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    "markdown_files_in_link_discovery": 232,
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      "id": "CVS2025",
      "title": "Quadratic Forms, Real Zeros and Echoes of the Spectral Action",
      "authors": [
        "Alain Connes",
        "Walter D. van Suijlekom"
      ],
      "year": 2025,
      "primary_urls": [
        "https://arxiv.org/abs/2511.23257v1",
        "https://arxiv.org/html/2511.23257v1",
        "https://link.springer.com/article/10.1007/s00220-025-05493-1"
      ],
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      "review_status": "PRIMARY_METADATA_AND_SELECTED_STATEMENT_CHECKED",
      "notes": "CMP 406, article 312; published 18 November 2025. arXiv v1 submitted 28 November 2025. DOI resolver failed in this tool but publisher URL succeeded; referee acknowledgement present.",
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      "id": "CCM2025",
      "title": "Zeta Spectral Triples",
      "authors": [
        "Alain Connes",
        "Caterina Consani",
        "Henri Moscovici"
      ],
      "year": 2025,
      "primary_urls": [
        "https://arxiv.org/abs/2511.22755v1",
        "https://arxiv.org/html/2511.22755v1",
        "https://ems.press/content/book-chapter-files/53351",
        "https://ems.press/content/book-chapter-files/53349"
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      "check_scope": "Proxy convergence is distinct from ES and the normalized comparison with actual Weil ground states.",
      "review_status": "PRIMARY_METADATA_AND_SELECTED_STATEMENT_CHECKED",
      "notes": "EMS contents identify chapter 3, pages 39–75 and its authors. This does not establish individual chapter peer review. The archived project tracks a scalar normalization separately.",
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    {
      "id": "CCM2024",
      "title": "Zeta zeros and prolate wave operators: Semilocal adelic operators",
      "authors": [
        "Alain Connes",
        "Caterina Consani",
        "Henri Moscovici"
      ],
      "year": 2024,
      "primary_urls": [
        "https://arxiv.org/abs/2310.18423v2",
        "https://arxiv.org/html/2310.18423v2"
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      "review_status": "PRIMARY_METADATA_AND_SELECTED_STATEMENT_CHECKED",
      "notes": "arXiv abstract lists the main title only; HTML supplies the subtitle. Ann. Funct. Anal. 15(4), 87 (2024) is corroborated by the CvS publisher bibliography, not separately rechecked at that journal.",
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    {
      "id": "CC2023",
      "title": "Spectral triples and ζ-cycles",
      "authors": [
        "Alain Connes",
        "Caterina Consani"
      ],
      "year": 2023,
      "primary_urls": [
        "https://ems.press/journals/lem/articles/11033001"
      ],
      "checked_locator": "Publisher metadata and abstract",
      "check_scope": "Publication identity and arithmetic/prolate context; the exact radical proof is not newly reconstructed in this publication review.",
      "review_status": "PRIMARY_METADATA_AND_ABSTRACT_CHECKED",
      "notes": "Enseign. Math. 69(1–2), 93–148; DOI 10.4171/LEM/1049. Historical scoped source audits remain separate.",
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    {
      "id": "LOCAL_RH_I",
      "title": "A Local Riemann Hypothesis, I",
      "authors": [
        "Daniel Bump",
        "Kwok-Kwong Choi",
        "Pär Kurlberg",
        "Jeffrey Vaaler"
      ],
      "year": 2000,
      "primary_urls": [
        "https://kurlberg.github.io/eprints/lrh1.pdf",
        "https://kurlberg.github.io/publications.html"
      ],
      "checked_locator": "Author-hosted preliminary text, Theorem 1, printed p.3; author publication list",
      "check_scope": "Hermite Mellin-polynomial zeros and stated orthogonality; does not establish a global zeta-zero theorem.",
      "review_status": "PRIMARY_METADATA_AND_SELECTED_STATEMENT_CHECKED",
      "notes": "PDF is a preliminary version dated 1996, not represented as the 2000 journal typesetting; author list confirms Mathematische Zeitschrift 233(1), 1–19.",
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    {
      "id": "LOCAL_RH_II",
      "title": "A Local Riemann Hypothesis II",
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      "primary_urls": [
        "https://kurlberg.github.io/eprints/lrh2.pdf",
        "https://kurlberg.github.io/publications.html"
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      "check_scope": "The cited nonarchimedean statement has odd residue characteristic; complex-place failure is kept distinct.",
      "review_status": "PRIMARY_METADATA_AND_SELECTED_STATEMENT_CHECKED",
      "notes": "Mathematische Zeitschrift 233(1), 21–37; author-hosted manuscript used.",
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      "id": "SAUVALLE2017",
      "title": "On weak Mellin transforms, second degree characters and the Riemann hypothesis",
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        "Bruno Sauvalle"
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      "year": 2017,
      "primary_urls": [
        "https://www.impan.pl/shop/en/publication/transaction/download/product/92045"
      ],
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      "check_scope": "Global weak Mellin zeros include Hecke-L zeros and local zeros under the theorem hypotheses; local real-zero input does not remove the global obligation.",
      "review_status": "PRIMARY_METADATA_AND_SELECTED_STATEMENT_CHECKED",
      "notes": "Acta Arith. 177.3, 219–275; DOI 10.4064/aa8240-7-2016, printed in PDF. DOI/arXiv retrieval failure did not prevent checking publisher text.",
      "full_independent_proof_verification": false
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      "id": "DEJEU2003",
      "title": "Determinate multidimensional measures, the extended Carleman theorem and quasi-analytic weights",
      "authors": [
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        "https://arxiv.org/pdf/math/0111019v2"
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      "checked_locator": "Theorem 2.3, printed p.5, equation (2.1); Theorem 1.1",
      "check_scope": "Positive finite all-moment measure and coordinate Carleman condition imply polynomial density in Lp. Even projection is a separate elementary application.",
      "review_status": "PRIMARY_METADATA_AND_SELECTED_STATEMENT_CHECKED",
      "notes": "v2 dated 17 June 2002; Ann. Probab. 31 (2003), 1205–1227; DOI 10.1214/aop/1055425776 from arXiv metadata. No form-core or growing-degree claim.",
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    {
      "id": "DLMF_XI",
      "title": "NIST Digital Library of Mathematical Functions: Gamma, zeta and completion formulas",
      "authors": [
        "NIST DLMF"
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      "year": null,
      "primary_urls": [
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        "https://dlmf.nist.gov/25.9#E3",
        "https://dlmf.nist.gov/25.4#E4"
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      "review_status": "OFFICIAL_REFERENCE_LOCATORS_CHECKED",
      "notes": "Dynamic reference, not a new 2026 research paper.",
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      "id": "SIMONIC_STARICHKOVA2023",
      "title": "Atkinson's formula for the mean square of ζ(s) with an explicit error term",
      "authors": [
        "Aleksander Simonič",
        "Valeriia V. Starichkova"
      ],
      "year": 2023,
      "primary_urls": [
        "https://arxiv.org/abs/2105.06821v3",
        "https://arxiv.org/html/2105.06821v3"
      ],
      "checked_locator": "v3, 13 December 2022; Theorem 3, Section 7",
      "check_scope": "Supplementary explicit mean-square error with large-height hypotheses; cyclicity does not depend on this refinement.",
      "review_status": "PRIMARY_METADATA_AND_SELECTED_STATEMENT_CHECKED",
      "notes": "J. Number Theory 244, 111–168; DOI 10.1016/j.jnt.2022.09.010 from arXiv metadata.",
      "full_independent_proof_verification": false
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    {
      "id": "GAUTSCHI1975",
      "title": "Norm Estimates for Inverses of Vandermonde Matrices",
      "authors": [
        "Walter Gautschi"
      ],
      "year": 1975,
      "primary_urls": [
        "https://www.cs.purdue.edu/homes/wxg/selected_works/section_01/051.pdf"
      ],
      "checked_locator": "Section 3 p.339 equation (3.3); Section 4 p.340 equation (4.1)",
      "check_scope": "Cardinal inverse and inverse-norm bound; transpose changes the original infinity norm to the present 1-norm.",
      "review_status": "PRIMARY_METADATA_AND_SELECTED_STATEMENT_CHECKED",
      "notes": "Numer. Math. 23, 337–347; current square-node and Xi-weight calculations are scoped applications, not claims in the source.",
      "full_independent_proof_verification": false
    },
    {
      "id": "BRUBECK2021",
      "title": "Vandermonde with Arnoldi",
      "authors": [
        "Pablo D. Brubeck",
        "Yuji Nakatsukasa",
        "Lloyd N. Trefethen"
      ],
      "year": 2021,
      "primary_urls": [
        "https://people.maths.ox.ac.uk/trefethen/vandermonde_arnoldi.pdf"
      ],
      "checked_locator": "Section 4, p.409, equations (4.2)–(4.5); first-page metadata",
      "check_scope": "Same polynomial represented in QR/orthogonal coordinates; does not identify the head Gram with the physical Gram.",
      "review_status": "PRIMARY_METADATA_AND_SELECTED_STATEMENT_CHECKED",
      "notes": "SIAM Review 63(2), 405–415; DOI 10.1137/19M130100X printed in author-hosted publisher PDF. DOI tool failure is not a metadata discrepancy.",
      "full_independent_proof_verification": false
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    {
      "id": "DLMF_ORTHOGONAL",
      "title": "NIST DLMF: General Orthogonal Polynomials",
      "authors": [
        "NIST DLMF"
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        "https://dlmf.nist.gov/18.2#E5",
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      "check_scope": "Discrete orthogonality and Christoffel–Darboux conventions; no physical lift-cost theorem is inferred.",
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      "notes": "",
      "full_independent_proof_verification": false
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      "authors": [
        "Albert Cohen",
        "Mark A. Davenport",
        "Dany Leviatan"
      ],
      "year": 2018,
      "primary_urls": [
        "https://arxiv.org/abs/1111.4422",
        "https://arxiv.org/pdf/1111.4422",
        "https://arxiv.org/pdf/1111.4422v3"
      ],
      "checked_locator": "Theorem 1 p.3 equation (1.2); v3 metadata",
      "check_scope": "Independent samples from the prescribed measure are required by the quoted concentration theorem. No direct fixed-grid Xi-weighted certificate.",
      "review_status": "PRIMARY_METADATA_AND_SELECTED_STATEMENT_CHECKED",
      "notes": "First submitted 2011; reviewed revision is 15 June 2018. English reference now version-fixed. Other deterministic sampling results in the paper are not denied.",
      "full_independent_proof_verification": false
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      "id": "WEIL1952",
      "title": "Sur les formules explicites de la théorie des nombres premiers",
      "authors": [
        "André Weil"
      ],
      "year": 1952,
      "primary_urls": [
        "https://cds.cern.ch/record/471308"
      ],
      "checked_locator": "Requested CERN record",
      "check_scope": "No fresh title/theorem verification at this URL because bot-protection page was returned.",
      "review_status": "RETRIEVAL_BLOCKED",
      "notes": "Historical entry retained, not promoted. Alternate Weil-criterion sources were checked; do not report this link as freshly verified.",
      "full_independent_proof_verification": false
    },
    {
      "id": "CONNES1998",
      "title": "Trace formula in noncommutative geometry and the zeros of the Riemann zeta function",
      "authors": [
        "Alain Connes"
      ],
      "year": 1998,
      "primary_urls": [
        "https://arxiv.org/abs/math/9811068v1"
      ],
      "checked_locator": "Fixed-version arXiv metadata and abstract",
      "check_scope": "Trace framework and RH-related missing positivity/trace implication; not a completed RH proof.",
      "review_status": "PRIMARY_METADATA_AND_ABSTRACT_CHECKED",
      "notes": "",
      "full_independent_proof_verification": false
    },
    {
      "id": "CCM2007",
      "title": "The Weil proof and the geometry of the adeles class space",
      "authors": [
        "Alain Connes",
        "Caterina Consani",
        "Matilde Marcolli"
      ],
      "year": 2007,
      "primary_urls": [
        "https://arxiv.org/abs/math/0703392v1"
      ],
      "checked_locator": "Fixed-version arXiv metadata and abstract",
      "check_scope": "Arithmetic trace pairing, with positivity obligation kept explicit.",
      "review_status": "PRIMARY_METADATA_AND_ABSTRACT_CHECKED",
      "notes": "",
      "full_independent_proof_verification": false
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      "id": "DELIGNE1974",
      "title": "La conjecture de Weil. I",
      "authors": [
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      "primary_urls": [
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      ],
      "checked_locator": "First page and Theorem 1.6",
      "check_scope": "Finite-field geometric purity; not a supplied number-field zeta pairing.",
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      "notes": "Publ. Math. IHES 43, 273–307.",
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      "id": "GILLET_SOULE1990",
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      "authors": [
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        "Christophe Soulé"
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      "year": 1990,
      "primary_urls": [
        "https://www.numdam.org/item/10.1007/BF02699132.pdf"
      ],
      "checked_locator": "First pages and bibliographic header",
      "check_scope": "Identity and subject relevance checked; the entire intersection theory was not reconstructed.",
      "review_status": "PRIMARY_METADATA_AND_CONTEXT_CHECKED",
      "notes": "Publ. Math. IHES 72, 93–174.",
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        "Terence Tao"
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      "check_scope": "Nonnegativity of the threshold is not the missing upper bound at time zero.",
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