{
  "schema": "AN04-hyperbolicity-necessity-foundations-proof-map/v1",
  "proofs": [
    {
      "id": "HN0:C1",
      "source": "convex-support-and-finite-jets.md",
      "source_sha256": "aaa9d154547b46751ea23310325d9e73ea64f87f796657457c5571c816709cbe",
      "proof_locator": "## C1.",
      "dependencies": [
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS",
        "U001:F0-COMP"
      ],
      "scope": "All finite convex Taylor jets, top-derivative modulus and reexpanded polynomial compatibility including k0 and singleton K"
    },
    {
      "id": "HN0:C2",
      "source": "convex-support-and-finite-jets.md",
      "source_sha256": "aaa9d154547b46751ea23310325d9e73ea64f87f796657457c5571c816709cbe",
      "proof_locator": "## C2.",
      "dependencies": [
        "U001:U001-A4",
        "U001:F0-COMP",
        "P3:M2",
        "U001:P21.4",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Actual maximal dyadic cube cover, parent constants, bounded overlap and full smooth partition estimates"
    },
    {
      "id": "HN0:C3",
      "source": "convex-support-and-finite-jets.md",
      "source_sha256": "aaa9d154547b46751ea23310325d9e73ea64f87f796657457c5571c816709cbe",
      "proof_locator": "## C3.",
      "dependencies": [
        "HN0:C1",
        "HN0:C2",
        "U001:U001-A4",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Constructive Ck extension of all jets, complete differentiability at K and same-order norm bound"
    },
    {
      "id": "HN0:C4",
      "source": "convex-support-and-finite-jets.md",
      "source_sha256": "aaa9d154547b46751ea23310325d9e73ea64f87f796657457c5571c816709cbe",
      "proof_locator": "## C4.",
      "dependencies": [
        "CH:T0",
        "P3:L3",
        "P3:M3",
        "P3:M4",
        "U001:U001-A4",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Ck extension of a finite-order distribution; flat-jet annihilation with actual support cutoffs and no derivative loss"
    },
    {
      "id": "HN0:C5",
      "source": "convex-support-and-finite-jets.md",
      "source_sha256": "aaa9d154547b46751ea23310325d9e73ea64f87f796657457c5571c816709cbe",
      "proof_locator": "## C5.",
      "dependencies": [
        "HN0:C3",
        "HN0:C4",
        "CH:T0",
        "PS:PS5",
        "U001:U001-A4"
      ],
      "scope": "Same-order compact-convex support estimate, empty case, and precise Hermitian half-ball/cone application"
    },
    {
      "id": "HN0:F1",
      "source": "constant-coefficient-fundamental-solutions.md",
      "source_sha256": "02d9f3d9bb862436fefca4459dddf760bfefc8a5142c8db4b5e1f1d4666a17f7",
      "proof_locator": "## F1.",
      "dependencies": [
        "QF:A1",
        "U001:F0-COMP",
        "U001:U001-A4",
        "U001:P14.3",
        "U001:P16.2",
        "U001:P21.4",
        "P3:M3",
        "P3:M4",
        "P3:M8"
      ],
      "scope": "Polynomial direction selection and finite zero avoidance, actual smooth rotation average with support and integral"
    },
    {
      "id": "HN0:F2",
      "source": "constant-coefficient-fundamental-solutions.md",
      "source_sha256": "02d9f3d9bb862436fefca4459dddf760bfefc8a5142c8db4b5e1f1d4666a17f7",
      "proof_locator": "## F2.",
      "dependencies": [
        "HN0:F1",
        "U001:F0-COMP",
        "U001:U001-A4",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Finite coefficient-sphere partition and jointly smooth normalized averaging kernel with uniform denominator gap"
    },
    {
      "id": "HN0:F3",
      "source": "constant-coefficient-fundamental-solutions.md",
      "source_sha256": "02d9f3d9bb862436fefca4459dddf760bfefc8a5142c8db4b5e1f1d4666a17f7",
      "proof_locator": "## F3.",
      "dependencies": [
        "HN0:F2",
        "U001:P15.1",
        "U001:P15.2",
        "U001:P13.2-series",
        "U001:P16.2",
        "U001:P21.4",
        "P3:M3",
        "P3:M4",
        "P3:M8"
      ],
      "scope": "Entire test-transform averaging identity from uniform exponential series and actual affine changes"
    },
    {
      "id": "HN0:F4",
      "source": "constant-coefficient-fundamental-solutions.md",
      "source_sha256": "02d9f3d9bb862436fefca4459dddf760bfefc8a5142c8db4b5e1f1d4666a17f7",
      "proof_locator": "## F4.",
      "dependencies": [
        "HN0:F3",
        "HN0:F2",
        "U001:Q3",
        "U001:Q4",
        "P3:L3",
        "P3:M3",
        "P3:M4",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "General constant-coefficient fundamental solution with all absolute convergence, distribution-order and transpose signs"
    },
    {
      "id": "HN0:F5",
      "source": "constant-coefficient-fundamental-solutions.md",
      "source_sha256": "02d9f3d9bb862436fefca4459dddf760bfefc8a5142c8db4b5e1f1d4666a17f7",
      "proof_locator": "## F5.",
      "dependencies": [
        "HN0:F4",
        "CH:T0",
        "P3:L3",
        "U001:U001-A4",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Global smooth output and fixed-patch local right inverse, every passive parameter bound and same-domain finite recursion"
    }
  ],
  "earlier_maps": [
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    "../20261004-free-canonical-composition/proof-map.json",
    "../20261005-restored-oscillatory/proof-map.json",
    "../20261005-restored-phase-space/proof-map.json",
    "../20261005-restored-phase-equivalence/proof-map.json",
    "../20261005-restored-intrinsic-regularity/proof-map.json",
    "../20261005-restored-tangent-zoom/proof-map.json",
    "../20261005-restored-gaussian-symbols/proof-map.json",
    "../20261005-restored-linear-reduction/proof-map.json",
    "../20261005-restored-analytic-composition/proof-map.json",
    "../20261005-restored-subprincipal-transport/proof-map.json",
    "../20261005-restored-graph-egorov/proof-map.json",
    "../20261005-restored-corank-continuity/proof-map.json",
    "../20261005-restored-submanifolds/proof-map.json",
    "../20261005-restored-cubic-scaling/proof-map.json",
    "../20261005-restored-smooth-descent/proof-map.json",
    "../20261005-restored-simultaneous-reflections/proof-map.json",
    "../20261005-restored-folded-forms/proof-map.json",
    "../20261005-restored-symplectic-reflections/proof-map.json",
    "../20261005-restored-canonical-folds/proof-map.json",
    "../20261005-restored-fold-densities/proof-map.json",
    "../20261005-restored-airy-models/proof-map.json",
    "../20261005-restored-invariant-folds/proof-map.json",
    "../20261005-restored-prescribed-coordinates/proof-map.json",
    "../20261005-restored-clean-pairs/proof-map.json",
    "../20261005-restored-function-normal-forms/proof-map.json",
    "../20261005-restored-quadratic-forms/proof-map.json",
    "../20261005-restored-positive-ideals/proof-map.json",
    "../20261005-restored-complex-fios/proof-map.json",
    "../20261005-restored-maslov-topology/proof-map.json",
    "../20261005-restored-real-principal/proof-map.json",
    "../20261005-cauchy-foundations/proof-map.json",
    "../20261005-restored-first-order-cauchy/proof-map.json",
    "../20261005-mixed-halfspace-foundations/proof-map.json",
    "../20261005-conormal-test-foundations/proof-map.json",
    "../20261005-normal-extension/proof-map.json",
    "../20261005-local-boundary-calculus/proof-map.json",
    "../20261005-positive-boundary-orders/proof-map.json",
    "../20261005-conormal-symbols-and-corners/proof-map.json",
    "../20261005-global-boundary-operators/proof-map.json",
    "../20261005-boundary-wavefront-and-tangential/proof-map.json",
    "../20261005-restored-higher-order-cauchy/proof-map.json"
  ],
  "external_dependency_policy": {
    "record": "../20261004-free-stationary-phase/external-proof-dependencies.json",
    "notice": "The elementary proof providers have exact earlier-programme routes in C10/C20, with public PDF destinations and editable TeX passages. The author English edition remains available. Human source text and figures stay external to this CC0 export and retain their own terms.",
    "mathematical_proofs_rewritten": false
  }
}