{
  "schema": "AN04-metric-weyl-calculus-proof-map/v1",
  "proofs": [
    {
      "id": "WY:W1",
      "source": "metric-weyl-products.md",
      "source_sha256": "8c0fb854ed5734841fe322e96f06a79d23626e82c0bf66a664fe4b0060cc38f8",
      "proof_locator": "## 1.",
      "dependencies": [
        "P2:F1",
        "P2:F2",
        "P2:F3",
        "U001:Q5",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Symplectic duality, exact infimum convolution, cross parameter and both mean-metric inequalities"
    },
    {
      "id": "WY:W2",
      "source": "metric-weyl-products.md",
      "source_sha256": "8c0fb854ed5734841fe322e96f06a79d23626e82c0bf66a664fe4b0060cc38f8",
      "proof_locator": "## 2.",
      "dependencies": [
        "WY:W1",
        "P2:ML1",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Complete two-segment metric transport, exact distance bases, mean slow variation and full two-way cross-weight equivalence"
    },
    {
      "id": "WY:W3",
      "source": "metric-weyl-products.md",
      "source_sha256": "8c0fb854ed5734841fe322e96f06a79d23626e82c0bf66a664fe4b0060cc38f8",
      "proof_locator": "## 3.",
      "dependencies": [
        "WY:W1",
        "WY:W2",
        "P2:QG1",
        "P2:QG5"
      ],
      "scope": "Full diagonal metric/weight criterion, necessity and sufficiency, reflected intermediate point and actual phase-dual form"
    },
    {
      "id": "WY:W4",
      "source": "metric-weyl-products.md",
      "source_sha256": "8c0fb854ed5734841fe322e96f06a79d23626e82c0bf66a664fe4b0060cc38f8",
      "proof_locator": "## 4.",
      "dependencies": [
        "P3:L1",
        "P3:L2",
        "P3:L3",
        "P2:OP0",
        "P2:OP1",
        "U001:Q3",
        "U001:Q4",
        "U001:P21.4",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Direct Weyl kernel for all tempered symbols, determinant-one coordinates, strong-dual action, polynomial distribution coefficients and exact adjoint"
    },
    {
      "id": "WY:W5",
      "source": "metric-weyl-products.md",
      "source_sha256": "8c0fb854ed5734841fe322e96f06a79d23626e82c0bf66a664fe4b0060cc38f8",
      "proof_locator": "## 5.",
      "dependencies": [
        "WY:W4",
        "P3:L3",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Exact left affine product and derivative signs on distributional kernels"
    },
    {
      "id": "WY:W6",
      "source": "metric-weyl-products.md",
      "source_sha256": "8c0fb854ed5734841fe322e96f06a79d23626e82c0bf66a664fe4b0060cc38f8",
      "proof_locator": "**Proposition 5.1",
      "dependencies": [
        "WY:W4",
        "WY:W5",
        "P3:L1",
        "P3:L3",
        "P3:M3",
        "P3:M4",
        "P3:M5",
        "P3:M6",
        "P3:M7",
        "U001:Q3",
        "U001:U001-A4",
        "U001:P15.1",
        "U001:P15.2",
        "U001:P21.4",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Full affine selfadjoint closure, multiplication adjoint domain and core, quadratic gauge and explicit unitary group including c0"
    },
    {
      "id": "WY:W7",
      "source": "metric-weyl-products.md",
      "source_sha256": "8c0fb854ed5734841fe322e96f06a79d23626e82c0bf66a664fe4b0060cc38f8",
      "proof_locator": "**Editorial domain calculation in the original coordinates.**",
      "dependencies": [
        "WY:W6",
        "P3:L3",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Exact original-coordinate gauge, full distributional sum domain, no separate summand domains, phase difference and zero-vector cases"
    },
    {
      "id": "WY:W8",
      "source": "metric-weyl-products.md",
      "source_sha256": "8c0fb854ed5734841fe322e96f06a79d23626e82c0bf66a664fe4b0060cc38f8",
      "proof_locator": "For later use write",
      "dependencies": [
        "WY:W6",
        "WY:W7",
        "P3:L1",
        "P3:M4",
        "U001:P15.2",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Full unitary plane-wave formula and ordered phase cocycle, Schwartz Fourier superposition"
    },
    {
      "id": "WY:W9",
      "source": "metric-weyl-products.md",
      "source_sha256": "8c0fb854ed5734841fe322e96f06a79d23626e82c0bf66a664fe4b0060cc38f8",
      "proof_locator": "## 6.",
      "dependencies": [
        "WY:W8",
        "WY:W4",
        "WY:W5",
        "P2:QG1",
        "P3:L1",
        "P3:L3",
        "P3:M4",
        "U001:Q3",
        "U001:Q4",
        "U001:P21.4"
      ],
      "scope": "Exact Schwartz Weyl product, pi normalization, phase sign, diagonal restriction and full 16-fold phase-dual scaling"
    },
    {
      "id": "WY:W10",
      "source": "metric-weyl-products.md",
      "source_sha256": "8c0fb854ed5734841fe322e96f06a79d23626e82c0bf66a664fe4b0060cc38f8",
      "proof_locator": "## 7.",
      "dependencies": [
        "WY:W1",
        "WY:W2",
        "WY:W3",
        "WY:W9",
        "P2:ML7",
        "P2:QG7",
        "P2:QG8",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Full compatible-metric product with H<=1, every finite remainder, tensor/diagonal/four factors, legitimate H weights and bounded-set uniqueness"
    },
    {
      "id": "WY:W11",
      "source": "metric-weyl-products.md",
      "source_sha256": "8c0fb854ed5734841fe322e96f06a79d23626e82c0bf66a664fe4b0060cc38f8",
      "proof_locator": "For scalar \\(b\\),",
      "dependencies": [
        "WY:W10",
        "WY:W5"
      ],
      "scope": "Exact scalar self-product cancellation and order-two symbol remainder, no unproved operator bound"
    },
    {
      "id": "WY:A1",
      "source": "weyl-action-and-covariance.md",
      "source_sha256": "b8cfbf92557e2762cbecc6b856ec98f84d8e64163113de31add3fd1bbf136b2f",
      "proof_locator": "## 1.",
      "dependencies": [
        "WY:W2",
        "U001:Q3",
        "P3:L1",
        "P3:L3",
        "P3:M3",
        "P3:M5",
        "TG:B1",
        "TG:B2",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Full polynomial growth in original coordinates, equivalent Schwartz L2 norms and completeness, strong-dual bounded sets by Baire"
    },
    {
      "id": "WY:A2",
      "source": "weyl-action-and-covariance.md",
      "source_sha256": "b8cfbf92557e2762cbecc6b856ec98f84d8e64163113de31add3fd1bbf136b2f",
      "proof_locator": "## 2.",
      "dependencies": [
        "WY:W8",
        "P3:L1",
        "P3:M3",
        "P3:M4",
        "P3:M5",
        "P3:M6",
        "P3:M7",
        "U001:P21.4",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Complete affine-invariant Fourier L1 operator bound with explicit Hilbert Riemann integration and compact-support estimate"
    },
    {
      "id": "WY:A3",
      "source": "weyl-action-and-covariance.md",
      "source_sha256": "b8cfbf92557e2762cbecc6b856ec98f84d8e64163113de31add3fd1bbf136b2f",
      "proof_locator": "**Editorial reconstruction:",
      "dependencies": [
        "WY:A2",
        "P2:F1",
        "P2:F2",
        "U001:Q5",
        "U001:P21.4",
        "P3:L1",
        "P3:M4",
        "P3:M5",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "All original-form Fourier Jacobians, multinomial derivatives, exact support volume and finite s>n threshold"
    },
    {
      "id": "WY:A4",
      "source": "weyl-action-and-covariance.md",
      "source_sha256": "b8cfbf92557e2762cbecc6b856ec98f84d8e64163113de31add3fd1bbf136b2f",
      "proof_locator": "## 3.",
      "dependencies": [
        "WY:A1",
        "WY:W1",
        "P2:ML1",
        "P2:ML2",
        "P2:ML3",
        "P2:ML4"
      ],
      "scope": "Reference metric, sum-dual distance and frozen localization with fixed support margins"
    },
    {
      "id": "WY:A5",
      "source": "weyl-action-and-covariance.md",
      "source_sha256": "b8cfbf92557e2762cbecc6b856ec98f84d8e64163113de31add3fd1bbf136b2f",
      "proof_locator": "Here are the geometric and differential details.",
      "dependencies": [
        "WY:A4",
        "WY:A2",
        "WY:W5",
        "P2:F1",
        "P2:F3",
        "U001:F0-COMP",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Exact minimizing support functional, safe division and all reciprocal derivatives, right-affine iteration and uniform Schwartz-input decay"
    },
    {
      "id": "WY:A6",
      "source": "weyl-action-and-covariance.md",
      "source_sha256": "b8cfbf92557e2762cbecc6b856ec98f84d8e64163113de31add3fd1bbf136b2f",
      "proof_locator": "**Polynomial counting.**",
      "dependencies": [
        "WY:A1",
        "WY:A4",
        "WY:W2",
        "P2:ML2",
        "P2:F2",
        "P3:M2",
        "P3:M3",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Full distance-based center growth, both form bounds, volume overlap count and convergent dyadic tails"
    },
    {
      "id": "WY:A7",
      "source": "weyl-action-and-covariance.md",
      "source_sha256": "b8cfbf92557e2762cbecc6b856ec98f84d8e64163113de31add3fd1bbf136b2f",
      "proof_locator": "## 4.",
      "dependencies": [
        "WY:A1",
        "WY:A2",
        "WY:A4",
        "WY:A5",
        "WY:A6",
        "WY:W4",
        "WY:W5",
        "P2:ML4",
        "P3:L3"
      ],
      "scope": "All Schwartz seminorms, normal convergence, partition independence, bounded-set symbol continuity and full strong-dual hypocontinuity"
    },
    {
      "id": "WY:A8",
      "source": "weyl-action-and-covariance.md",
      "source_sha256": "b8cfbf92557e2762cbecc6b856ec98f84d8e64163113de31add3fd1bbf136b2f",
      "proof_locator": "The distinction from unrestricted joint continuity is necessary.",
      "dependencies": [
        "WY:A1",
        "WY:W4",
        "P3:L3",
        "U001:U001-A4",
        "U001:P15.1",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Exact high-frequency multiplier counterexample with the original unrestricted strong-dual topology"
    },
    {
      "id": "WY:A9",
      "source": "weyl-action-and-covariance.md",
      "source_sha256": "b8cfbf92557e2762cbecc6b856ec98f84d8e64163113de31add3fd1bbf136b2f",
      "proof_locator": "**Theorem 4.2",
      "dependencies": [
        "WY:A7",
        "WY:W9",
        "WY:W10",
        "P2:ML7",
        "P3:L3",
        "U001:U001-A4",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Full operator composition on Schwartz and all tempered distributions, equicontinuity and explicit weak mollifier/cutoff density"
    },
    {
      "id": "WY:A10",
      "source": "weyl-action-and-covariance.md",
      "source_sha256": "b8cfbf92557e2762cbecc6b856ec98f84d8e64163113de31add3fd1bbf136b2f",
      "proof_locator": "## 6.",
      "dependencies": [
        "WY:W1",
        "U001:P2",
        "U001:Q5",
        "QF:A1",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Complete affine symplectic generation, complex positive Gram matrix, polynomial root count, singular position block and ordered factorization"
    },
    {
      "id": "WY:A11",
      "source": "weyl-action-and-covariance.md",
      "source_sha256": "b8cfbf92557e2762cbecc6b856ec98f84d8e64163113de31add3fd1bbf136b2f",
      "proof_locator": "**Theorem 6.1",
      "dependencies": [
        "WY:A10",
        "WY:W4",
        "WY:W6",
        "WY:W7",
        "P3:L1",
        "P3:L3",
        "U001:Q3",
        "U001:P21.4",
        "U001:P15.1",
        "U001:P15.2",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Explicit generators and exact unitary/Schwartz/distribution maps, affine intertwining on complete closed domains"
    },
    {
      "id": "WY:A12",
      "source": "weyl-action-and-covariance.md",
      "source_sha256": "b8cfbf92557e2762cbecc6b856ec98f84d8e64163113de31add3fd1bbf136b2f",
      "proof_locator": "We justify both uniqueness",
      "dependencies": [
        "WY:A11",
        "WY:W6",
        "P3:L1",
        "P3:M3",
        "P3:M4",
        "P3:M5",
        "P3:M6",
        "P3:M7",
        "P3:L3",
        "U001:U001-A4",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Full unitary uniqueness through groups, measurable multiplication, a.e. subsequence/Fatou, translation invariance and mollifiers"
    },
    {
      "id": "WY:A13",
      "source": "weyl-action-and-covariance.md",
      "source_sha256": "b8cfbf92557e2762cbecc6b856ec98f84d8e64163113de31add3fd1bbf136b2f",
      "proof_locator": "For covariance of symbols,",
      "dependencies": [
        "WY:A11",
        "WY:A12",
        "WY:W8",
        "WY:W4",
        "WY:A9",
        "P3:L1",
        "P3:M4",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Actual affine groups imply plane-wave covariance, Fourier integration and weak-density extension to every tempered symbol"
    },
    {
      "id": "WY:A14",
      "source": "weyl-action-and-covariance.md",
      "source_sha256": "b8cfbf92557e2762cbecc6b856ec98f84d8e64163113de31add3fd1bbf136b2f",
      "proof_locator": "The metric version follows directly.",
      "dependencies": [
        "WY:A10",
        "WY:A13",
        "WY:W1",
        "WY:W2",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Exact pullback of metric, dual, Planck function and all directional seminorms with unchanged structural constants"
    },
    {
      "id": "WY:A15",
      "source": "weyl-action-and-covariance.md",
      "source_sha256": "b8cfbf92557e2762cbecc6b856ec98f84d8e64163113de31add3fd1bbf136b2f",
      "proof_locator": "## A8.",
      "dependencies": [
        "WY:A11",
        "WY:A14",
        "P2:F2",
        "U001:Q5",
        "U001:P16.1",
        "U001:P16.2",
        "U001:P21.4",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Exact shear sign, determinant/area/Planck parameter and both ellipse parameterizations"
    },
    {
      "id": "WY:Q1",
      "source": "reflection-and-quantization.md",
      "source_sha256": "bcb07a18780b6bc2c7f66d4d45791c9183b26e42c6d8f1e411a6d5746e1a3fb7",
      "proof_locator": "## 7.",
      "dependencies": [
        "WY:W1",
        "WY:W2",
        "WY:W10",
        "WY:A1",
        "P2:QG1",
        "P2:QG7",
        "P2:QG8"
      ],
      "scope": "Reflection-compatible actual phase, symplectic dual factor4/k2, original distance base and full small-parameter conversion"
    },
    {
      "id": "WY:Q2",
      "source": "reflection-and-quantization.md",
      "source_sha256": "bcb07a18780b6bc2c7f66d4d45791c9183b26e42c6d8f1e411a6d5746e1a3fb7",
      "proof_locator": "**The derivative weight used in finite steps.**",
      "dependencies": [
        "WY:W1",
        "WY:W10",
        "U001:Q5",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Complete singular-frame contraction proof giving h^j gain for every mixed differential power and output derivative"
    },
    {
      "id": "WY:Q3",
      "source": "reflection-and-quantization.md",
      "source_sha256": "bcb07a18780b6bc2c7f66d4d45791c9183b26e42c6d8f1e411a6d5746e1a3fb7",
      "proof_locator": "**Every real parameter on the same metric.**",
      "dependencies": [
        "WY:Q1",
        "WY:Q2",
        "WY:A1",
        "P3:L1",
        "P3:L3",
        "U001:Q3",
        "U001:P15.1",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Exact finite-step proof for all real k with every remainder, N0/k0, finite seminorm chains, bounded-set continuity and inverse group"
    },
    {
      "id": "WY:Q4",
      "source": "reflection-and-quantization.md",
      "source_sha256": "bcb07a18780b6bc2c7f66d4d45791c9183b26e42c6d8f1e411a6d5746e1a3fb7",
      "proof_locator": "Here is the kernel coordinate calculation",
      "dependencies": [
        "WY:W4",
        "WY:W8",
        "WY:A9",
        "WY:Q3",
        "P3:L1",
        "P3:L3",
        "U001:P21.4"
      ],
      "scope": "Complete plane-wave kernel calculation with actual base point, all tempered symbols, unique left/right/Weyl conversion signs"
    },
    {
      "id": "WY:Q5",
      "source": "reflection-and-quantization.md",
      "source_sha256": "bcb07a18780b6bc2c7f66d4d45791c9183b26e42c6d8f1e411a6d5746e1a3fb7",
      "proof_locator": "There is an elementary action proof",
      "dependencies": [
        "WY:A1",
        "WY:A7",
        "WY:Q3",
        "WY:Q4",
        "WY:W4",
        "P3:L1",
        "U001:Q3",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Retained vertical-bound action proof, frequency derivative exponent independent of alpha, all output derivatives and moments"
    },
    {
      "id": "WY:Q6",
      "source": "reflection-and-quantization.md",
      "source_sha256": "bcb07a18780b6bc2c7f66d4d45791c9183b26e42c6d8f1e411a6d5746e1a3fb7",
      "proof_locator": "## Q8.",
      "dependencies": [
        "WY:Q1",
        "WY:Q2",
        "WY:Q3",
        "WY:Q4",
        "WY:W4",
        "P2:OP2",
        "CE:G1",
        "U001:FTC-TAYLOR-COMPACT-PARAMETERS"
      ],
      "scope": "Exact ordinary real order-two Weyl correction, bounded S0 error, symmetric part and polynomial sign check; FP remains separate"
    }
  ],
  "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"
  ],
  "component_proofs_complete": true,
  "U033_restored": false,
  "full_course_complete": false,
  "public_release_authorized": false
}