaves the uniform affine theorem open.",
      "oeisId": null
    },
    {
      "schemaVersion": "1.0",
      "releaseSlug": "degree-difference-affine-slices",
      "releaseTitle": "The degree-difference principle and affine slices of binary-form factorisation spaces",
      "releaseUrl": "https://evidencepress.org/releases/degree-difference-affine-slices/",
      "releaseDoi": "10.5281/zenodo.21647593",
      "releaseVersion": "0.1-candidate",
      "releaseStatus": "unrefereed-candidate",
      "id": "ep-math:degree-difference-affine-slices:multiplication-resultant-jacobian",
      "kind": "identity",
      "label": "Multiplication-resultant Jacobian determinant",
      "plainText": "det D Phi_(r,s)(A,B) = (-1)^(s(r+1)) (r-s) Res(A,B)^2",
      "latex": "\\det D\\Phi_{r,s}=(-1)^{s(r+1)}(r-s)\\operatorname{Res}(A,B)^2",
      "status": "claimed-result",
      "scope": "All-degree determinant identity asserted by the anonymous unrefereed candidate in characteristic zero; only explicit low-degree polynomial identities received bounded computational checks.",
      "sequenceTerms": [],
      "oeisId": null
    },
    {
      "schemaVersion": "1.0",
      "releaseSlug": "vr2-k4-equals-20",
      "releaseTitle": "VR2(K4) = 20: twenty vertices force two vertex-disjoint monochromatic K4s",
      "releaseUrl": "https://evidencepress.org/releases/vr2-k4-equals-20/",
      "releaseDoi": "10.5281/zenodo.21647654",
      "releaseVersion": "0.1-candidate",
      "releaseStatus": "unrefereed-candidate",
      "id": "ep-math:vr2-k4-equals-20:two-copy-ramsey-k4",
      "kind": "statement",
      "label": "Two vertex-disjoint monochromatic K4s",
      "plainText": "VR_2(K_4) = 20",
      "latex": "\\mathrm{VR}_2(K_4)=20",
      "status": "claimed-result",
      "scope": "Principal statement of this anonymous unrefereed preprint; the upper bound inherits the z(20)=6 fixed-core certificate and encoding-soundness boundary.",
      "sequenceTerms": [],
      "oeisId": null
    },
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      "schemaVersion": "1.0",
      "releaseSlug": "z20-equals-6",
      "releaseTitle": "z(20) = 6: resolving the first open case of Erdős problem 758",
      "releaseUrl": "https://evidencepress.org/releases/z20-equals-6/",
      "releaseDoi": "10.5281/zenodo.21647645",
      "releaseVersion": "candidate-2026-07-26",
      "releaseStatus": "unrefereed-candidate",
      "id": "ep-math:z20-equals-6:cochromatic-number-20",
      "kind": "statement",
      "label": "Cochromatic number at 20",
      "plainText": "z(20) = 6",
      "latex": "z(20)=6",
      "status": "claimed-result",
      "scope": "Principal statement of this anonymous unrefereed candidate; producer-side certificate replay is reported, while independent reproduction, end-to-end formalisation and peer review remain absent.",
      "sequenceTerms": [],
      "oeisId": null
    }
  ]
}