{
  "schemaVersion": "1.0.0",
  "engineVersion": "1.1.0",
  "receiptVersion": "1.0.0",
  "validationDate": "2026-08-15",
  "precisionModel": "IEEE 754 double precision (64-bit)",
  "sourceSha256": "beeed0c48e6c96cdc8a3475b311e3c61df6b98dedf022463f379c4190b5b159f",
  "suites": {
    "engineVectors": {
      "total": 169,
      "passed": 169,
      "failed": 0
    },
    "referenceVectors": {
      "total": 57,
      "passed": 57,
      "failed": 0
    },
    "invariants": {
      "total": 1500,
      "passed": 1500,
      "failed": 0,
      "seed": 1554098974,
      "iterations": 150
    },
    "totalChecks": 1726,
    "totalPassed": 1726,
    "totalFailed": 0
  },
  "referenceVectorCategories": {
    "precedence": {
      "total": 5,
      "passed": 5,
      "failed": 0
    },
    "unary-exponent": {
      "total": 4,
      "passed": 4,
      "failed": 0
    },
    "percentages": {
      "total": 6,
      "passed": 6,
      "failed": 0
    },
    "trig-deg": {
      "total": 5,
      "passed": 5,
      "failed": 0
    },
    "trig-rad": {
      "total": 3,
      "passed": 3,
      "failed": 0
    },
    "inverse-trig": {
      "total": 4,
      "passed": 4,
      "failed": 0
    },
    "hyperbolic": {
      "total": 4,
      "passed": 4,
      "failed": 0
    },
    "log-exp": {
      "total": 5,
      "passed": 5,
      "failed": 0
    },
    "roots": {
      "total": 4,
      "passed": 4,
      "failed": 0
    },
    "factorial": {
      "total": 3,
      "passed": 3,
      "failed": 0
    },
    "combinatorics": {
      "total": 4,
      "passed": 4,
      "failed": 0
    },
    "formatting": {
      "total": 4,
      "passed": 4,
      "failed": 0
    },
    "domain-error": {
      "total": 6,
      "passed": 6,
      "failed": 0
    }
  },
  "failures": {
    "engineVectors": [],
    "referenceVectors": [],
    "invariants": []
  },
  "referenceVectors": [
    {
      "id": "ref-prec-01",
      "category": "precedence",
      "expression": "2+3*4",
      "mode": "deg",
      "expected": "14",
      "actual": "14",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: multiplication binds before addition; 3*4=12, 12+2=14."
    },
    {
      "id": "ref-prec-02",
      "category": "precedence",
      "expression": "(2+3)*4",
      "mode": "deg",
      "expected": "20",
      "actual": "20",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: parentheses first; 5*4=20."
    },
    {
      "id": "ref-prec-03",
      "category": "precedence",
      "expression": "2^3^2",
      "mode": "deg",
      "expected": "512",
      "actual": "512",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: exponentiation is right-associative; 2^(3^2)=2^9=512."
    },
    {
      "id": "ref-prec-04",
      "category": "precedence",
      "expression": "(2^3)^2",
      "mode": "deg",
      "expected": "64",
      "actual": "64",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: 8^2=64."
    },
    {
      "id": "ref-prec-05",
      "category": "precedence",
      "expression": "2*3+4*5",
      "mode": "deg",
      "expected": "26",
      "actual": "26",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: 6+20=26."
    },
    {
      "id": "ref-unary-01",
      "category": "unary-exponent",
      "expression": "-2^2",
      "mode": "deg",
      "expected": "-4",
      "actual": "-4",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: unary minus binds looser than ^; -(2^2)=-4."
    },
    {
      "id": "ref-unary-02",
      "category": "unary-exponent",
      "expression": "(-2)^2",
      "mode": "deg",
      "expected": "4",
      "actual": "4",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: (-2)*(-2)=4."
    },
    {
      "id": "ref-unary-03",
      "category": "unary-exponent",
      "expression": "2^-2",
      "mode": "deg",
      "expected": "0.25",
      "actual": "0.25",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: 1/2^2 = 1/4 = 0.25."
    },
    {
      "id": "ref-unary-04",
      "category": "unary-exponent",
      "expression": "-3^0",
      "mode": "deg",
      "expected": "-1",
      "actual": "-1",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: -(3^0) = -(1) = -1."
    },
    {
      "id": "ref-pct-01",
      "category": "percentages",
      "expression": "50%",
      "mode": "deg",
      "expected": "0.5",
      "actual": "0.5",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: % divides its operand by 100; 50/100 = 0.5."
    },
    {
      "id": "ref-pct-02",
      "category": "percentages",
      "expression": "3*20%",
      "mode": "deg",
      "expected": "0.6",
      "actual": "0.6000000000000001",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Exact math 3*(20/100)=0.6; decimal has IEEE-754 rounding, checked to 1e-12."
    },
    {
      "id": "ref-pct-03",
      "category": "percentages",
      "expression": "200+5%",
      "mode": "deg",
      "expected": "200.05",
      "actual": "200.05",
      "tolerance": 1e-10,
      "status": "pass",
      "provenance": "Exact: postfix % gives 200 + 0.05 = 200.05 (the additive-percent trap)."
    },
    {
      "id": "ref-pct-04",
      "category": "percentages",
      "expression": "200-5%",
      "mode": "deg",
      "expected": "199.95",
      "actual": "199.95",
      "tolerance": 1e-10,
      "status": "pass",
      "provenance": "Exact: 200 - 0.05 = 199.95."
    },
    {
      "id": "ref-pct-05",
      "category": "percentages",
      "expression": "200*(1+5%)",
      "mode": "deg",
      "expected": "210",
      "actual": "210",
      "tolerance": 1e-10,
      "status": "pass",
      "provenance": "Exact: 200*1.05 = 210 (commercial \"increase by 5%\")."
    },
    {
      "id": "ref-pct-06",
      "category": "percentages",
      "expression": "200*(1-5%)",
      "mode": "deg",
      "expected": "190",
      "actual": "190",
      "tolerance": 1e-10,
      "status": "pass",
      "provenance": "Exact: 200*0.95 = 190 (commercial \"decrease by 5%\")."
    },
    {
      "id": "ref-trig-01",
      "category": "trig-deg",
      "expression": "sin(30)",
      "mode": "deg",
      "expected": "0.5",
      "actual": "0.49999999999999994",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Exact: sin(30°)=1/2."
    },
    {
      "id": "ref-trig-02",
      "category": "trig-deg",
      "expression": "cos(60)",
      "mode": "deg",
      "expected": "0.5",
      "actual": "0.5000000000000001",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Exact: cos(60°)=1/2."
    },
    {
      "id": "ref-trig-03",
      "category": "trig-deg",
      "expression": "sin(45)",
      "mode": "deg",
      "expected": "0.7071067811865476",
      "actual": "0.7071067811865475",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Reference constant √2/2 transcribed to 17 significant figures."
    },
    {
      "id": "ref-trig-04",
      "category": "trig-deg",
      "expression": "tan(45)",
      "mode": "deg",
      "expected": "1",
      "actual": "0.9999999999999999",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Exact: tan(45°)=1."
    },
    {
      "id": "ref-trig-05",
      "category": "trig-deg",
      "expression": "cos(30)",
      "mode": "deg",
      "expected": "0.8660254037844386",
      "actual": "0.8660254037844387",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Reference constant √3/2 transcribed to 17 significant figures."
    },
    {
      "id": "ref-trigr-01",
      "category": "trig-rad",
      "expression": "sin(pi/6)",
      "mode": "rad",
      "expected": "0.5",
      "actual": "0.49999999999999994",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Exact: sin(π/6)=1/2."
    },
    {
      "id": "ref-trigr-02",
      "category": "trig-rad",
      "expression": "cos(pi/3)",
      "mode": "rad",
      "expected": "0.5",
      "actual": "0.5000000000000001",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Exact: cos(π/3)=1/2."
    },
    {
      "id": "ref-trigr-03",
      "category": "trig-rad",
      "expression": "tan(pi/4)",
      "mode": "rad",
      "expected": "1",
      "actual": "0.9999999999999999",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Exact: tan(π/4)=1."
    },
    {
      "id": "ref-inv-01",
      "category": "inverse-trig",
      "expression": "asin(0.5)",
      "mode": "deg",
      "expected": "30",
      "actual": "30.000000000000004",
      "tolerance": 1e-10,
      "status": "pass",
      "provenance": "Exact: arcsin(1/2)=30°."
    },
    {
      "id": "ref-inv-02",
      "category": "inverse-trig",
      "expression": "acos(0.5)",
      "mode": "deg",
      "expected": "60",
      "actual": "60.00000000000001",
      "tolerance": 1e-10,
      "status": "pass",
      "provenance": "Exact: arccos(1/2)=60°."
    },
    {
      "id": "ref-inv-03",
      "category": "inverse-trig",
      "expression": "atan(1)",
      "mode": "deg",
      "expected": "45",
      "actual": "45",
      "tolerance": 1e-10,
      "status": "pass",
      "provenance": "Exact: arctan(1)=45°."
    },
    {
      "id": "ref-inv-04",
      "category": "inverse-trig",
      "expression": "atan(1)",
      "mode": "rad",
      "expected": "0.7853981633974483",
      "actual": "0.7853981633974483",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Reference constant π/4 transcribed to 17 significant figures."
    },
    {
      "id": "ref-hyp-01",
      "category": "hyperbolic",
      "expression": "sinh(1)",
      "mode": "deg",
      "expected": "1.1752011936438014",
      "actual": "1.1752011936438014",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Reference value of sinh(1)=(e−1/e)/2, transcribed decimal literal."
    },
    {
      "id": "ref-hyp-02",
      "category": "hyperbolic",
      "expression": "cosh(1)",
      "mode": "deg",
      "expected": "1.5430806348152437",
      "actual": "1.5430806348152437",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Reference value of cosh(1)=(e+1/e)/2, transcribed decimal literal."
    },
    {
      "id": "ref-hyp-03",
      "category": "hyperbolic",
      "expression": "tanh(1)",
      "mode": "deg",
      "expected": "0.7615941559557649",
      "actual": "0.7615941559557649",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Reference value of tanh(1), transcribed decimal literal."
    },
    {
      "id": "ref-hyp-04",
      "category": "hyperbolic",
      "expression": "cosh(0)",
      "mode": "deg",
      "expected": "1",
      "actual": "1",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: cosh(0)=1."
    },
    {
      "id": "ref-log-01",
      "category": "log-exp",
      "expression": "log(1000)",
      "mode": "deg",
      "expected": "3",
      "actual": "3",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Exact: log10(1000)=3."
    },
    {
      "id": "ref-log-02",
      "category": "log-exp",
      "expression": "ln(2)",
      "mode": "deg",
      "expected": "0.6931471805599453",
      "actual": "0.6931471805599453",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Reference constant ln(2) transcribed to 17 significant figures."
    },
    {
      "id": "ref-log-03",
      "category": "log-exp",
      "expression": "exp(1)",
      "mode": "deg",
      "expected": "2.718281828459045",
      "actual": "2.718281828459045",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Reference constant e transcribed to 17 significant figures."
    },
    {
      "id": "ref-log-04",
      "category": "log-exp",
      "expression": "log(100)",
      "mode": "deg",
      "expected": "2",
      "actual": "2",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Exact: log10(100)=2."
    },
    {
      "id": "ref-log-05",
      "category": "log-exp",
      "expression": "exp(0)",
      "mode": "deg",
      "expected": "1",
      "actual": "1",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: e^0=1."
    },
    {
      "id": "ref-root-01",
      "category": "roots",
      "expression": "sqrt(2)",
      "mode": "deg",
      "expected": "1.4142135623730951",
      "actual": "1.4142135623730951",
      "tolerance": 1e-12,
      "status": "pass",
      "provenance": "Reference constant √2 transcribed to 17 significant figures."
    },
    {
      "id": "ref-root-02",
      "category": "roots",
      "expression": "sqrt(9)",
      "mode": "deg",
      "expected": "3",
      "actual": "3",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: √9=3."
    },
    {
      "id": "ref-root-03",
      "category": "roots",
      "expression": "cbrt(27)",
      "mode": "deg",
      "expected": "3",
      "actual": "3",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: ∛27=3."
    },
    {
      "id": "ref-root-04",
      "category": "roots",
      "expression": "cbrt(-8)",
      "mode": "deg",
      "expected": "-2",
      "actual": "-2",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: ∛(−8)=−2."
    },
    {
      "id": "ref-fact-01",
      "category": "factorial",
      "expression": "5!",
      "mode": "deg",
      "expected": "120",
      "actual": "120",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: 5!=120."
    },
    {
      "id": "ref-fact-02",
      "category": "factorial",
      "expression": "10!",
      "mode": "deg",
      "expected": "3628800",
      "actual": "3628800",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: 10!=3,628,800."
    },
    {
      "id": "ref-fact-03",
      "category": "factorial",
      "expression": "0!",
      "mode": "deg",
      "expected": "1",
      "actual": "1",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: 0!=1 by definition."
    },
    {
      "id": "ref-comb-01",
      "category": "combinatorics",
      "expression": "nCr(10,3)",
      "mode": "deg",
      "expected": "120",
      "actual": "120",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: C(10,3)=120."
    },
    {
      "id": "ref-comb-02",
      "category": "combinatorics",
      "expression": "nCr(52,5)",
      "mode": "deg",
      "expected": "2598960",
      "actual": "2598960",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: C(52,5)=2,598,960 (poker hands)."
    },
    {
      "id": "ref-comb-03",
      "category": "combinatorics",
      "expression": "nPr(10,3)",
      "mode": "deg",
      "expected": "720",
      "actual": "720",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: P(10,3)=720."
    },
    {
      "id": "ref-comb-04",
      "category": "combinatorics",
      "expression": "nCr(6,3)",
      "mode": "deg",
      "expected": "20",
      "actual": "20",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: C(6,3)=20."
    },
    {
      "id": "ref-fmt-01",
      "category": "formatting",
      "expression": "1/3",
      "mode": "deg",
      "expected": "0.333333333333",
      "actual": "0.333333333333",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: 1/3 formatted to the engine default of 12 significant figures."
    },
    {
      "id": "ref-fmt-02",
      "category": "formatting",
      "expression": "1000000000000",
      "mode": "deg",
      "expected": "1e+12",
      "actual": "1e+12",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: values ≥ 1e12 switch to scientific notation."
    },
    {
      "id": "ref-fmt-03",
      "category": "formatting",
      "expression": "0.000000001",
      "mode": "deg",
      "expected": "1e-9",
      "actual": "1e-9",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Exact: values < 1e-9 switch to scientific notation."
    },
    {
      "id": "ref-fmt-04",
      "category": "formatting",
      "expression": "6.02e23",
      "mode": "deg",
      "expected": "6.02e+23",
      "actual": "6.02e+23",
      "tolerance": 1000000000000,
      "status": "pass",
      "provenance": "Exact: Avogadro-scale magnitude parsed from scientific-notation input; absolute tolerance scaled to magnitude."
    },
    {
      "id": "ref-err-01",
      "category": "domain-error",
      "expression": "sqrt(-1)",
      "mode": "deg",
      "expected": "error:DOMAIN_ERROR",
      "actual": "error:DOMAIN_ERROR",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Real sqrt of a negative number is undefined → DOMAIN_ERROR."
    },
    {
      "id": "ref-err-02",
      "category": "domain-error",
      "expression": "log(0)",
      "mode": "deg",
      "expected": "error:DOMAIN_ERROR",
      "actual": "error:DOMAIN_ERROR",
      "tolerance": 0,
      "status": "pass",
      "provenance": "log10(0) is undefined → DOMAIN_ERROR."
    },
    {
      "id": "ref-err-03",
      "category": "domain-error",
      "expression": "asin(2)",
      "mode": "deg",
      "expected": "error:DOMAIN_ERROR",
      "actual": "error:DOMAIN_ERROR",
      "tolerance": 0,
      "status": "pass",
      "provenance": "arcsin argument outside [−1,1] → DOMAIN_ERROR."
    },
    {
      "id": "ref-err-04",
      "category": "domain-error",
      "expression": "tan(90)",
      "mode": "deg",
      "expected": "error:TRIG_SINGULARITY",
      "actual": "error:TRIG_SINGULARITY",
      "tolerance": 0,
      "status": "pass",
      "provenance": "tan(90°) is a singularity → TRIG_SINGULARITY."
    },
    {
      "id": "ref-err-05",
      "category": "domain-error",
      "expression": "1/0",
      "mode": "deg",
      "expected": "error:DIVISION_BY_ZERO",
      "actual": "error:DIVISION_BY_ZERO",
      "tolerance": 0,
      "status": "pass",
      "provenance": "Division by zero → DIVISION_BY_ZERO."
    },
    {
      "id": "ref-err-06",
      "category": "domain-error",
      "expression": "171!",
      "mode": "deg",
      "expected": "error:OVERFLOW",
      "actual": "error:OVERFLOW",
      "tolerance": 0,
      "status": "pass",
      "provenance": "171! exceeds the largest finite IEEE-754 double → OVERFLOW."
    }
  ]
}