t27/conformance/FORMAT-SPEC-001.json at master · gHashTag/t27 · GitHub

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{
  "format_family": "GoldenFloat",
  "version": "1.1",
  "canonical_reference": "THM-009 (phi_ratio optimality) — see specs/numeric/phi_ratio.t27 and docs/nona-02-organism/NUMERIC-STANDARD-001.md",
  "normative_markdown": "docs/nona-02-organism/NUMERIC-STANDARD-001.md",
  "value_formula": "(-1)^S * 2^(E - bias) * (1 + M / 2^mant_bits)",
  "phi_identity": {
    "theorem": "phi_squared_equals_phi_plus_one",
    "statement": "φ² = φ + 1 (exact in f64, Ring 45 proven)",
    "phi_f64_hex": "0x1.9E3779B97F4A8p+0",
    "phi_sq_f64_hex": "0x1.4F1BBCDCBFA54p+1",
    "phi_plus_one_f64_hex": "0x1.4F1BBCDCBFA54p+1",
    "residual_f64": 0.0,
    "tolerance": 1e-15,
    "verdict": "PASS",
    "ring_proven": 45,
    "reference": "Kernel/Phi.v (L5 IDENTITY proof)"
  },
  "formats": {
    "GF4": { "bits": 4, "sign": 1, "exp": 1, "mant": 2, "bias": 0, "phi_dist": 0.118 },
    "GF8": { "bits": 8, "sign": 1, "exp": 3, "mant": 4, "bias": 3, "phi_dist": 0.132 },
    "GF12": { "bits": 12, "sign": 1, "exp": 4, "mant": 7, "bias": 7, "phi_dist": 0.047 },
    "GF16": {
      "bits": 16,
      "sign": 1,
      "exp": 6,
      "mant": 9,
      "bias": 31,
      "phi_dist": 0.0486326415435630,
      "primary": true
    },
    "GF20": { "bits": 20, "sign": 1, "exp": 7, "mant": 12, "bias": 63, "phi_dist": 0.035 },
    "GF24": { "bits": 24, "sign": 1, "exp": 9, "mant": 14, "bias": 255, "phi_dist": 0.025 },
    "GF32": { "bits": 32, "sign": 1, "exp": 12, "mant": 19, "bias": 2047, "phi_dist": 0.014 },
    "GF64": { "bits": 64, "sign": 1, "exp": 24, "mant": 39, "bias": 8388607, "phi_dist": 0.00265, "extension": true }
  },
  "sacred_constants": {
    "PHI": { "value": 1.6180339887498948482, "tolerance": 1e-15 },
    "TRINITY": { "value": 3.0, "tolerance": 0.0 }
  }
}