{
  "schema": "AN04-restored-local-signed-proof-map/v1",
  "proofs": [
    {
      "id": "LP:N0",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "The nonradial condition is essential;",
      "dependencies": [
        "FN:R0",
        "FN:R1"
      ],
      "scope": "Exact scalar half-density degree-one hypotheses and dimension-one radial obstruction"
    },
    {
      "id": "LP:M0",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "Use model coordinates",
      "dependencies": [
        "RP:K0",
        "RP:K1",
        "RP:K2",
        "RP:F2"
      ],
      "scope": "Actual signed distributions, both signs and complete diagonal wavefront including noncharacteristic directions"
    },
    {
      "id": "LP:M1",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "Choose an even smooth function",
      "dependencies": [
        "LP:M0",
        "U001:P14.3",
        "RC:C1",
        "U001:F0-COMP"
      ],
      "scope": "Displacement cutoff equals one on the whole diagonal and gives both proper projections"
    },
    {
      "id": "LP:M2",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "Since the delta distribution sets",
      "dependencies": [
        "LP:M1",
        "P3:M3",
        "P3:M4",
        "P3:L1",
        "KS:S1",
        "U001:Q3",
        "U001:Q4"
      ],
      "scope": "Actual finite-measure convolution, exact all-real multiplier bound, dense extension and test-function-topology agreement"
    },
    {
      "id": "LP:M3",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "The complete wavefront bound is",
      "dependencies": [
        "LP:M0",
        "LP:M1",
        "RP:F1",
        "RP:F2",
        "CH:W1"
      ],
      "scope": "Full reflected-input diagonal plus signed flow, with no ordinary-class claim for the whole signed kernel"
    },
    {
      "id": "LP:R0",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "The distributional product rule,",
      "dependencies": [
        "LP:M1",
        "RP:K0",
        "P3:L2"
      ],
      "scope": "Full signed product including the exact identity multiplier and cancellation of every zero-time jump"
    },
    {
      "id": "LP:R1",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "On the positive derivative support",
      "dependencies": [
        "LP:R0",
        "OSC:O2",
        "OSC:O3",
        "RP:F3"
      ],
      "scope": "Exact normalized conormal amplitude, minus-one-half order and the strict delayed band"
    },
    {
      "id": "LP:R2",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "The actual full wavefront bound is",
      "dependencies": [
        "LP:R1",
        "CH:W1",
        "RP:F1"
      ],
      "scope": "Full ambient wavefront with no zero endpoint and a genuine gap from the characteristic diagonal"
    },
    {
      "id": "LP:D0",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "The difference retains one ordinary class",
      "dependencies": [
        "LP:R1",
        "RP:F3",
        "GS:Z11"
      ],
      "scope": "Actual signed difference, correct normalization and ordinary ellipticity at the characteristic diagonal"
    },
    {
      "id": "LP:C0",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "The real homogeneous normal form gives",
      "dependencies": [
        "LP:N0",
        "FN:R1",
        "GE:D9",
        "GE:D11",
        "GE:D12",
        "GE:D13",
        "GE:D14",
        "GE:D15",
        "GE:D16",
        "GE:D17",
        "GE:D18",
        "GE:D19"
      ],
      "scope": "One exact canonical map and both full graph inverses with the entire ordinary lower symbol removed"
    },
    {
      "id": "LP:C1",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "Choose the representatives with their full",
      "dependencies": [
        "LP:C0",
        "GE:D8",
        "GE:D9",
        "GE:D12",
        "CH:W2",
        "CH:W4",
        "K:K3",
        "K:K4",
        "RC:C1"
      ],
      "scope": "Nested full graph and base cutoffs preserve all identities on the fixed interior cones"
    },
    {
      "id": "LP:C2",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "Let \\(V\\) be an interior model cone",
      "dependencies": [
        "LP:C1",
        "K:K4",
        "CH:W4",
        "U001:P14.3"
      ],
      "scope": "Actual proper order-zero source cutoff with full microsupport and compact base support"
    },
    {
      "id": "LP:C3",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "Here the closure and distance are taken",
      "dependencies": [
        "LP:C2",
        "LP:M3",
        "U001:F0-COMP"
      ],
      "scope": "One common displacement radius from compact normalized covectors and homogeneous extension"
    },
    {
      "id": "LP:C4",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "The corresponding kernel matching inclusion",
      "dependencies": [
        "LP:C3",
        "RC:C0",
        "RC:C1",
        "RC:C4"
      ],
      "scope": "Entire properly defined kernel product, uniform reflected matching and all endpoint exclusions"
    },
    {
      "id": "LP:C5",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "We also retain a useful defect.",
      "dependencies": [
        "LP:C0",
        "LP:C1",
        "LP:C3",
        "LP:C4",
        "RC:C1",
        "CH:W4"
      ],
      "scope": "Exact intertwining defect, both inverse-defect terms and actual smoothing on the entire localized base product"
    },
    {
      "id": "LP:F0",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "After the fixed local support cutoffs,",
      "dependencies": [
        "LP:C1",
        "LP:C2",
        "LP:C4",
        "LP:M1",
        "RC:C1"
      ],
      "scope": "Actual compact support through every proper factor and distributional continuity"
    },
    {
      "id": "LP:F1",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "Indeed the diagonal model matching",
      "dependencies": [
        "LP:C0",
        "LP:C4",
        "LP:F0",
        "G2:G0",
        "GF:L4",
        "GF:N3"
      ],
      "scope": "Full transformed diagonal and signed relation with exact Hamilton time orientation"
    },
    {
      "id": "LP:F2",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "Compute the complete right residual,",
      "dependencies": [
        "LP:R1",
        "LP:R2",
        "LP:C5",
        "LP:F0",
        "LP:F1",
        "RC:C7",
        "RC:C8",
        "RC:C9"
      ],
      "scope": "Entire right residual including both smooth terms, zero excess, exact order and strict signed wavefront"
    },
    {
      "id": "LP:F3",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "To check this neighborhood assertion,",
      "dependencies": [
        "LP:F2",
        "LP:C3",
        "U001:F0-COMP"
      ],
      "scope": "Compact normalized separation survives canonical conjugation and rules out limiting diagonal singularities"
    },
    {
      "id": "LP:F4",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "At a characteristic diagonal point where",
      "dependencies": [
        "LP:D0",
        "LP:C0",
        "LP:F0",
        "RC:C8",
        "RC:C9",
        "GE:D9",
        "GS:Z11"
      ],
      "scope": "Actual difference and noncharacteristic ordinary symbol with inverse derivative bounds on full rays"
    },
    {
      "id": "LP:F5",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "Use the order-zero mapping of",
      "dependencies": [
        "LP:M2",
        "LP:F0",
        "GE:D7",
        "KS:S1",
        "RC:C1"
      ],
      "scope": "All-real Sobolev product bound and actual distributional extension using one slightly larger compact approximation support"
    },
    {
      "id": "LP:G0",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "For the unit-scale cutoff",
      "dependencies": [
        "LP:R0",
        "LP:R1",
        "DT:D0",
        "DT:D1",
        "DT:D2",
        "KC:C0"
      ],
      "scope": "Exact signed flat correction, zero-time normalization, ordinary class and corrected kernel identity"
    },
    {
      "id": "LP:G1",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "The corrected inverse ceases to be",
      "dependencies": [
        "LP:G0",
        "RP:K2",
        "DT:X2"
      ],
      "scope": "Noncompact signed tails, loss of global properness and retained local distribution/Sobolev action"
    },
    {
      "id": "LP:V0",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "*The picture is the",
      "dependencies": [
        "LP:R2",
        "LP:G0"
      ],
      "scope": "Exact affine diagram coordinates, signed residual-band inclusion and the omitted nonzero-time diagonal directions"
    },
    {
      "id": "LP:X1",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "**1. The entire signed cutoff",
      "dependencies": [
        "LP:G0",
        "LP:G1",
        "LP:D0"
      ],
      "scope": "Complete unchanged signed derivatives, oriented primitives, difference and properness counterexample"
    },
    {
      "id": "LP:X2",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "**2. A cutoff in absolute",
      "dependencies": [
        "LP:R0",
        "LP:M3",
        "RP:F2",
        "CH:W1"
      ],
      "scope": "Complete unchanged absolute-cutoff diagonal counterexample with explicit noncancellation at all relevant diagonal directions"
    },
    {
      "id": "LP:X3",
      "source": "local-signed-parametrices-and-delayed-errors.md",
      "source_sha256": "86521b4554a81a42d7c377d43416d9c80de5b6aa4d4be4809e91afdaf8fd8b55",
      "proof_locator": "**3. Arbitrary graph orders",
      "dependencies": [
        "LP:F2",
        "LP:F4",
        "LP:F5",
        "GE:D19"
      ],
      "scope": "Complete unchanged real graph-order cancellation on the exact Sobolev scales"
    }
  ],
  "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",
    "../20261005-hyperbolicity-necessity-foundations/proof-map.json",
    "../20261005-restored-hyperbolicity-necessity/proof-map.json",
    "../20261005-positivity-foundations/proof-map.json",
    "../20261005-metric-weyl-calculus/proof-map.json",
    "../20261005-metric-positivity/proof-map.json",
    "../20261005-restored-principal-boundary/proof-map.json",
    "../20261005-restored-sobolev-propagation/proof-map.json",
    "../20261005-restored-compact-tube/proof-map.json",
    "../20261005-restored-singular-ray/proof-map.json",
    "../20261005-restored-compact-solvability/proof-map.json",
    "../20261006-restored-global-solvability/proof-map.json",
    "../20261006-restored-global-flow/proof-map.json",
    "../20261006-restored-directional-transport/proof-map.json",
    "../20261006-restored-kernel-corrections/proof-map.json"
  ],
  "component_proofs_complete": true,
  "full_course_complete": false,
  "public_release_authorized": false,
  "U044_restored": true
}