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  "schema": "AN04-restored-tangent-zoom-proof-map/v1",
  "proofs": [
    {
      "id": "TZ:Z0",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "bd20c2f0bff91b85d1c1b5559dcd3ead8c7258777308abd042e2fc61c78248ed",
      "proof_locator": "## 1. Two scales",
      "dependencies": [
        "IR:R2",
        "IR:R3",
        "U001:Q3",
        "U001:Q4"
      ],
      "scope": "Normalized graph symbol, affine half-density scaling and tempered quadratic model"
    },
    {
      "id": "TZ:Z1",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "bd20c2f0bff91b85d1c1b5559dcd3ead8c7258777308abd042e2fc61c78248ed",
      "proof_locator": "**Theorem 2.1",
      "dependencies": [
        "TZ:Z0",
        "TG:T1",
        "TG:T4"
      ],
      "scope": "Full ordinary-symbol asymptotic comparison, frozen central coefficient, negative-order tails and smooth errors"
    },
    {
      "id": "TZ:Z2",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "bd20c2f0bff91b85d1c1b5559dcd3ead8c7258777308abd042e2fc61c78248ed",
      "proof_locator": "If \\(b\\) is classical",
      "dependencies": [
        "TZ:Z1",
        "TG:T2",
        "U001:P14.2-powers"
      ],
      "scope": "Classical real-degree limit and the additional complex-degree oscillation"
    },
    {
      "id": "TZ:Z3",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "bd20c2f0bff91b85d1c1b5559dcd3ead8c7258777308abd042e2fc61c78248ed",
      "proof_locator": "**Proposition 3.1.",
      "dependencies": [
        "TG:T3",
        "TG:T4",
        "TG:U1",
        "CH:W1"
      ],
      "scope": "Arbitrary regular-covector zoom, global polynomial Fourier bound and moving nonlinear phase tests"
    },
    {
      "id": "TZ:Z4",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "bd20c2f0bff91b85d1c1b5559dcd3ead8c7258777308abd042e2fc61c78248ed",
      "proof_locator": "**Lemma 4.1",
      "dependencies": [
        "TG:T5",
        "TG:U1"
      ],
      "scope": "Conjugated nonlinear charts, inverse maps, common compact test supports, scalar and half-density pullbacks"
    },
    {
      "id": "TZ:Z5",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "bd20c2f0bff91b85d1c1b5559dcd3ead8c7258777308abd042e2fc61c78248ed",
      "proof_locator": "The function \\(\\psi\\) is also a choice.",
      "dependencies": [
        "TZ:Z4",
        "TG:T5"
      ],
      "scope": "Frame value at the base point and transitive quadratic phase changes"
    },
    {
      "id": "TZ:Z6",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "bd20c2f0bff91b85d1c1b5559dcd3ead8c7258777308abd042e2fc61c78248ed",
      "proof_locator": "## 5. Evaluate the model",
      "dependencies": [
        "TZ:Z0",
        "TG:T6",
        "U001:Q6"
      ],
      "scope": "Exact singular-Hessian Gaussian, kernel delta, every normalization/sign and empty-block conventions"
    },
    {
      "id": "TZ:Z7",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "bd20c2f0bff91b85d1c1b5559dcd3ead8c7258777308abd042e2fc61c78248ed",
      "proof_locator": "The phase in (1.6) has critical equation",
      "dependencies": [
        "TZ:Z6",
        "TG:T7"
      ],
      "scope": "Radial degeneracy, both tangent Lagrangian planes and the canonical quadratic shear"
    },
    {
      "id": "TZ:E1",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "bd20c2f0bff91b85d1c1b5559dcd3ead8c7258777308abd042e2fc61c78248ed",
      "proof_locator": "**Exercise 6.1 ",
      "dependencies": [
        "TZ:Z1",
        "U001:F0-DIFF"
      ],
      "scope": "Preserved Exercise 6.1 and full unchanged solution"
    },
    {
      "id": "TZ:E2",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "bd20c2f0bff91b85d1c1b5559dcd3ead8c7258777308abd042e2fc61c78248ed",
      "proof_locator": "**Exercise 6.2 ",
      "dependencies": [
        "TZ:Z6",
        "TZ:Z7"
      ],
      "scope": "Preserved Exercise 6.2 and full unchanged solution"
    },
    {
      "id": "TZ:E3",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "bd20c2f0bff91b85d1c1b5559dcd3ead8c7258777308abd042e2fc61c78248ed",
      "proof_locator": "**Exercise 6.3 ",
      "dependencies": [
        "TZ:Z1",
        "TZ:Z6",
        "OSC:O4",
        "IR:R3",
        "U001:Q3"
      ],
      "scope": "Preserved Exercise 6.3 and full unchanged solution"
    },
    {
      "id": "TZ:E4",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "bd20c2f0bff91b85d1c1b5559dcd3ead8c7258777308abd042e2fc61c78248ed",
      "proof_locator": "**Exercise 6.4 ",
      "dependencies": [
        "TZ:Z4"
      ],
      "scope": "Preserved Exercise 6.4 and full unchanged solution"
    },
    {
      "id": "TZ:E5",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "bd20c2f0bff91b85d1c1b5559dcd3ead8c7258777308abd042e2fc61c78248ed",
      "proof_locator": "**Exercise 6.5 ",
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        "TZ:Z5",
        "TZ:Z6",
        "U001:Q3"
      ],
      "scope": "Preserved Exercise 6.5 and full unchanged solution"
    },
    {
      "id": "TZ:E6",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "bd20c2f0bff91b85d1c1b5559dcd3ead8c7258777308abd042e2fc61c78248ed",
      "proof_locator": "**Exercise 6.6 ",
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        "TZ:Z1",
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        "IR:R3",
        "U001:Q3"
      ],
      "scope": "Preserved Exercise 6.6 and full unchanged solution"
    }
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