{
  "scope": "Complete tangent comparison, Gaussian-symbol identification and selected prerequisite proofs.",
  "proofs": [
    {
      "id": "TG:B0",
      "source": "prerequisites/complete-test-spaces.md",
      "source_sha256": "dd6ef2acb9397a228b1c80d4cc64d46d8839248b4f1d27d938be68e694d745ec",
      "proof_locator": "## 19.",
      "dependencies": [
        "U001:A0",
        "U001:P6.0",
        "U001:P6.4-ball"
      ]
    },
    {
      "id": "TG:B1",
      "source": "prerequisites/complete-test-spaces.md",
      "source_sha256": "dd6ef2acb9397a228b1c80d4cc64d46d8839248b4f1d27d938be68e694d745ec",
      "proof_locator": "## 6.",
      "dependencies": [
        "TG:B0",
        "U001:P6.0",
        "U001:P6.4-ball",
        "U001:P6.5"
      ]
    },
    {
      "id": "TG:B2",
      "source": "prerequisites/complete-test-spaces.md",
      "source_sha256": "dd6ef2acb9397a228b1c80d4cc64d46d8839248b4f1d27d938be68e694d745ec",
      "proof_locator": "### 14.1.",
      "dependencies": [
        "U001:A0",
        "U001:P13.2-series",
        "U001:P6.0"
      ]
    },
    {
      "id": "TG:B3",
      "source": "prerequisites/complete-test-spaces.md",
      "source_sha256": "dd6ef2acb9397a228b1c80d4cc64d46d8839248b4f1d27d938be68e694d745ec",
      "proof_locator": "### 14.2.",
      "dependencies": [
        "TG:B2",
        "U001:L2.4.5",
        "U001:P13.1",
        "U001:L5.3.1",
        "U001:P12.6",
        "U001:P12.7"
      ]
    },
    {
      "id": "TG:U1",
      "source": "prerequisites/uniform-distribution-bounds.md",
      "source_sha256": "c9ab47509beb5f947e853825e650baf3a9893b6b78ef77d4fabe5f78e2eb1874",
      "proof_locator": "**Theorem U1",
      "dependencies": [
        "TG:B1",
        "TG:B3",
        "U001:L2.4.5"
      ]
    },
    {
      "id": "TG:T0",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "be0d026c0703af59eaf9058f563bb0ed72e6a9d9d46ea50b1c40ada2ac7ffd95",
      "proof_locator": "The integral means",
      "dependencies": [
        "U001:Q3",
        "U001:Q4",
        "U001:U001-A4",
        "PH:F6",
        "K:K7",
        "GR:G12-forward"
      ]
    },
    {
      "id": "TG:T1",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "be0d026c0703af59eaf9058f563bb0ed72e6a9d9d46ea50b1c40ada2ac7ffd95",
      "proof_locator": "**Theorem T1",
      "dependencies": [
        "TG:T0",
        "U001:Q1",
        "U001:Q3",
        "U001:F0-DIFF",
        "U001:F0-COMP",
        "U001:P12.6",
        "U001:P12.7"
      ]
    },
    {
      "id": "TG:T2",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "be0d026c0703af59eaf9058f563bb0ed72e6a9d9d46ea50b1c40ada2ac7ffd95",
      "proof_locator": "**Corollary T2",
      "dependencies": [
        "TG:T1",
        "U001:P14.2-powers",
        "U001:Q1"
      ]
    },
    {
      "id": "TG:T3",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "be0d026c0703af59eaf9058f563bb0ed72e6a9d9d46ea50b1c40ada2ac7ffd95",
      "proof_locator": "**Lemma T3",
      "dependencies": [
        "U001:Q3",
        "U001:Q4",
        "U001:U001-A4",
        "U001:F0-DIFF",
        "U001:F0-COMP"
      ]
    },
    {
      "id": "TG:T4",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "be0d026c0703af59eaf9058f563bb0ed72e6a9d9d46ea50b1c40ada2ac7ffd95",
      "proof_locator": "**Theorem T4",
      "dependencies": [
        "TG:T3",
        "U001:Q3",
        "U001:P12.6",
        "U001:P12.7"
      ]
    },
    {
      "id": "TG:T5",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "be0d026c0703af59eaf9058f563bb0ed72e6a9d9d46ea50b1c40ada2ac7ffd95",
      "proof_locator": "**Lemma T5",
      "dependencies": [
        "TG:U1",
        "U001:F0-DIFF",
        "U001:F0-COMP",
        "U001:P3",
        "U001:P8-smooth",
        "U001:P14.2-powers"
      ]
    },
    {
      "id": "TG:T6",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "be0d026c0703af59eaf9058f563bb0ed72e6a9d9d46ea50b1c40ada2ac7ffd95",
      "proof_locator": "**Theorem T6",
      "dependencies": [
        "TG:T0",
        "U001:Q1",
        "U001:Q2",
        "U001:Q3",
        "U001:Q5",
        "U001:Q6",
        "U001:P3",
        "U001:F0-DIFF"
      ]
    },
    {
      "id": "TG:T7",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "be0d026c0703af59eaf9058f563bb0ed72e6a9d9d46ea50b1c40ada2ac7ffd95",
      "proof_locator": "## 6. The two tangent",
      "dependencies": [
        "GEO:C0",
        "TG:T0",
        "U001:Q5",
        "U001:P3",
        "U001:F0-DIFF"
      ]
    },
    {
      "id": "TG:E1",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "be0d026c0703af59eaf9058f563bb0ed72e6a9d9d46ea50b1c40ada2ac7ffd95",
      "proof_locator": "**Exercise 1",
      "dependencies": [
        "TG:T1",
        "U001:F0-DIFF"
      ]
    },
    {
      "id": "TG:E2",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "be0d026c0703af59eaf9058f563bb0ed72e6a9d9d46ea50b1c40ada2ac7ffd95",
      "proof_locator": "**Exercise 2",
      "dependencies": [
        "TG:T6",
        "U001:P8-smooth",
        "U001:F0-DIFF"
      ]
    },
    {
      "id": "TG:E3",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "be0d026c0703af59eaf9058f563bb0ed72e6a9d9d46ea50b1c40ada2ac7ffd95",
      "proof_locator": "**Exercise 3",
      "dependencies": [
        "TG:T1",
        "TG:T6",
        "TG:T0",
        "U001:Q3",
        "U001:Q4",
        "U001:Q1",
        "U001:P12.6"
      ]
    },
    {
      "id": "TG:E4",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "be0d026c0703af59eaf9058f563bb0ed72e6a9d9d46ea50b1c40ada2ac7ffd95",
      "proof_locator": "**Exercise 4",
      "dependencies": [
        "TG:T5",
        "U001:Q4"
      ]
    },
    {
      "id": "TG:E5",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "be0d026c0703af59eaf9058f563bb0ed72e6a9d9d46ea50b1c40ada2ac7ffd95",
      "proof_locator": "**Exercise 5",
      "dependencies": [
        "TG:T0",
        "TG:T5",
        "TG:T6",
        "TG:Z4"
      ]
    },
    {
      "id": "TG:E6",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "be0d026c0703af59eaf9058f563bb0ed72e6a9d9d46ea50b1c40ada2ac7ffd95",
      "proof_locator": "**Exercise 6",
      "dependencies": [
        "TG:T2",
        "TG:T3",
        "TG:T6",
        "U001:U001-A4"
      ]
    },
    {
      "id": "TG:T8",
      "source": "tangent-zoom-and-quadratic-models.md",
      "source_sha256": "be0d026c0703af59eaf9058f563bb0ed72e6a9d9d46ea50b1c40ada2ac7ffd95",
      "proof_locator": "**Theorem T8",
      "dependencies": [
        "TG:Z5",
        "TG:Z6",
        "TG:Z7"
      ]
    },
    {
      "id": "TG:Z0",
      "source": "prerequisites/gaussian-symbol-line.md",
      "source_sha256": "8182e3fe14a3bdf02fc7b546f0826ebda955e71d09dfe5a03b542fca8283561c",
      "proof_locator": "## Z0. Objects and exact earlier proofs",
      "dependencies": [
        "GEO:C0",
        "ML:M5",
        "PS:PS2",
        "U001:F0-DIFF"
      ]
    },
    {
      "id": "TG:Z1",
      "source": "prerequisites/gaussian-symbol-line.md",
      "source_sha256": "8182e3fe14a3bdf02fc7b546f0826ebda955e71d09dfe5a03b542fca8283561c",
      "proof_locator": "## Z1. From the intrinsic class to the graph used by the zoom theorem",
      "dependencies": [
        "TG:Z0",
        "GEO:C3",
        "GEO:C4",
        "PH:F6",
        "K:K7",
        "CH:W4",
        "GR:G12-forward",
        "PS:PS3",
        "TG:T4",
        "U001:Q4",
        "U001:Q5"
      ]
    },
    {
      "id": "TG:Z2",
      "source": "prerequisites/gaussian-symbol-line.md",
      "source_sha256": "8182e3fe14a3bdf02fc7b546f0826ebda955e71d09dfe5a03b542fca8283561c",
      "proof_locator": "## Z2. Nonzero Gaussian frames, including changes of rank",
      "dependencies": [
        "TG:T6",
        "TG:T0",
        "U001:Q1",
        "U001:Q3",
        "U001:U001-A4",
        "U001:F0-DIFF"
      ]
    },
    {
      "id": "TG:Z3",
      "source": "prerequisites/gaussian-symbol-line.md",
      "source_sha256": "8182e3fe14a3bdf02fc7b546f0826ebda955e71d09dfe5a03b542fca8283561c",
      "proof_locator": "## Z3. Realize any fibre value by a local leading homogeneous symbol",
      "dependencies": [
        "TG:Z1",
        "PH:F2",
        "PH:F3",
        "PH:F6",
        "K:K6",
        "PS:PS3",
        "ML:M5",
        "ML:M6",
        "U001:U001-A4",
        "U001:F0-COMP",
        "U001:P14.2-powers"
      ]
    },
    {
      "id": "TG:Z4",
      "source": "prerequisites/gaussian-symbol-line.md",
      "source_sha256": "8182e3fe14a3bdf02fc7b546f0826ebda955e71d09dfe5a03b542fca8283561c",
      "proof_locator": "## Z4. The intrinsic Gaussian line and its canonical map",
      "dependencies": [
        "TG:Z2",
        "TG:Z3",
        "TG:T1",
        "TG:T2",
        "TG:T5",
        "ML:M5",
        "U001:F0-DIFF"
      ]
    },
    {
      "id": "TG:Z5",
      "source": "prerequisites/gaussian-symbol-line.md",
      "source_sha256": "8182e3fe14a3bdf02fc7b546f0826ebda955e71d09dfe5a03b542fca8283561c",
      "proof_locator": "## Z5. Ordinary intrinsic symbols and the actual tangent comparison",
      "dependencies": [
        "TG:Z1",
        "TG:Z4",
        "PS:PS2",
        "PS:PS3",
        "ML:M5",
        "ML:M6",
        "TG:T1",
        "TG:T2",
        "TG:T4",
        "TG:T5"
      ]
    },
    {
      "id": "TG:Z6",
      "source": "prerequisites/gaussian-symbol-line.md",
      "source_sha256": "8182e3fe14a3bdf02fc7b546f0826ebda955e71d09dfe5a03b542fca8283561c",
      "proof_locator": "## Z6. Dilation and the signature on a constant-rank stratum",
      "dependencies": [
        "TG:Z4",
        "TG:Z5",
        "ML:M7",
        "TG:T6",
        "U001:Q3",
        "U001:F0-DIFF"
      ]
    },
    {
      "id": "TG:Z7",
      "source": "prerequisites/gaussian-symbol-line.md",
      "source_sha256": "8182e3fe14a3bdf02fc7b546f0826ebda955e71d09dfe5a03b542fca8283561c",
      "proof_locator": "## Z7. A nonlinear chart with a nontrivial fourth-root factor",
      "dependencies": [
        "TG:Z6",
        "TG:T6",
        "U001:F0-DIFF",
        "U001:P3"
      ]
    }
  ],
  "earlier_intrinsic_map": "../20261004-free-intrinsic-graph/proof-map.json",
  "earlier_stationary_map": "../20261004-free-stationary-phase/proof-map.json",
  "declared_logical_axioms": [
    "Earlier U001 A0",
    "Zorn maximality principle, with needed selection consequence proved in B0"
  ],
  "full_course_complete": false,
  "public_release_authorized": false,
  "all_dependency_ids_resolve": true,
  "acyclic": true,
  "transitive_intrinsic_nodes": 94,
  "transitive_U001_nodes": 219
}