TFPT scientific source excerpt Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/hodge_complement_20261028/check_e8_a4_response.py Original file SHA-256: 9659806dfc92ec5f7d322a066d8e6f5b7b7c80e9a5cc285257d5d44bc57ea1f0 Inclusive original lines: 401-526 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. 000401 | need(set(ranks.values()) == {12} and len(ranks) == 50, 000402 | 'all50 actual insertion maps have rank12') 000403 | need(set(input_gain.values()) == {12} and len(input_gain) == 50, 000404 | 'sum Bdagger B is12 I50') 000405 | need(set(output_gain.values()) == {12} and len(output_gain) == 50, 000406 | 'sum B Bdagger is12 I50') 000407 | need(signed_factor_edges == 600, 'all600 signed factors verified') 000408 | need(dual_coordinate_edges == 600, 000409 | 'all600 fixed dual-coordinate amplitudes verified') 000410 | 000411 | # Independent finite channel counts: C_m/sqrt3 is Petersen, while 000412 | # A_ab/2 is the complete-graph wedge/contraction channel on five states. 000413 | carrier_population = {} 000414 | for ij in sorted({carrier_label(r, '10') for r in inputs}): 000415 | targets = Counter() 000416 | for m in range(5): 000417 | if m not in ij: 000418 | kl = tuple(sorted(all_five-set(ij)-{m})) 000419 | targets[kl] += 1 000420 | need(len(targets) == 3 and set(targets.values()) == {1}, 000421 | 'Hodge channel has three Petersen neighbours') 000422 | need(all(set(ij).isdisjoint(kl) for kl in targets), 000423 | 'Hodge population is Petersen disjointness') 000424 | carrier_population[','.join(map(str, ij))] = [','.join(map(str, kl)) 000425 | for kl in sorted(targets)] 000426 | family_population = {} 000427 | for q in range(5): 000428 | targets = Counter() 000429 | for a in range(5): 000430 | for b in range(a+1, 5): 000431 | if q in (a, b): 000432 | targets[b if q == a else a] += 1 000433 | need(len(targets) == 4 and set(targets.values()) == {1}, 000434 | 'family wedge channel has four neighbours') 000435 | family_population[str(q)] = sorted(targets) 000436 | 000437 | result = { 000438 | 'scope': ('Actual weight-one E8 current response in the given carrier ' 000439 | 'SU5 frame; no physical source selection or time law.'), 000440 | 'root_partition': { 000441 | 'carrier_A4_roots': len(carrier_roots), 000442 | 'centralizer_A4_roots': len(family_roots), 000443 | 'input_(10,bar5)': len(inputs), 000444 | 'insertion_(5,10)': len(insertions), 000445 | 'output_(bar10,5)': len(outputs), 000446 | 'conjugate_sector_(bar5,bar10)': len(sectors['bar5']), 000447 | }, 000448 | 'overlap_with_old_D5xA3_grading': old_sector_overlap, 000449 | 'family_simple_roots': [list(r) for r in family_simple], 000450 | 'family_cartan': cartan, 000451 | 'bracket_signed_edges': bracket_equations, 000452 | 'literal_epsilon_dual_coordinate_edges': dual_coordinate_edges, 000453 | 'neutral_A4xA4_signed_edges': covariance_edges, 000454 | 'phase_variables': len(phase_roots), 000455 | 'phase_rank': len(pivots), 000456 | 'kraus_count': len(insertions), 000457 | 'kraus_rank': 12, 000458 | 'source_gain': '12 I50', 000459 | 'source_response_denominator': 12, 000460 | 'factorization': ('E8 response = Hodge Petersen channel tensor ' 000461 | 'family wedge channel in the joint cocycle chart'), 000462 | 'carrier_channel': '1/3 sum_m C_m rho C_m*; population A_Petersen/3', 000463 | 'family_channel': '1/4 sum_ab A_ab rho A_ab*; population (J-I)/4 on five', 000464 | 'p2_X': list(X), 000465 | 'p2_X_convention': ('q_input=X_i+X_j, q_insertion=X_m, ' 000466 | 'q_output=-(X_k+X_l); equivalently ' 000467 | 'q_output+q_environment=q_input with ' 000468 | 'q_environment=-X_m'), 000469 | 'p2_X_charge_edge_counts': { 000470 | ','.join(map(str, key)): value 000471 | for key, value in sorted(xcharge_edges.items()) 000472 | }, 000473 | 'carrier_population': carrier_population, 000474 | 'family_population': family_population, 000475 | 'chart_caveat': ('The diagonal cocycle transport is a joint tensor ' 000476 | 'chart; no product phase gauge or raw-coordinate ' 000477 | 'partial trace is asserted.'), 000478 | 'dual_coordinate_conversion': { 000479 | 'input_bar5': 'h_q = sign(complement(q),q)', 000480 | 'output_bar10': 'h_kl = sign(complement(kl),k,l)', 000481 | 'verified_amplitude': 'h_kl * B_wedge * h_q = epsilon(m,i,j,k,l) A_ab', 000482 | }, 000483 | 'state_phases': { 000484 | ','.join(map(str, r)): str((-1)**((solution >> phase_index[r]) & 1)) 000485 | for r in inputs + insertions + outputs 000486 | }, 000487 | 'input_bar5_phase_chart': { 000488 | ','.join(map(str, r)): str( 000489 | (-1)**((solution >> phase_index[r]) & 1) 000490 | * perm_sign(tuple(sorted(all_five-{labels[r][1]}))+(labels[r][1],)) 000491 | ) 000492 | for r in inputs 000493 | }, 000494 | 'insertion_phase_chart': { 000495 | ','.join(map(str, r)): str((-1)**((solution >> phase_index[r]) & 1)) 000496 | for r in insertions 000497 | }, 000498 | 'output_bar10_phase_chart': { 000499 | ','.join(map(str, r)): str( 000500 | (-1)**((solution >> phase_index[r]) & 1) 000501 | * perm_sign(tuple(sorted(all_five-set(labels[r][0])))+labels[r][0]) 000502 | ) 000503 | for r in outputs 000504 | }, 000505 | 'neutral_root_phases': { 000506 | ','.join(map(str, r)): str((-1)**((solution >> phase_index[r]) & 1)) 000507 | for r in carrier_roots + family_roots 000508 | }, 000509 | 'sources': [ 000510 | source_hash('tfpt_explorer/current_block_geometry.py'), 000511 | source_hash('verification/v498_celestial_wp5b_singular_vector.py'), 000512 | ], 000513 | } 000514 | output_path = Path(__file__).with_name('e8-a4-results.json') 000515 | output_path.write_text(json.dumps(result, indent=2)+'\n') 000516 | print(json.dumps({k: v for k, v in result.items() 000517 | if k not in ('state_phases', 'input_bar5_phase_chart', 000518 | 'insertion_phase_chart', 000519 | 'output_bar10_phase_chart', 000520 | 'neutral_root_phases', 000521 | 'carrier_population', 'family_population')}, 000522 | indent=2)) 000523 | 000524 | 000525 | if __name__ == '__main__': 000526 | main()