{
  "schema_version": "1.1.0",
  "volume_id": "riemann",
  "title": "The Music of the Primes",
  "subtitle": "A guided journey from the Euler product to the critical line",
  "status": "Open Millennium Prize Problem; analytic-number-theory documentary; no zero-free proof claim",
  "claim_boundary": "Browser-native, source-normalized exposition of the Riemann Hypothesis. Functional-equation symmetry, finite zero verification, zero-density and critical-line proportion theorems, equivalent criteria, random-matrix agreement, prime-error heuristics, the de Bruijn–Newman constant, and Hilbert–Pólya analogies are not promoted to the universal assertion that every nontrivial zero has real part one half.",
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  "plates": [
    {
      "id": "cover",
      "label": "Cover",
      "title": "The Music of the Primes",
      "asset": "assets/documentaries/riemann/cover.svg",
      "alt": "An illuminated prime spiral rises into the critical strip and the zeta function.",
      "authority": "pedagogical_orientation_only"
    },
    {
      "id": "euler",
      "label": "Plate I",
      "title": "The Euler product",
      "asset": "assets/documentaries/riemann/euler.svg",
      "alt": "Prime factors become local notes whose infinite product forms the zeta function.",
      "authority": "pedagogical_orientation_only"
    },
    {
      "id": "strip",
      "label": "Plate II",
      "title": "The critical strip",
      "asset": "assets/documentaries/riemann/strip.svg",
      "alt": "Trivial zeros, the pole, symmetry, and nontrivial zeros are arranged around the critical line.",
      "authority": "pedagogical_orientation_only"
    },
    {
      "id": "explicit",
      "label": "Plate III",
      "title": "The zeros speak to the primes",
      "asset": "assets/documentaries/riemann/explicit.svg",
      "alt": "An explicit-formula bridge sends waves from complex zeros into prime-counting fluctuations.",
      "authority": "pedagogical_orientation_only"
    },
    {
      "id": "evidence",
      "label": "Plate IV",
      "title": "Evidence is not the infinite quantifier",
      "asset": "assets/documentaries/riemann/evidence.svg",
      "alt": "Finite verification, critical-line proportions, random matrices, and spectral analogies stop before the universal claim.",
      "authority": "pedagogical_orientation_only"
    }
  ],
  "chapters": [
    {
      "id": "reader-note",
      "title": "How to Read the Music",
      "source_heading": "A Note to the Reader",
      "claim_classes": [
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    {
      "id": "euler-product",
      "title": "Primes Become an Analytic Function",
      "source_heading": "Primes and the Euler Product",
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    {
      "id": "continuation",
      "title": "Beyond the Half-Plane",
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    {
      "id": "zeros",
      "title": "The Critical Strip",
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      "id": "explicit-formula",
      "title": "How Zeros Conduct the Primes",
      "source_heading": "The Explicit Formula",
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      "id": "evidence",
      "title": "The Infinite Quantifier",
      "source_heading": "Evidence, Equivalences, and the Open Frontier",
      "claim_classes": [
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  ],
  "appendices": [
    {
      "id": "appendix-xi",
      "title": "The Completed Xi-Function",
      "source_heading": "Technical Appendix: The Completed Function",
      "claim_classes": [
        "established"
      ]
    },
    {
      "id": "appendix-counting",
      "title": "Zero Counting and Prime Error",
      "source_heading": "Technical Appendix: Zero Counting and Explicit Formulae",
      "claim_classes": [
        "imported",
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    {
      "id": "appendix-computation",
      "title": "Rigorous Computation and Equivalent Criteria",
      "source_heading": "Technical Appendix: Computation and Criteria",
      "claim_classes": [
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    },
    {
      "id": "appendix-trust",
      "title": "Spectral Analogies and Trust Matrix",
      "source_heading": "Technical Appendix: Heuristics and Trust Matrix",
      "claim_classes": [
        "open",
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    }
  ],
  "sources": [
    "https://www.claymath.org/millennium/riemann-hypothesis/",
    "https://www.claymath.org/wp-content/uploads/2022/05/riemann.pdf",
    "https://www.claymath.org/library/historical/riemann/r.html",
    "https://dlmf.nist.gov/25.10",
    "https://doi.org/10.1112/plms/s3-32.1.193"
  ]
}