| {"created_at": "2026-04-06T00:00:00Z", "description": "Phi ratio split optimizations and invariants for GoldenFloat formats", "format_family": "PhiRatio", "schema_version": 2, "seal": "sha256:0d5a7f65f0e0d14024bcee0fd125927fd4f50bfe8621b92664d019b614b6c091", "test_vectors": [{"description": "GF4 phi-split: 3 available bits -> exp=1, mant=2", "expected": {"exp_bits": 1, "mant_bits": 2, "phi_dist_less_than": 0.01}, "input": {"bits": 4}, "name": "phi_split_gf4", "verdict": "CLEAN"}, {"description": "GF8 phi-split: 7 available bits -> exp=2, mant=5", "expected": {"exp_bits": 2, "mant_bits": 5, "phi_dist_less_than": 0.25}, "input": {"bits": 8}, "name": "phi_split_gf8", "verdict": "CLEAN"}, {"description": "GF12 phi-split: 11 available bits -> exp=3, mant=8", "expected": {"exp_bits": 3, "mant_bits": 8, "phi_dist_less_than": 0.25}, "input": {"bits": 12}, "name": "phi_split_gf12", "verdict": "CLEAN"}, {"description": "GF16 phi-split: 15 available bits -> exp=4, mant=11", "expected": {"exp_bits": 4, "mant_bits": 11, "phi_dist_less_than": 0.05}, "input": {"bits": 16}, "name": "phi_split_gf16", "verdict": "CLEAN"}, {"description": "GF32 phi-split: 31 available bits -> exp=8, mant=23", "expected": {"exp_bits": 8, "mant_bits": 23, "phi_dist_less_than": 0.02}, "input": {"bits": 32}, "name": "phi_split_gf32", "verdict": "CLEAN"}, {"description": "exp_bits + mant_bits must equal bits - 1", "expected": {"sum_equals": 15}, "input": {"bits": 16}, "name": "phi_split_sum_constraint", "verdict": "CLEAN"}, {"description": "GF16 actual format (6/9) has phi distance > 0.04", "expected": {"phi_dist_greater_than": 0.04}, "input": {"exp": 6, "mant": 9}, "name": "phi_distance_gf16_actual", "verdict": "CLEAN"}, {"description": "GF16 phi-split (4/11) is phi-optimal within 0.05", "expected": {"is_optimal": true}, "input": {"exp": 4, "mant": 11, "tolerance": 0.05}, "name": "is_phi_optimal_gf16_split", "verdict": "CLEAN"}, {"description": "PHI_RATIO_TARGET equals 1/phi", "expected": {"tolerance": 1e-15, "value": 0.6180339887498949}, "input": {}, "name": "phi_ratio_target", "verdict": "CLEAN"}, {"description": "Proof string contains '1/phi'", "expected": {"contains": "1/phi"}, "input": {}, "name": "phi_optimality_proof_content", "verdict": "CLEAN"}, {"description": "Invariant: PHI_RATIO_TARGET > 0.0", "expected": {"value": true}, "input": {"assertion": "PHI_RATIO_TARGET > 0.0"}, "name": "inv_phi_ratio_target_positive", "verdict": "CLEAN"}, {"description": "Invariant: PHI_RATIO_TARGET < 1.0", "expected": {"value": true}, "input": {"assertion": "PHI_RATIO_TARGET < 1.0"}, "name": "inv_phi_ratio_target_less_than_one", "verdict": "CLEAN"}, {"description": "Invariant: exp_bits + mant_bits == bits - 1", "expected": {"value": true}, "input": {"assertion": "phi_split(bits).exp_bits + phi_split(bits).mant_bits == bits - 1"}, "name": "inv_phi_split_sum_equals_available", "verdict": "CLEAN"}, {"description": "Invariant: compute_phi_distance(exp, mant) >= 0.0", "expected": {"value": true}, "input": {"assertion": "compute_phi_distance(exp, mant) >= 0.0"}, "name": "inv_phi_distance_non_negative", "verdict": "CLEAN"}, {"description": "Invariant: phi_split(4).phi_dist < 0.01", "expected": {"value": true}, "input": {"assertion": "phi_split(4).phi_dist < 0.01"}, "name": "inv_gf4_format_is_phi_optimal", "verdict": "CLEAN"}, {"description": "Invariant: exp_bits < bits for all valid bits", "expected": {"value": true}, "input": {"assertion": "phi_split(bits).exp_bits < bits"}, "name": "inv_exp_bits_less_than_total", "verdict": "CLEAN"}, {"description": "Invariant: mant_bits < bits for all valid bits", "expected": {"value": true}, "input": {"assertion": "phi_split(bits).mant_bits < bits"}, "name": "inv_mant_bits_less_than_total", "verdict": "CLEAN"}, {"description": "Invariant: round(-x) == -round(x)", "expected": {"value": true}, "input": {"assertion": "round(-x) == -round(x)"}, "name": "inv_phi_round_symmetric", "verdict": "CLEAN"}, {"description": "Invariant: floor(x1) <= floor(x2) when x1 <= x2", "expected": {"value": true}, "input": {"assertion": "floor(x1) <= floor(x2) when x1 <= x2"}, "name": "inv_phi_floor_monotonic", "verdict": "CLEAN"}], "updated_at": "2026-04-06T00:00:00Z", "validated_at": "2026-04-06T00:00:00Z", "vector_name": "Phi Ratio Conformance Vectors", "verdict": "CLEAN", "version": "2.0"} | |