{
  "schema": "AN04-restored-directional-transport-proof-map/v1",
  "proofs": [
    {
      "id": "DT:G0",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "## 1. Signed time",
      "dependencies": [
        "GF:T0",
        "GF:S3",
        "GF:N0",
        "GF:N1",
        "GF:N2",
        "GF:N3",
        "GF:L2",
        "GF:L3"
      ],
      "scope": "Intrinsic signed relations, global fixed times, empty case and actual diagonal section for first-factor flow"
    },
    {
      "id": "DT:B0",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "Let \\(L=M_",
      "dependencies": [
        "DT:G0",
        "GS:Z6",
        "GS:Z10",
        "GS:Z11",
        "GS:Z12",
        "ST:T0",
        "ST:T1",
        "ST:T10"
      ],
      "scope": "Actual Maslov-valued half-density symbol and kernel order, exact scalar degree-zero transport equation"
    },
    {
      "id": "DT:B1",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "The whole domain above",
      "dependencies": [
        "DT:G0",
        "U001:F0-CALC"
      ],
      "scope": "Three-stage contraction stays inside the actual variable interval-fiber domain"
    },
    {
      "id": "DT:B2",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "A flat line on this domain",
      "dependencies": [
        "DT:B0",
        "DT:B1",
        "MT:I0",
        "MT:I4",
        "GS:Z6",
        "U001:F0-COMP"
      ],
      "scope": "Full path continuation, finite-square mesh, vertex transition cancellation and smooth parallel frame compatible with dilation"
    },
    {
      "id": "DT:B3",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "In a quotient coordinate chart",
      "dependencies": [
        "DT:B2",
        "GS:Z10",
        "ST:T1",
        "U001:P14.2-powers"
      ],
      "scope": "Exact n/2 homogeneous frame and zero density divergence along the first time"
    },
    {
      "id": "DT:B4",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "On overlapping charts its transition factor",
      "dependencies": [
        "DT:B3",
        "U001:P2",
        "U001:F0-CALC"
      ],
      "scope": "Triangular quotient Jacobian, time/radius-independent transition, inverse and every compact derivative bound"
    },
    {
      "id": "DT:T0",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "Write \\(f=wg\\)",
      "dependencies": [
        "DT:B3",
        "GF:S1",
        "ST:T12",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Exact complex integrating factor with both signs and zero-diagonal uniqueness"
    },
    {
      "id": "DT:T1",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "In particular differentiation",
      "dependencies": [
        "DT:T0",
        "GF:S1",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Explicit moving lower endpoint and actual complex exponential convention"
    },
    {
      "id": "DT:T2",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "For a compact set of \\((q,t,s)\\)",
      "dependencies": [
        "DT:T1",
        "GF:S0",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS",
        "U001:F0-COMP"
      ],
      "scope": "Fixed interpolation, every mixed base and radial derivative, diagonal and backward orientation, exact order and continuous local symbol map"
    },
    {
      "id": "DT:T3",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "On an overlap the scalar transition",
      "dependencies": [
        "DT:T2",
        "DT:B4"
      ],
      "scope": "Unique local scalar solutions glue to the full global symbol-line solution"
    },
    {
      "id": "DT:M0",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "For a symbol section, its microsupport",
      "dependencies": [
        "DT:B4",
        "GF:S0",
        "GS:Z10"
      ],
      "scope": "Frame and coordinate independence of rapid conic decay; closedness and dilation invariance"
    },
    {
      "id": "DT:H0",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "Let \\(S\\) be a closed conic",
      "dependencies": [
        "DT:G0"
      ],
      "scope": "Reflexive forward hull, exact composition and retained source endpoint"
    },
    {
      "id": "DT:H1",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "This hull is closed,",
      "dependencies": [
        "DT:H0",
        "GF:N3",
        "U001:F0-COMP"
      ],
      "scope": "Actual ambient closure via compact relation interpolation and witness subsequence; exclusion of the diagonal"
    },
    {
      "id": "DT:H2",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "**Proof.** Fix a point outside",
      "dependencies": [
        "DT:H1",
        "DT:M0",
        "DT:T3",
        "U001:F0-COMP",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "One uniform quotient neighborhood avoiding all source witnesses, finite rapid-decay cover at radius one and every symbol derivative for all radii"
    },
    {
      "id": "DT:H3",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "For backward forcing use",
      "dependencies": [
        "DT:H2",
        "DT:G0"
      ],
      "scope": "Backward orientation, closed reflexive hull and complete signed transport bound"
    },
    {
      "id": "DT:T4",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "**Directional transport theorem.**",
      "dependencies": [
        "DT:T3",
        "DT:H2",
        "DT:H3"
      ],
      "scope": "Full global line-valued directional symbol theorem and actual closed support bound"
    },
    {
      "id": "DT:D0",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "Write \\(K_0=",
      "dependencies": [
        "RP:F3",
        "CH:W1",
        "CH:W3",
        "CH:W4"
      ],
      "scope": "Exact coefficient-times-delta wavefront through local smooth inversion and closure at flat support boundaries"
    },
    {
      "id": "DT:D1",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "The smooth functions in Exercise 1",
      "dependencies": [
        "DT:D0",
        "U001:P14.3",
        "RC:C0"
      ],
      "scope": "Actual flat positive cutoffs, compact input bump, ordinary phase nondegeneracy and exact conormal order"
    },
    {
      "id": "DT:D2",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "For Exercise 2, the compact time convolution",
      "dependencies": [
        "KS:S1",
        "P3:L1",
        "P3:L2",
        "P3:M4",
        "P3:M7",
        "RC:K6",
        "RC:K7"
      ],
      "scope": "Fourier extension agrees with the actual distribution action at every Sobolev order, with fixed enlarged supports for approximation"
    },
    {
      "id": "DT:X1",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "**1. Zero travel time",
      "dependencies": [
        "DT:D0",
        "DT:D1",
        "DT:H0",
        "DT:H1",
        "DT:H2",
        "CH:W4",
        "RC:C0",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Full unchanged forcing-boundary kernel, exact reflexive correction and strict-hull impossibility for every correction"
    },
    {
      "id": "DT:X2",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "**2. Signed fundamental kernels",
      "dependencies": [
        "RP:K0",
        "RP:K1",
        "RP:F3",
        "RC:C2",
        "DT:D2",
        "P3:M4",
        "P3:L1",
        "P3:L3",
        "U001:F0-CALC"
      ],
      "scope": "Full unchanged two-sided identities, formal adjoints, elliptic difference and every real local Sobolev bound including the complete compact-multiplier proof"
    },
    {
      "id": "DT:X3",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "**3. Why the symbol frame",
      "dependencies": [
        "DT:B3",
        "DT:B4",
        "GS:Z10"
      ],
      "scope": "Full unchanged solved density-degree calculation and exact scalar symbol order"
    },
    {
      "id": "DT:V0",
      "source": "directional-transport-for-characteristic-symbols.md",
      "source_sha256": "38f61dd274f68bb55186f4b18085b038114f9aa83993a4146090c3a6bb508c6f",
      "proof_locator": "The figure fixes",
      "dependencies": [
        "DT:X1"
      ],
      "scope": "Exact fixed-input wavefront slice, filled versus excluded endpoints, coordinate scale and unbounded rays"
    }
  ],
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    "../20261005-restored-prescribed-coordinates/proof-map.json",
    "../20261005-restored-clean-pairs/proof-map.json",
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    "../20261005-restored-real-principal/proof-map.json",
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    "../20261005-restored-first-order-cauchy/proof-map.json",
    "../20261005-mixed-halfspace-foundations/proof-map.json",
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  "component_proofs_complete": true,
  "U041_restored": true,
  "full_course_complete": false,
  "public_release_authorized": false
}