{
  "schema_version": "1.1.0",
  "volume_id": "poincare",
  "title": "The Shape of a Sphere",
  "subtitle": "A gentle illustrated guide to the Poincaré theorem",
  "status": "Solved classical theorem; Archival reconstruction; no new-proof claim",
  "claim_boundary": "Illustrated, source-normalized exposition of the Hamilton–Perelman route. The analytic Ricci-flow and manifold-level topology theorems remain imported; the bounded formal certificate concerns finite event bookkeeping conditional on source-bound event relations.",
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    "navy": "#07182F",
    "parchment": "#F3EAD5",
    "gold": "#BD913A",
    "ink": "#182033"
  },
  "plates": [
    {
      "id": "cover",
      "label": "Cover",
      "title": "The Shape of a Sphere",
      "asset": "assets/documentaries/poincare/cover.svg",
      "alt": "An illuminated navy and gold cover showing a luminous three-dimensional world beneath a starry sky.",
      "authority": "pedagogical_orientation_only"
    },
    {
      "id": "question",
      "label": "Plate I",
      "title": "The question hidden inside a loop",
      "asset": "assets/documentaries/poincare/plate_question.svg",
      "alt": "A visual analogy comparing contractible loops on a sphere with a loop trapped around a torus hole.",
      "authority": "pedagogical_orientation_only"
    },
    {
      "id": "geometry",
      "label": "Plate II",
      "title": "When geometry becomes an engine",
      "asset": "assets/documentaries/poincare/plate_geometry.svg",
      "alt": "A curved geometry smoothing under Ricci flow while a concentrated curvature region signals a singularity.",
      "authority": "pedagogical_orientation_only"
    },
    {
      "id": "surgery",
      "label": "Plate III",
      "title": "The craft of controlled surgery",
      "asset": "assets/documentaries/poincare/plate_surgery.svg",
      "alt": "A neck-like region is cut along controlled spheres and replaced by standard caps.",
      "authority": "pedagogical_orientation_only"
    },
    {
      "id": "extinction",
      "label": "Plate IV",
      "title": "Extinction, reversal, and the sphere",
      "asset": "assets/documentaries/poincare/plate_extinction.svg",
      "alt": "A finite surgery history is read backward into factors, after which simple connectivity leaves the sphere.",
      "authority": "pedagogical_orientation_only"
    }
  ],
  "chapters": [
    {
      "id": "reader-note",
      "title": "A Note to the Reader",
      "source_heading": "A Note to the Reader",
      "claim_classes": [
        "exposition",
        "guardrail"
      ]
    },
    {
      "id": "loops",
      "title": "The Question Hidden Inside a Loop",
      "source_heading": "The Question Hidden Inside a Loop",
      "claim_classes": [
        "established",
        "guardrail"
      ]
    },
    {
      "id": "geometry",
      "title": "When Geometry Becomes an Engine",
      "source_heading": "When Geometry Becomes an Engine",
      "claim_classes": [
        "exposition",
        "imported",
        "guardrail"
      ]
    },
    {
      "id": "surgery",
      "title": "The Craft of Controlled Surgery",
      "source_heading": "The Craft of Controlled Surgery",
      "claim_classes": [
        "imported",
        "guardrail"
      ]
    },
    {
      "id": "extinction",
      "title": "Extinction, Reversal, and the Sphere",
      "source_heading": "Extinction, Reversal, and the Sphere",
      "claim_classes": [
        "imported",
        "formal_bounded",
        "established",
        "guardrail"
      ]
    }
  ],
  "appendices": [
    {
      "id": "appendix-categories",
      "title": "Definitions and Category Bridges",
      "source_heading": "Technical Appendix: Definitions and Category Bridges",
      "claim_classes": [
        "established",
        "imported",
        "guardrail"
      ]
    },
    {
      "id": "appendix-flow",
      "title": "Ricci Flow and Its Controls",
      "source_heading": "Technical Appendix: Ricci Flow and Its Controls",
      "claim_classes": [
        "imported",
        "guardrail"
      ]
    },
    {
      "id": "appendix-trust",
      "title": "Claim-Level Trust Matrix",
      "source_heading": "Technical Appendix: Claim-Level Trust Matrix",
      "claim_classes": [
        "guardrail"
      ]
    }
  ],
  "sources": [
    "https://arxiv.org/abs/math/0211159",
    "https://arxiv.org/abs/math/0303109",
    "https://arxiv.org/abs/math/0307245",
    "https://arxiv.org/abs/math/0605667",
    "https://www.claymath.org/resource/ricci-flow-and-the-poincare-conjecture/"
  ]
}