{
  "scope": "Canonical geometry, ordinary Fourier-integral calculus, and general homogeneous symbol transport with complete symbol topology and asymptotics.",
  "proofs": [
    {
      "id": "CC:C0",
      "source": "clean-canonical-composition.md",
      "source_sha256": "04ef63df898e5d6a4c0d5ee3cc02d0ae2bf27f02b51b8c3d4558e3687369a433",
      "proof_locator": "## C0. Conventions and the exact prerequisites",
      "dependencies": [
        "GEO:C0"
      ]
    },
    {
      "id": "CC:C1",
      "source": "clean-canonical-composition.md",
      "source_sha256": "04ef63df898e5d6a4c0d5ee3cc02d0ae2bf27f02b51b8c3d4558e3687369a433",
      "proof_locator": "## C1. The linear fibre product, excess and composed Lagrangian",
      "dependencies": [
        "CC:C0"
      ]
    },
    {
      "id": "CC:C2",
      "source": "clean-canonical-composition.md",
      "source_sha256": "04ef63df898e5d6a4c0d5ee3cc02d0ae2bf27f02b51b8c3d4558e3687369a433",
      "proof_locator": "## C2. Clean smooth composition and its exact tangent rank",
      "dependencies": [
        "CC:C1",
        "U001:P3",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ]
    },
    {
      "id": "CC:C3",
      "source": "clean-canonical-composition.md",
      "source_sha256": "04ef63df898e5d6a4c0d5ee3cc02d0ae2bf27f02b51b8c3d4558e3687369a433",
      "proof_locator": "## C3. A complete global embedding criterion",
      "dependencies": [
        "CC:C2",
        "U001:F0-COMP"
      ]
    },
    {
      "id": "CC:C4",
      "source": "clean-canonical-composition.md",
      "source_sha256": "04ef63df898e5d6a4c0d5ee3cc02d0ae2bf27f02b51b8c3d4558e3687369a433",
      "proof_locator": "## C4. The density isomorphism, with its normalization",
      "dependencies": [
        "CC:C1",
        "U001:P8-smooth"
      ]
    },
    {
      "id": "CC:C5",
      "source": "clean-canonical-composition.md",
      "source_sha256": "04ef63df898e5d6a4c0d5ee3cc02d0ae2bf27f02b51b8c3d4558e3687369a433",
      "proof_locator": "## C5. Smooth density composition and integration over the fibre",
      "dependencies": [
        "CC:C2",
        "CC:C3",
        "CC:C4",
        "U001:U001-A4",
        "U001:P21.3",
        "U001:P21.4",
        "U001:P20.4",
        "U001:P20.5",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ]
    },
    {
      "id": "CC:C-EX1",
      "source": "clean-canonical-composition.md",
      "source_sha256": "04ef63df898e5d6a4c0d5ee3cc02d0ae2bf27f02b51b8c3d4558e3687369a433",
      "proof_locator": "**Exercise C1 —",
      "dependencies": [
        "CC:C1",
        "CC:C4",
        "CC:C5"
      ]
    },
    {
      "id": "CC:C-EX2",
      "source": "clean-canonical-composition.md",
      "source_sha256": "04ef63df898e5d6a4c0d5ee3cc02d0ae2bf27f02b51b8c3d4558e3687369a433",
      "proof_locator": "**Exercise C2 —",
      "dependencies": [
        "CC:C1",
        "CC:C4",
        "CC:C5"
      ]
    },
    {
      "id": "CC:C-EX3",
      "source": "clean-canonical-composition.md",
      "source_sha256": "04ef63df898e5d6a4c0d5ee3cc02d0ae2bf27f02b51b8c3d4558e3687369a433",
      "proof_locator": "**Exercise C3 —",
      "dependencies": [
        "CC:C2"
      ]
    },
    {
      "id": "CC:C-EX4",
      "source": "clean-canonical-composition.md",
      "source_sha256": "04ef63df898e5d6a4c0d5ee3cc02d0ae2bf27f02b51b8c3d4558e3687369a433",
      "proof_locator": "**Exercise C4 —",
      "dependencies": [
        "CC:C3",
        "U001:EXPONENTIAL-TRIGONOMETRIC"
      ]
    },
    {
      "id": "MC:G0",
      "source": "maslov-composition-and-gaussian-factors.md",
      "source_sha256": "e2e6b9dd44b83ac52dcaa6222575bb20dea37ca0054772f721e0d14e5d9bff78",
      "proof_locator": "## G0. Exact inputs and conventions",
      "dependencies": [
        "CC:C0",
        "ML:M0a",
        "ML:M1",
        "ML:M2",
        "ML:M3",
        "ML:M4",
        "ML:M5",
        "ML:M6",
        "U001:Q4",
        "U001:Q5",
        "U001:Q6"
      ]
    },
    {
      "id": "MC:G1",
      "source": "maslov-composition-and-gaussian-factors.md",
      "source_sha256": "e2e6b9dd44b83ac52dcaa6222575bb20dea37ca0054772f721e0d14e5d9bff78",
      "proof_locator": "## G1. Quadratic presentations and their complete equivalence proof",
      "dependencies": [
        "MC:G0"
      ]
    },
    {
      "id": "MC:G2",
      "source": "maslov-composition-and-gaussian-factors.md",
      "source_sha256": "e2e6b9dd44b83ac52dcaa6222575bb20dea37ca0054772f721e0d14e5d9bff78",
      "proof_locator": "## G2. Gaussian phase frames in the relative Maslov line",
      "dependencies": [
        "MC:G1"
      ]
    },
    {
      "id": "MC:G3",
      "source": "maslov-composition-and-gaussian-factors.md",
      "source_sha256": "e2e6b9dd44b83ac52dcaa6222575bb20dea37ca0054772f721e0d14e5d9bff78",
      "proof_locator": "## G3. Compose quadratic phases and remove exactly the excess",
      "dependencies": [
        "MC:G1",
        "CC:C1"
      ]
    },
    {
      "id": "MC:G4",
      "source": "maslov-composition-and-gaussian-factors.md",
      "source_sha256": "e2e6b9dd44b83ac52dcaa6222575bb20dea37ca0054772f721e0d14e5d9bff78",
      "proof_locator": "## G4. The canonical Maslov composition map",
      "dependencies": [
        "MC:G2",
        "MC:G3",
        "U001:P2"
      ]
    },
    {
      "id": "MC:G5",
      "source": "maslov-composition-and-gaussian-factors.md",
      "source_sha256": "e2e6b9dd44b83ac52dcaa6222575bb20dea37ca0054772f721e0d14e5d9bff78",
      "proof_locator": "## G5. Identity, conjugation and associativity",
      "dependencies": [
        "MC:G4",
        "CC:C4"
      ]
    },
    {
      "id": "MC:G6",
      "source": "maslov-composition-and-gaussian-factors.md",
      "source_sha256": "e2e6b9dd44b83ac52dcaa6222575bb20dea37ca0054772f721e0d14e5d9bff78",
      "proof_locator": "## G6. The complete symbol-fibre map and proper-support integration",
      "dependencies": [
        "MC:G4",
        "CC:C5"
      ]
    },
    {
      "id": "MC:G7",
      "source": "maslov-composition-and-gaussian-factors.md",
      "source_sha256": "e2e6b9dd44b83ac52dcaa6222575bb20dea37ca0054772f721e0d14e5d9bff78",
      "proof_locator": "## G7. Positive dilation and the clean half-order shift",
      "dependencies": [
        "MC:G6",
        "CC:C4"
      ]
    },
    {
      "id": "MC:G-EX1",
      "source": "maslov-composition-and-gaussian-factors.md",
      "source_sha256": "e2e6b9dd44b83ac52dcaa6222575bb20dea37ca0054772f721e0d14e5d9bff78",
      "proof_locator": "**Exercise G1 —",
      "dependencies": [
        "MC:G2",
        "MC:G3",
        "MC:G6"
      ]
    },
    {
      "id": "MC:G-EX2",
      "source": "maslov-composition-and-gaussian-factors.md",
      "source_sha256": "e2e6b9dd44b83ac52dcaa6222575bb20dea37ca0054772f721e0d14e5d9bff78",
      "proof_locator": "**Exercise G2 —",
      "dependencies": [
        "MC:G3",
        "MC:G6"
      ]
    },
    {
      "id": "MC:G-EX3",
      "source": "maslov-composition-and-gaussian-factors.md",
      "source_sha256": "e2e6b9dd44b83ac52dcaa6222575bb20dea37ca0054772f721e0d14e5d9bff78",
      "proof_locator": "**Exercise G3 —",
      "dependencies": [
        "MC:G2",
        "MC:G3",
        "MC:G6"
      ]
    },
    {
      "id": "MC:G-EX4",
      "source": "maslov-composition-and-gaussian-factors.md",
      "source_sha256": "e2e6b9dd44b83ac52dcaa6222575bb20dea37ca0054772f721e0d14e5d9bff78",
      "proof_locator": "**Exercise G4 —",
      "dependencies": [
        "MC:G1",
        "MC:G2",
        "MC:G5"
      ]
    },
    {
      "id": "AC:A0",
      "source": "analytic-clean-composition.md",
      "source_sha256": "9271bfc92062fb965504e6a2fde3afda9aa62981083bbc636b5ccab902a4e5bb",
      "proof_locator": "## A0. Statement, supports and exact earlier proofs",
      "dependencies": [
        "CC:C2",
        "CC:C3",
        "MC:G6",
        "PH:F0",
        "PS:PS0"
      ]
    },
    {
      "id": "AC:A1",
      "source": "analytic-clean-composition.md",
      "source_sha256": "9271bfc92062fb965504e6a2fde3afda9aa62981083bbc636b5ccab902a4e5bb",
      "proof_locator": "## A1. Smooth action, adjoints and uniform frequency cutoffs",
      "dependencies": [
        "AC:A0",
        "PH:F2",
        "P2:OP0",
        "P2:OP5",
        "CH:T0",
        "U001:Q1",
        "U001:P18.5"
      ]
    },
    {
      "id": "AC:A2",
      "source": "analytic-clean-composition.md",
      "source_sha256": "9271bfc92062fb965504e6a2fde3afda9aa62981083bbc636b5ccab902a4e5bb",
      "proof_locator": "## A2. Unequal frequencies give a smooth kernel",
      "dependencies": [
        "AC:A1",
        "U001:U001-A4",
        "U001:U001-2.1"
      ]
    },
    {
      "id": "AC:A3",
      "source": "analytic-clean-composition.md",
      "source_sha256": "9271bfc92062fb965504e6a2fde3afda9aa62981083bbc636b5ccab902a4e5bb",
      "proof_locator": "## A3. A genuine homogeneous phase and its exact Jacobian",
      "dependencies": [
        "AC:A2",
        "U001:F0-DIFF",
        "U001:P21.3",
        "U001:P21.4"
      ]
    },
    {
      "id": "AC:A4",
      "source": "analytic-clean-composition.md",
      "source_sha256": "9271bfc92062fb965504e6a2fde3afda9aa62981083bbc636b5ccab902a4e5bb",
      "proof_locator": "## A4. The combined phase is clean of the geometric excess",
      "dependencies": [
        "AC:A3",
        "CC:C1",
        "CC:C2",
        "PH:F1",
        "PH:F6"
      ]
    },
    {
      "id": "AC:A5",
      "source": "analytic-clean-composition.md",
      "source_sha256": "9271bfc92062fb965504e6a2fde3afda9aa62981083bbc636b5ccab902a4e5bb",
      "proof_locator": "## A5. Equality with the composed operator and all remainders",
      "dependencies": [
        "AC:A1",
        "AC:A4",
        "PH:F2",
        "PH:F3",
        "PH:F4",
        "PH:F5",
        "P2:OP0",
        "U001:P18.5"
      ]
    },
    {
      "id": "AC:A6",
      "source": "analytic-clean-composition.md",
      "source_sha256": "9271bfc92062fb965504e6a2fde3afda9aa62981083bbc636b5ccab902a4e5bb",
      "proof_locator": "## A6. Ordinary symbol estimates for the fibre integral",
      "dependencies": [
        "AC:A0",
        "CC:C5",
        "MC:G7",
        "PS:PS2",
        "U001:F0-DIFF"
      ]
    },
    {
      "id": "AC:A7",
      "source": "analytic-clean-composition.md",
      "source_sha256": "9271bfc92062fb965504e6a2fde3afda9aa62981083bbc636b5ccab902a4e5bb",
      "proof_locator": "## A7. The density and signature comparison in full",
      "dependencies": [
        "AC:A3",
        "AC:A6",
        "MC:G1",
        "MC:G2",
        "MC:G4",
        "ML:M0a",
        "PS:PS1",
        "GEO:C3",
        "U001:P3",
        "U001:U001-A5"
      ]
    },
    {
      "id": "AC:A8",
      "source": "analytic-clean-composition.md",
      "source_sha256": "9271bfc92062fb965504e6a2fde3afda9aa62981083bbc636b5ccab902a4e5bb",
      "proof_locator": "## A8. Principal symbol, its constant and the lower-order criterion",
      "dependencies": [
        "AC:A5",
        "AC:A7",
        "PH:F3",
        "PH:F6a",
        "PS:PS3",
        "PS:PS6"
      ]
    },
    {
      "id": "AC:A9",
      "source": "analytic-clean-composition.md",
      "source_sha256": "9271bfc92062fb965504e6a2fde3afda9aa62981083bbc636b5ccab902a4e5bb",
      "proof_locator": "## A9. Global assembly, support and the precise continuity obtained",
      "dependencies": [
        "AC:A5",
        "AC:A6",
        "AC:A8",
        "PS:PS5",
        "PH:F6",
        "K:K6",
        "CC:C5"
      ]
    },
    {
      "id": "AC:A-EX1",
      "source": "analytic-clean-composition.md",
      "source_sha256": "9271bfc92062fb965504e6a2fde3afda9aa62981083bbc636b5ccab902a4e5bb",
      "proof_locator": "**Exercise A1 —",
      "dependencies": [
        "AC:A2"
      ]
    },
    {
      "id": "AC:A-EX2",
      "source": "analytic-clean-composition.md",
      "source_sha256": "9271bfc92062fb965504e6a2fde3afda9aa62981083bbc636b5ccab902a4e5bb",
      "proof_locator": "**Exercise A2 —",
      "dependencies": [
        "AC:A3",
        "AC:A4"
      ]
    },
    {
      "id": "AC:A-EX3",
      "source": "analytic-clean-composition.md",
      "source_sha256": "9271bfc92062fb965504e6a2fde3afda9aa62981083bbc636b5ccab902a4e5bb",
      "proof_locator": "**Exercise A3 —",
      "dependencies": [
        "AC:A8",
        "MC:G5",
        "CC:C4",
        "U001:Q4"
      ]
    },
    {
      "id": "AC:A-EX4",
      "source": "analytic-clean-composition.md",
      "source_sha256": "9271bfc92062fb965504e6a2fde3afda9aa62981083bbc636b5ccab902a4e5bb",
      "proof_locator": "**Exercise A4 —",
      "dependencies": [
        "AC:A8",
        "AC:A-EX3",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ]
    },
    {
      "id": "WM:W0",
      "source": "fio-sobolev-mapping.md",
      "source_sha256": "9ff6f087f9cd802caf4e3e9503e59b5bdb752f5ee47aa5f727cf2758222d2f25",
      "proof_locator": "## W0. Statement, conventions and exact inputs",
      "dependencies": [
        "AC:A0",
        "PH:F0",
        "P1:B1"
      ]
    },
    {
      "id": "WM:W1",
      "source": "fio-sobolev-mapping.md",
      "source_sha256": "9ff6f087f9cd802caf4e3e9503e59b5bdb752f5ee47aa5f727cf2758222d2f25",
      "proof_locator": "## W1. Smooth kernels and a preliminary distribution bound",
      "dependencies": [
        "WM:W0",
        "AC:A1",
        "P1:B1",
        "P1:B4",
        "P1:B5",
        "P3:M4",
        "P3:M5",
        "P3:M6",
        "P3:M7",
        "P3:L3",
        "CH:T0"
      ]
    },
    {
      "id": "WM:W2",
      "source": "fio-sobolev-mapping.md",
      "source_sha256": "9ff6f087f9cd802caf4e3e9503e59b5bdb752f5ee47aa5f727cf2758222d2f25",
      "proof_locator": "## W2. Adjoint, diagonal and the graph estimate",
      "dependencies": [
        "WM:W1",
        "AC:A4",
        "AC:A5",
        "AC:A9",
        "PH:F4",
        "PH:F5",
        "PH:F6",
        "P2:OP0",
        "P2:OP2",
        "P2:OP5",
        "P1:B3",
        "P1:B4",
        "PS:PS5"
      ]
    },
    {
      "id": "WM:W3",
      "source": "fio-sobolev-mapping.md",
      "source_sha256": "9ff6f087f9cd802caf4e3e9503e59b5bdb752f5ee47aa5f727cf2758222d2f25",
      "proof_locator": "## W3. The rank matrix and the slicing subspaces",
      "dependencies": [
        "WM:W0",
        "PH:F1",
        "GEO:C0",
        "GEO:C2",
        "U001:F0-DIFF"
      ]
    },
    {
      "id": "WM:W4",
      "source": "fio-sobolev-mapping.md",
      "source_sha256": "9ff6f087f9cd802caf4e3e9503e59b5bdb752f5ee47aa5f727cf2758222d2f25",
      "proof_locator": "## W4. Actual graph slices and the quarter-codimension shift",
      "dependencies": [
        "WM:W2",
        "WM:W3",
        "PH:F1",
        "AC:A1",
        "P2:OP0",
        "U001:P3",
        "U001:P21.3",
        "U001:P21.4"
      ]
    },
    {
      "id": "WM:W5",
      "source": "fio-sobolev-mapping.md",
      "source_sha256": "9ff6f087f9cd802caf4e3e9503e59b5bdb752f5ee47aa5f727cf2758222d2f25",
      "proof_locator": "## W5. Integrating the graph estimates",
      "dependencies": [
        "WM:W1",
        "WM:W2",
        "WM:W4",
        "PS:PS5",
        "P3:M4",
        "P3:M5",
        "P3:M6",
        "P3:M7",
        "P1:B5"
      ]
    },
    {
      "id": "WM:W6",
      "source": "fio-sobolev-mapping.md",
      "source_sha256": "9ff6f087f9cd802caf4e3e9503e59b5bdb752f5ee47aa5f727cf2758222d2f25",
      "proof_locator": "## W6. All real Sobolev orders and proper supports",
      "dependencies": [
        "WM:W1",
        "WM:W5",
        "AC:A9",
        "K:K0",
        "K:K1",
        "K:K2",
        "K:K3",
        "K:K4",
        "P2:OP4",
        "P2:OP5",
        "P1:B4",
        "P1:B5"
      ]
    },
    {
      "id": "WM:W-EX1",
      "source": "fio-sobolev-mapping.md",
      "source_sha256": "9ff6f087f9cd802caf4e3e9503e59b5bdb752f5ee47aa5f727cf2758222d2f25",
      "proof_locator": "**Exercise W1 —",
      "dependencies": [
        "WM:W3",
        "WM:W4",
        "WM:W5",
        "P3:M5",
        "P3:L3",
        "U001:Q4"
      ]
    },
    {
      "id": "WM:W-EX2",
      "source": "fio-sobolev-mapping.md",
      "source_sha256": "9ff6f087f9cd802caf4e3e9503e59b5bdb752f5ee47aa5f727cf2758222d2f25",
      "proof_locator": "**Exercise W2 —",
      "dependencies": [
        "WM:W-EX1",
        "P3:L3",
        "P2:OP1"
      ]
    },
    {
      "id": "WM:W-EX3",
      "source": "fio-sobolev-mapping.md",
      "source_sha256": "9ff6f087f9cd802caf4e3e9503e59b5bdb752f5ee47aa5f727cf2758222d2f25",
      "proof_locator": "**Exercise W3 —",
      "dependencies": [
        "WM:W3"
      ]
    },
    {
      "id": "WM:W-EX4",
      "source": "fio-sobolev-mapping.md",
      "source_sha256": "9ff6f087f9cd802caf4e3e9503e59b5bdb752f5ee47aa5f727cf2758222d2f25",
      "proof_locator": "**Exercise W4 —",
      "dependencies": [
        "WM:W4",
        "WM:W6"
      ]
    },
    {
      "id": "CT:T0",
      "source": "compactness-and-essential-norms.md",
      "source_sha256": "e7d95ebec427aad2efdebca345c724a414014beee88160ea87b51adab87cea12",
      "proof_locator": "## T0. Precise statements and supplied prerequisites",
      "dependencies": [
        "WM:W0",
        "PS:PS2",
        "MC:G4"
      ]
    },
    {
      "id": "CT:T1",
      "source": "compactness-and-essential-norms.md",
      "source_sha256": "e7d95ebec427aad2efdebca345c724a414014beee88160ea87b51adab87cea12",
      "proof_locator": "## T1. The Hilbert-space facts, with proofs",
      "dependencies": [
        "P3:M5",
        "P3:M6",
        "GEO:C0",
        "U001:L7.1.4"
      ]
    },
    {
      "id": "CT:T2",
      "source": "compactness-and-essential-norms.md",
      "source_sha256": "e7d95ebec427aad2efdebca345c724a414014beee88160ea87b51adab87cea12",
      "proof_locator": "## T2. Square-integrable kernels and negative orders",
      "dependencies": [
        "CT:T1",
        "P3:M4",
        "P3:M7",
        "P3:L3",
        "P1:B4",
        "P2:OP4",
        "P2:OP5",
        "PS:PS5"
      ]
    },
    {
      "id": "CT:T3",
      "source": "compactness-and-essential-norms.md",
      "source_sha256": "e7d95ebec427aad2efdebca345c724a414014beee88160ea87b51adab87cea12",
      "proof_locator": "## T3. Packets that measure a symbol at infinity",
      "dependencies": [
        "CT:T1",
        "P3:M3",
        "P3:M4",
        "P3:M5",
        "P3:L1",
        "P3:L3",
        "P2:OP1",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS",
        "U001:P21.3"
      ]
    },
    {
      "id": "CT:T4",
      "source": "compactness-and-essential-norms.md",
      "source_sha256": "e7d95ebec427aad2efdebca345c724a414014beee88160ea87b51adab87cea12",
      "proof_locator": "## T4. The exact ordinary essential norm, including matrices",
      "dependencies": [
        "CT:T2",
        "CT:T3",
        "K:K2",
        "P2:OP2",
        "P2:OP3",
        "P2:OP4",
        "P2:OP5",
        "P2:OP6",
        "P1:B4",
        "PS:PS5",
        "U001:P3",
        "U001:P8-smooth",
        "U001:P16.1"
      ]
    },
    {
      "id": "CT:T5",
      "source": "compactness-and-essential-norms.md",
      "source_sha256": "e7d95ebec427aad2efdebca345c724a414014beee88160ea87b51adab87cea12",
      "proof_locator": "## T5. The normalization on a canonical graph",
      "dependencies": [
        "WM:W2",
        "AC:A8",
        "AC:A9",
        "CC:C4",
        "MC:G4",
        "MC:G5",
        "PS:PS2",
        "CT:T1"
      ]
    },
    {
      "id": "CT:T6",
      "source": "compactness-and-essential-norms.md",
      "source_sha256": "e7d95ebec427aad2efdebca345c724a414014beee88160ea87b51adab87cea12",
      "proof_locator": "## T6. One graph: compactness and the sharp essential norm",
      "dependencies": [
        "CT:T1",
        "CT:T4",
        "CT:T5",
        "WM:W2"
      ]
    },
    {
      "id": "CT:T7",
      "source": "compactness-and-essential-norms.md",
      "source_sha256": "e7d95ebec427aad2efdebca345c724a414014beee88160ea87b51adab87cea12",
      "proof_locator": "## T7. Local graphs, proper support and Sobolev compactness",
      "dependencies": [
        "CT:T1",
        "CT:T2",
        "CT:T3",
        "CT:T6",
        "WM:W0",
        "WM:W5",
        "WM:W6",
        "AC:A9",
        "PS:PS5",
        "PS:PS6",
        "K:K4",
        "P3:L3",
        "P3:M3",
        "P3:M4",
        "P2:OP0",
        "P2:OP1",
        "PH:F2",
        "PH:F3",
        "U001:P14.1",
        "U001:P15.1",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ]
    },
    {
      "id": "CT:T-EX1",
      "source": "compactness-and-essential-norms.md",
      "source_sha256": "e7d95ebec427aad2efdebca345c724a414014beee88160ea87b51adab87cea12",
      "proof_locator": "**Exercise T1 —",
      "dependencies": [
        "CT:T4",
        "K:K2",
        "U001:P8-smooth",
        "U001:P14.1",
        "U001:P14.3"
      ]
    },
    {
      "id": "CT:T-EX2",
      "source": "compactness-and-essential-norms.md",
      "source_sha256": "e7d95ebec427aad2efdebca345c724a414014beee88160ea87b51adab87cea12",
      "proof_locator": "**Exercise T2 —",
      "dependencies": [
        "CT:T4",
        "U001:P8-smooth",
        "U001:P14.1",
        "U001:P16.1",
        "U001:P16.2"
      ]
    },
    {
      "id": "CT:T-EX3",
      "source": "compactness-and-essential-norms.md",
      "source_sha256": "e7d95ebec427aad2efdebca345c724a414014beee88160ea87b51adab87cea12",
      "proof_locator": "**Exercise T3 —",
      "dependencies": [
        "CT:T5",
        "CT:T6",
        "U001:P21.3"
      ]
    },
    {
      "id": "CT:T-EX4",
      "source": "compactness-and-essential-norms.md",
      "source_sha256": "e7d95ebec427aad2efdebca345c724a414014beee88160ea87b51adab87cea12",
      "proof_locator": "**Exercise T4 —",
      "dependencies": [
        "CT:T1",
        "CT:T7",
        "P3:M5",
        "U001:P15.1",
        "U001:P16.2",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ]
    },
    {
      "id": "HT:H0",
      "source": "homogeneous-symbol-transport.md",
      "source_sha256": "69f7d6fe44bbeb876ef516fce68914e1a47786f64fc51d2cc398dab18fbb18f9",
      "proof_locator": "## H0. Classes, conventions and exact inputs",
      "dependencies": [
        "U001:P8-smooth",
        "PH:F4"
      ]
    },
    {
      "id": "HT:H1",
      "source": "homogeneous-symbol-transport.md",
      "source_sha256": "69f7d6fe44bbeb876ef516fce68914e1a47786f64fc51d2cc398dab18fbb18f9",
      "proof_locator": "## H1. A complete locally convex symbol space",
      "dependencies": [
        "U001:L2.4.5",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS",
        "U001:P2",
        "U001:L7.4.11"
      ]
    },
    {
      "id": "HT:H2",
      "source": "homogeneous-symbol-transport.md",
      "source_sha256": "69f7d6fe44bbeb876ef516fce68914e1a47786f64fc51d2cc398dab18fbb18f9",
      "proof_locator": "## H2. The full homogeneous pullback theorem",
      "dependencies": [
        "HT:H1",
        "U001:L8.3.7",
        "U001:L7.4.11"
      ]
    },
    {
      "id": "HT:H3",
      "source": "homogeneous-symbol-transport.md",
      "source_sha256": "69f7d6fe44bbeb876ef516fce68914e1a47786f64fc51d2cc398dab18fbb18f9",
      "proof_locator": "## H3. Conic manifolds and equivariant vector bundles",
      "dependencies": [
        "HT:H1",
        "HT:H2",
        "PS:PS5"
      ]
    },
    {
      "id": "HT:H4",
      "source": "homogeneous-symbol-transport.md",
      "source_sha256": "69f7d6fe44bbeb876ef516fce68914e1a47786f64fc51d2cc398dab18fbb18f9",
      "proof_locator": "## H4. Submersions, reflection and a continuous left inverse",
      "dependencies": [
        "HT:H2",
        "HT:H3",
        "U001:P3",
        "PS:PS5"
      ]
    },
    {
      "id": "HT:H5",
      "source": "homogeneous-symbol-transport.md",
      "source_sha256": "69f7d6fe44bbeb876ef516fce68914e1a47786f64fc51d2cc398dab18fbb18f9",
      "proof_locator": "## H5. What properness supplies",
      "dependencies": [
        "HT:H2",
        "HT:H4",
        "U001:L7.4.11",
        "U001:F0-COMP"
      ]
    },
    {
      "id": "HT:H6",
      "source": "homogeneous-symbol-transport.md",
      "source_sha256": "69f7d6fe44bbeb876ef516fce68914e1a47786f64fc51d2cc398dab18fbb18f9",
      "proof_locator": "## H6. Asymptotic summation with every derivative controlled",
      "dependencies": [
        "HT:H1",
        "HT:H3",
        "U001:P3",
        "U001:U001-A4"
      ]
    },
    {
      "id": "HT:H7",
      "source": "homogeneous-symbol-transport.md",
      "source_sha256": "69f7d6fe44bbeb876ef516fce68914e1a47786f64fc51d2cc398dab18fbb18f9",
      "proof_locator": "## H7. Recovering differentiated asymptotics from value estimates",
      "dependencies": [
        "HT:H1",
        "HT:H6",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ]
    },
    {
      "id": "HT:H8",
      "source": "homogeneous-symbol-transport.md",
      "source_sha256": "69f7d6fe44bbeb876ef516fce68914e1a47786f64fc51d2cc398dab18fbb18f9",
      "proof_locator": "## H8. Bounded-set convergence and frequency cutoffs",
      "dependencies": [
        "HT:H1",
        "HT:H6",
        "HT:H7",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS",
        "U001:L7.4.11"
      ]
    },
    {
      "id": "HT:H9",
      "source": "homogeneous-symbol-transport.md",
      "source_sha256": "69f7d6fe44bbeb876ef516fce68914e1a47786f64fc51d2cc398dab18fbb18f9",
      "proof_locator": "## H9. Transport of expansions and the exact scope now proved",
      "dependencies": [
        "HT:H2",
        "HT:H3",
        "HT:H4",
        "HT:H5",
        "HT:H6",
        "HT:H7",
        "HT:H8"
      ]
    },
    {
      "id": "HT:H-EX1",
      "source": "homogeneous-symbol-transport.md",
      "source_sha256": "69f7d6fe44bbeb876ef516fce68914e1a47786f64fc51d2cc398dab18fbb18f9",
      "proof_locator": "**Exercise H1 —",
      "dependencies": [
        "HT:H2",
        "U001:P14.1",
        "U001:P15.1"
      ]
    },
    {
      "id": "HT:H-EX2",
      "source": "homogeneous-symbol-transport.md",
      "source_sha256": "69f7d6fe44bbeb876ef516fce68914e1a47786f64fc51d2cc398dab18fbb18f9",
      "proof_locator": "**Exercise H2 —",
      "dependencies": [
        "HT:H2",
        "U001:U001-A4"
      ]
    },
    {
      "id": "HT:H-EX3",
      "source": "homogeneous-symbol-transport.md",
      "source_sha256": "69f7d6fe44bbeb876ef516fce68914e1a47786f64fc51d2cc398dab18fbb18f9",
      "proof_locator": "**Exercise H3 —",
      "dependencies": [
        "HT:H4",
        "HT:H5"
      ]
    },
    {
      "id": "HT:H-EX4",
      "source": "homogeneous-symbol-transport.md",
      "source_sha256": "69f7d6fe44bbeb876ef516fce68914e1a47786f64fc51d2cc398dab18fbb18f9",
      "proof_locator": "**Exercise H4 —",
      "dependencies": [
        "HT:H8"
      ]
    }
  ],
  "earlier_intrinsic_map": "../20261004-free-intrinsic-graph/proof-map.json",
  "earlier_stationary_map": "../20261004-free-stationary-phase/proof-map.json",
  "declared_logical_axioms": "The earlier programme real/complex field, natural number, finite-dimensional algebra and set-theoretic axioms are retained; this component adds no choice or manifold theorem as an unproved import.",
  "all_dependency_ids_resolve": true,
  "acyclic": true,
  "transitive_U001_nodes": 219,
  "transitive_intrinsic_nodes": 96,
  "full_course_complete": false,
  "public_release_authorized": false,
  "Maslov_component_nodes": 12,
  "Maslov_component_earlier_programme_nodes": 20,
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  "analytic_component_nodes": 14,
  "analytic_component_earlier_programme_nodes": 110,
  "ordinary_rank_Sobolev_mapping_proved": true,
  "graph_L2_mapping_proved": true,
  "mapping_component_nodes": 11,
  "mapping_component_earlier_programme_nodes": 119,
  "mapping_transitive_U001_nodes": 219,
  "graph_compactness_criterion_proved": true,
  "single_graph_essential_norm_proved": true,
  "ordinary_matrix_PDO_essential_norm_proved": true,
  "relative_frequency_branch_filter_proved": true,
  "compactness_component_nodes": 12,
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  "symbol_topology_and_asymptotics_proved": true,
  "derivative_loss_FIO_analytic_calculus_proved": false,
  "transport_component_nodes": 14,
  "transport_component_earlier_programme_nodes": 95,
  "transport_transitive_U001_nodes": 220
}