{
  "schema_version": "1.1.0",
  "volume_id": "p_vs_np",
  "title": "The Shape of Computational Truth",
  "subtitle": "A guided journey through efficient solution, verification, and reduction",
  "status": "Open Millennium Prize Problem; machine-normalized documentary; no algorithm or lower-bound claim",
  "claim_boundary": "Browser-native, source-normalized exposition of the machine-and-encoding question P versus NP. Fast heuristics, finite experiments, average-case success, quantum algorithms, oracle separations, special-case algorithms, restricted circuit lower bounds, and proof-complexity results are not promoted to P = NP or P ≠ NP.",
  "asset_base": "docs_root",
  "math_rendering": {
    "provider": "MathJax",
    "version": "3.2.2",
    "delivery": "version_pinned_cdn",
    "script_url": "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js",
    "archival_role": "enhancement_only",
    "fallback": "source_tex_remains_readable_without_javascript"
  },
  "palette": {
    "navy": "#11172B",
    "parchment": "#F3EBD8",
    "gold": "#C39A45",
    "ink": "#20243A"
  },
  "plates": [
    {
      "id": "cover",
      "label": "Cover",
      "title": "The Shape of Computational Truth",
      "asset": "assets/documentaries/p_vs_np/cover.svg",
      "alt": "An illuminated computational labyrinth joins a verifier seal to the unresolved equation P versus NP.",
      "authority": "pedagogical_orientation_only"
    },
    {
      "id": "verification",
      "label": "Plate I",
      "title": "Finding and checking",
      "asset": "assets/documentaries/p_vs_np/verification.svg",
      "alt": "A maze contrasts discovering a path with rapidly verifying a supplied path certificate.",
      "authority": "pedagogical_orientation_only"
    },
    {
      "id": "reduction",
      "label": "Plate II",
      "title": "The grammar of reduction",
      "asset": "assets/documentaries/p_vs_np/reduction.svg",
      "alt": "Directed gateways map one decision problem into another while preserving yes and no instances.",
      "authority": "pedagogical_orientation_only"
    },
    {
      "id": "complete",
      "label": "Plate III",
      "title": "The complete problems",
      "asset": "assets/documentaries/p_vs_np/complete.svg",
      "alt": "SAT sits at a hub linked to graph, scheduling, routing, and packing problems by polynomial reductions.",
      "authority": "pedagogical_orientation_only"
    },
    {
      "id": "barriers",
      "label": "Plate IV",
      "title": "The walls around the frontier",
      "asset": "assets/documentaries/p_vs_np/barriers.svg",
      "alt": "Relativization, natural proofs, and algebrization form distinct barriers around the unresolved central question.",
      "authority": "pedagogical_orientation_only"
    }
  ],
  "chapters": [
    {
      "id": "reader-note",
      "title": "How to Read the Machine",
      "source_heading": "A Note to the Reader",
      "claim_classes": [
        "exposition",
        "guardrail",
        "open"
      ]
    },
    {
      "id": "verification",
      "title": "Finding and Checking",
      "source_heading": "Solving and Checking",
      "claim_classes": [
        "established",
        "guardrail"
      ]
    },
    {
      "id": "classes",
      "title": "The Classes P and NP",
      "source_heading": "P and NP",
      "claim_classes": [
        "established",
        "open"
      ]
    },
    {
      "id": "reductions",
      "title": "Reductions Preserve Difficulty",
      "source_heading": "Reductions",
      "claim_classes": [
        "established",
        "guardrail"
      ]
    },
    {
      "id": "complete",
      "title": "The Complete Problems",
      "source_heading": "Cook--Levin and NP-Completeness",
      "claim_classes": [
        "imported",
        "established",
        "guardrail"
      ]
    },
    {
      "id": "barriers",
      "title": "The Frontier and Its Barriers",
      "source_heading": "Barriers and Nearby Complexity Classes",
      "claim_classes": [
        "imported",
        "open",
        "guardrail"
      ]
    }
  ],
  "appendices": [
    {
      "id": "appendix-machines",
      "title": "Machines, Encodings, and Clocks",
      "source_heading": "Technical Appendix: Machines and Encodings",
      "claim_classes": [
        "established",
        "guardrail"
      ]
    },
    {
      "id": "appendix-forms",
      "title": "Decision, Search, Optimization, and Counting",
      "source_heading": "Technical Appendix: Problem Forms",
      "claim_classes": [
        "established",
        "guardrail"
      ]
    },
    {
      "id": "appendix-lower-bounds",
      "title": "Circuits and Proof Complexity",
      "source_heading": "Technical Appendix: Lower Bounds and Proof Systems",
      "claim_classes": [
        "imported",
        "conditional",
        "guardrail"
      ]
    },
    {
      "id": "appendix-trust",
      "title": "Claim-Level Trust Matrix",
      "source_heading": "Technical Appendix: Claim-Level Trust Matrix",
      "claim_classes": [
        "guardrail",
        "open"
      ]
    }
  ],
  "sources": [
    "https://www.claymath.org/millennium/p-vs-np/",
    "https://www.claymath.org/wp-content/uploads/2022/06/pvsnp.pdf",
    "https://doi.org/10.1145/800157.805047",
    "https://doi.org/10.1137/0204037",
    "https://doi.org/10.1145/237814.237866",
    "https://doi.org/10.1145/780542.780545"
  ]
}