{
  "schema_version": "1.0",
  "operation": "section15_finite_checks",
  "evidence_status": "exact_finite_algebra_and_numerical_asymptotic_column",
  "conventions": {
    "h": "2*pi*b^2",
    "lambda": "h^(1/3)",
    "eta": "acos(1/3)-h^(2/3)*zeta/(6*sqrt(2))",
    "contour_orientation_in_algebra": "upward; dw/i"
  },
  "provenance": {
    "source_commit": "cf34fcbcd0ee867a2dee974d9c952238bc5c6ce6",
    "repository_dirty_at_start": false,
    "git_status_porcelain_at_start": [],
    "source_sha256": {
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      "experiments/section15/historical-table.json": "91ecc5703fe0089940825f8e165ab88e0693535067e8ca080736a0895f164011",
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    "python": "3.12.11",
    "mpmath": "1.3.0",
    "generated_at_utc": "2026-11-01T04:54:22.298552+00:00"
  },
  "historical_table_provenance": {
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    "source_path": "book/polyhedral_volumes_and_geodesic_identities.tex",
    "source_label": "sec:quantumAiry",
    "original_subsection": "A numerical check of the exact integral",
    "status": "transcription_of_printed_values_only",
    "raw_quantum_integral_output_available": false,
    "rounding_mode_of_original_quantum_output_known": false,
    "note": "reported_Q is retained historical input, not output of this driver. No original code, precision, contour, or tail record was supplied."
  },
  "chapter_retains_historical_rows": true,
  "algebra": {
    "arithmetic": "exact rational pairs a+b*sqrt(2)",
    "checks": [
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        "name": "cot(theta1) at fold",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "2"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "2"
        },
        "passed": true
      },
      {
        "name": "cot(theta2) at fold",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "1"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "1"
        },
        "passed": true
      },
      {
        "name": "cot(theta3) at fold",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "-11"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "-11"
        },
        "passed": true
      },
      {
        "name": "cot(s) at fold",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "1/2"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "1/2"
        },
        "passed": true
      },
      {
        "name": "cot(3s) at fold",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "-5/2"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "-5/2"
        },
        "passed": true
      },
      {
        "name": "sin(theta1) squared at fold",
        "actual": {
          "rational": "1/9",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "1/9",
          "sqrt2_coefficient": "0"
        },
        "passed": true
      },
      {
        "name": "sin(theta2) squared at fold",
        "actual": {
          "rational": "1/3",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "1/3",
          "sqrt2_coefficient": "0"
        },
        "passed": true
      },
      {
        "name": "sin(theta3) squared at fold",
        "actual": {
          "rational": "1/243",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "1/243",
          "sqrt2_coefficient": "0"
        },
        "passed": true
      },
      {
        "name": "sin(s)/sin(3s) at fold",
        "actual": {
          "rational": "3",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "3",
          "sqrt2_coefficient": "0"
        },
        "passed": true
      },
      {
        "name": "exp(2 G_v) positive-sine ratio",
        "actual": {
          "rational": "1",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "1",
          "sqrt2_coefficient": "0"
        },
        "passed": true
      },
      {
        "name": "exp(G_eta/6) positive-sine ratio",
        "actual": {
          "rational": "1",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "1",
          "sqrt2_coefficient": "0"
        },
        "passed": true
      },
      {
        "name": "A_star squared; A_star positive",
        "actual": {
          "rational": "81/16",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "81/16",
          "sqrt2_coefficient": "0"
        },
        "passed": true
      },
      {
        "name": "(log A)_v",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "7"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "7"
        },
        "passed": true
      },
      {
        "name": "G derivative v^2 eta^0",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "0"
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        "passed": true
      },
      {
        "name": "G derivative v^3 eta^0",
        "actual": {
          "rational": "54",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "54",
          "sqrt2_coefficient": "0"
        },
        "passed": true
      },
      {
        "name": "G derivative v^1 eta^1",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "18"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "18"
        },
        "passed": true
      },
      {
        "name": "G derivative v^0 eta^2",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "36"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "36"
        },
        "passed": true
      },
      {
        "name": "G derivative v^4 eta^0",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "-648"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "-648"
        },
        "passed": true
      },
      {
        "name": "G derivative v^2 eta^1",
        "actual": {
          "rational": "-18",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "-18",
          "sqrt2_coefficient": "0"
        },
        "passed": true
      },
      {
        "name": "Psi derivative numerator coefficient u^0",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "0"
        },
        "passed": true
      },
      {
        "name": "Psi derivative numerator coefficient u^1",
        "actual": {
          "rational": "2592",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "2592",
          "sqrt2_coefficient": "0"
        },
        "passed": true
      },
      {
        "name": "Psi derivative numerator coefficient u^2",
        "actual": {
          "rational": "9504",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "9504",
          "sqrt2_coefficient": "0"
        },
        "passed": true
      },
      {
        "name": "leading Y^3",
        "actual": {
          "rational": "1/3",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "1/3",
          "sqrt2_coefficient": "0"
        },
        "passed": true
      },
      {
        "name": "leading zeta Y",
        "actual": {
          "rational": "-1",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "-1",
          "sqrt2_coefficient": "0"
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        "passed": true
      },
      {
        "name": "correction coefficient Y",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "7/3"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "7/3"
        },
        "passed": true
      },
      {
        "name": "correction coefficient Y4",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "-1/3"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "-1/3"
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        "passed": true
      },
      {
        "name": "correction coefficient zetaY2",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "1/12"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "1/12"
        },
        "passed": true
      },
      {
        "name": "correction coefficient zeta2",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "1/4"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "1/4"
        },
        "passed": true
      },
      {
        "name": "integrated Ai prime coefficient",
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          "rational": "0",
          "sqrt2_coefficient": "-3"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "-3"
        },
        "passed": true
      },
      {
        "name": "integrated zeta^2 Ai cancellation",
        "actual": {
          "rational": "0",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "0",
          "sqrt2_coefficient": "0"
        },
        "passed": true
      },
      {
        "name": "coefficient of lambda/b after oriented Airy integral",
        "actual": {
          "rational": "3/4",
          "sqrt2_coefficient": "0"
        },
        "expected": {
          "rational": "3/4",
          "sqrt2_coefficient": "0"
        },
        "passed": true
      }
    ],
    "all_passed": true,
    "not_checked": [
      "G_star=0 Lobachevsky identity",
      "double-sine integral",
      "uniform remainders and contour deformation",
      "global transition theorem"
    ]
  },
  "approximation": {
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        "series_comparison_absolute_tolerance": "1.0e-70",
        "rows": [
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}