TFPT scientific source excerpt Original repository path: experiments/theory-contracts/original-admissible-source-closure-20261025/check_w8_stress_cyclic.py Original file SHA-256: 5caccc07fb478f1e68c756b4312619b015582968bb5e3a441c637d951b4f7923 Inclusive original lines: 200-286 Line numbers below refer to the original source. This bounded excerpt is source evidence; it is not a new proof/checker run. Conversation metadata and personal execution details are omitted where indicated. 000200 | def main(): 000201 | parser = argparse.ArgumentParser() 000202 | parser.add_argument('--source-dir', type=Path, default=Path( 000203 | [OMITTED: non-scientific conversation or execution metadata] 000204 | 'original-admissible-source-closure-20261025')) 000205 | parser.add_argument('--output', type=Path) 000206 | args = parser.parse_args() 000207 | inputs = {name: (args.source_dir / name).read_bytes() for name in ( 000208 | 'w8-source-twopoint-results.json', 'quantum-octic-completion-results.json')} 000209 | fold_path = args.source_dir.parent / 'v16-operator-pullback-20261014/fold-results.json' 000210 | fold_bytes = fold_path.read_bytes() 000211 | fold = sp.Matrix(json.loads(fold_bytes)['explicit_Weyl_matrix']) 000212 | need(fold.T * fold == sp.eye(8), 'old M is not orthogonal') 000213 | old = json.loads(inputs['w8-source-twopoint-results.json']) 000214 | completion = json.loads(inputs['quantum-octic-completion-results.json']) 000215 | coefficients = list(map(F, completion['coefficients'])) 000216 | pairs = completion['basis_after_H8'] 000217 | need(len(coefficients) == 17 and len(pairs) == 16 and coefficients[0] == 1, 000218 | 'the declared old W8 ansatz changed') 000219 | roots = roots_e8() 000220 | cases = {} 000221 | for quarter, case in old['cases'].items(): 000222 | d = tuple(map(F, case['d_standard'])) 000223 | d2 = dot(d, d) 000224 | h8 = sum((dot(a, d)**8 for a in roots), F(0)) - 30 * d2**4 000225 | gradient = tuple(sum((8 * dot(a, d)**7 * a[j] for a in roots), F(0)) 000226 | - 240 * d2**3 * d[j] for j in range(8)) 000227 | need(dot(d, gradient) == 8 * h8, 'Euler identity for H8') 000228 | onepoint, radial_correction = h8, F(0) 000229 | for coefficient, monomial in zip(coefficients[1:], pairs): 000230 | constant, first = contraction_constant_and_first(monomial, d) 000231 | onepoint += coefficient * constant 000232 | radial_correction += coefficient * first 000233 | v1 = tuple(x + radial_correction * y for x, y in zip(gradient, d)) 000234 | need(onepoint == F(case['onepoint']), 'onepoint differs from sparse PBW') 000235 | need(v1 == tuple(map(F, case['level_1_vector'])), 'v1 differs from sparse PBW') 000236 | need(dot(d, v1) == 8 * onepoint, 'primary Ward identity') 000237 | norm = dot(v1, v1) 000238 | need(norm == F(case['level_1_norm_squared']), 'first spectral norm') 000239 | perpendicular = tangential(v1, d) 000240 | need(perpendicular == tangential(gradient, d), 'intrinsic tangent gradient') 000241 | need(dot(perpendicular, d) == 0, 'orthogonality') 000242 | residual = dot(perpendicular, perpendicular) 000243 | parallel = dot(d, v1)**2 / d2 000244 | need(norm == parallel + residual, 'orthogonal norm decomposition') 000245 | need(residual == F(51311452775625, 9345848836096) > 0, 000246 | 'the expected nonzero transverse response') 000247 | need(residual == F(case['level_1_excess_over_cauchy_bound']), 000248 | 'old Cauchy excess differs') 000249 | # A purely radial comparison polynomial has no such component. 000250 | radial_control = tuple(8 * d2**3 * x for x in d) 000251 | need(tangential(radial_control, d) == (F(0),) * 8, 'radial control') 000252 | cases[quarter] = { 000253 | 'd_squared': str(d2), 'h_d': str(d2 / 2), 000254 | 'H8_value': str(h8), 'H8_gradient': list(map(str, gradient)), 000255 | 'all_16_Q_corrections_radial': True, 000256 | 'quantum_radial_correction': str(radial_correction), 000257 | 'onepoint': str(onepoint), 'level_one_vector': list(map(str, v1)), 000258 | 'level_one_norm_squared': str(norm), 000259 | 'folded_c8_Virasoro_level_one_space': 'span{Lhat_-1^d Omega_d}=span{d.h_-1 Omega_d}', 000260 | 'folded_c8_projection_norm_squared': str(parallel), 000261 | 'transverse_vector': list(map(str, perpendicular)), 000262 | 'transverse_norm_squared': str(residual), 000263 | 'transverse_fraction_of_level_one_norm': str(residual / norm), 000264 | 'not_a_TFPT_completion_fraction': True, 000265 | 'full_original_c1_stress_reconstruction': reconstruct_in_original_stress( 000266 | quarter, v1, fold, d), 000267 | } 000268 | need(cases['1/4']['transverse_norm_squared'] == cases['3/4']['transverse_norm_squared'], 000269 | 'quarter norm comparison') 000270 | result = { 000271 | 'claim': 'MATH.ORIGINAL-SEAM.W8-ORIGINAL-STRESS-RECONSTRUCTION.01', 000272 | 'status': 'EXACT_ORIGINAL_C1_RECONSTRUCTION_AND_SCOPED_FOLDED_C8_EXCLUSION', 000273 | 'input_sha256': {name: sha256(data).hexdigest() for name, data in inputs.items()}, 000274 | 'original_fold_sha256': sha256(fold_bytes).hexdigest(), 000275 | 'root_count': len(roots), 'cases': cases, 000276 | 'analytic_consequence': 'The full ORIGINAL c1 Virasoro cycle equals the entire fixed ' 000277 | 'CAR charge sector because h=1/32 is not a c1 Kac weight m^2/4. All W8 insertion ' 000278 | 'levels and their positive-semigroup-smoothed response are in its closure. Only ' 000279 | 'the smaller folded c8 cycle misses the tangential first-level direction.', 000280 | 'scope': 'No local P1 operator identification or single implemented stress pulse. ' 000281 | 'No new source or state, no all-P1 exclusion, no absolute physical time calibration.'} 000282 | encoded = json.dumps(result, indent=2, sort_keys=True) + '\n' 000283 | if args.output: 000284 | args.output.write_text(encoded) 000285 | else: 000286 | print(encoded, end='')