{
  "schema": "AN04-hyperbolicity-necessity-foundations-proof-map/v1",
  "proofs": [
    {
      "id": "HN0:C1",
      "source": "convex-support-and-finite-jets.md",
      "source_sha256": "de3055947bfeaf999fef5a6c717c2d425f26e04ebc5613ef5d234c648143faa3",
      "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": "de3055947bfeaf999fef5a6c717c2d425f26e04ebc5613ef5d234c648143faa3",
      "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": "de3055947bfeaf999fef5a6c717c2d425f26e04ebc5613ef5d234c648143faa3",
      "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": "de3055947bfeaf999fef5a6c717c2d425f26e04ebc5613ef5d234c648143faa3",
      "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": "de3055947bfeaf999fef5a6c717c2d425f26e04ebc5613ef5d234c648143faa3",
      "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": "39a7bddb274847a87ea27862123596e0f4881764beae5ed570837f361e875443",
      "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": "39a7bddb274847a87ea27862123596e0f4881764beae5ed570837f361e875443",
      "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": "39a7bddb274847a87ea27862123596e0f4881764beae5ed570837f361e875443",
      "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": "39a7bddb274847a87ea27862123596e0f4881764beae5ed570837f361e875443",
      "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": "39a7bddb274847a87ea27862123596e0f4881764beae5ed570837f361e875443",
      "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": [
    "../20261004-free-stationary-phase/proof-map.json",
    "../20261004-free-intrinsic-graph/proof-map.json",
    "../20261004-free-tangent-zoom/proof-map.json",
    "../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"
  ],
  "component_proofs_complete": true,
  "U032_restored": false,
  "full_course_complete": false,
  "public_release_authorized": false
}