{"_row_type": "meta", "created_at": "2026-04-06T15:54:08Z", "f64_phi_sq_eq_phi_plus_one": true, "flocq_layer": "coq/Kernel/PhiFloat.v", "formal_proof": "T27.Kernel.PhiFloat::phi_identity_contract", "formal_reference": "coq/Kernel/Phi.v", "format": "IEEE754-binary64", "format_family": "PhiRatio", "id": "PHI-IDENTITY-K2-F64", "identity_residual_bound_theory": 1.454e-15, "module": "PHI-IDENTITY-K2", "phi_dec": "1.618033988749895", "phi_hex": "0x1.9e3779b97f4a8p+0", "phi_plus_one_hex": "0x1.4f1bbcdcbfa54p+1", "phi_sq_hex": "0x1.4f1bbcdcbfa54p+1", "schema_version": 2, "seal": "sha256:99377061311b1fd1e594f5617ef9e14cef1ac5cc1cf2fcf41bc95c46df2949ec", "standard": "AXIOM-K2", "tolerance_formula": "5 * 2^-53 * phi^2 on R (Phi.v phi_tolerance / PhiFloat PHI_F64_TOLERANCE)", "updated_at": "2026-04-06T15:54:08Z", "validated_at": "2026-04-06T15:54:08Z", "validation_script": "scripts/validate_phi_f64.py", "vector_name": "phi_identity Vectors", "verdict": "CLEAN", "version": "2.0"}
{"_row_type": "vector", "claim": "Rabs(phi*phi - (phi+1)) = 0", "name": "phi_squared_identity_R", "verdict": "PASS"}
{"_row_type": "vector", "claim": "B2R(b64_mult NE phi phi) = B2R(b64_plus NE phi 1.0) (bit-identical floats)", "name": "phi_identity_f64_residual", "verdict": "PASS"}