| { |
| "kernel": "run_sabrina_low_hard_generator_nonclosure", |
| "role": "post-computation assertion only", |
| "schema": "ouroboros_scientific_reference_assertion_v1", |
| "scientific_payload": { |
| "claim_boundary": { |
| "capabilities_removed": [], |
| "full_soft_plus_hard_algebra_failure_claimed": false, |
| "hard_scalar_truncation_only": true, |
| "massless_qed_context_only": true |
| }, |
| "commutator_certificate": { |
| "angular_component": "0", |
| "checks": { |
| "angular_component_zero": true, |
| "connection_derivative_cancels": true, |
| "energy_component_exact": true, |
| "same_family_requires_zero_label": true, |
| "zero_obstruction_gives_zero_commutator": true |
| }, |
| "energy_component": "-(Gamma*Y*Z_1 - Gamma*Y_1*Z + Y*Z_2 - Y_2*Z)/E", |
| "expected_energy_component": "(-Gamma*(Y*Z_1 - Y_1*Z) - Y*Z_2 + Y_2*Z)/E" |
| }, |
| "exact_checks": { |
| "all_forty_nine_pairs_checked": true, |
| "all_mode_formulas_exact": true, |
| "angular_component_zero": true, |
| "archive_hash_matches": true, |
| "connection_derivative_cancels": true, |
| "decompressed_member_hash_matches": true, |
| "energy_component_exact": true, |
| "explicit_m1_n2_witness": true, |
| "generic_nonclosure_count": true, |
| "incoming_hard_charge_present": true, |
| "outgoing_hard_charge_present": true, |
| "same_family_requires_zero_label": true, |
| "scalar_hard_operator_present": true, |
| "soft_plus_hard_completion_present": true, |
| "source_blocks_match": true, |
| "ward_identity_present": true, |
| "zero_locus_exact": true, |
| "zero_obstruction_gives_zero_commutator": true |
| }, |
| "monomial_certificate": { |
| "checks": { |
| "all_forty_nine_pairs_checked": true, |
| "all_mode_formulas_exact": true, |
| "explicit_m1_n2_witness": true, |
| "generic_nonclosure_count": true, |
| "zero_locus_exact": true |
| }, |
| "rows": [ |
| { |
| "coefficient": "0", |
| "commutator_zero": true, |
| "formula_exact": true, |
| "m": 0, |
| "n": 0 |
| }, |
| { |
| "coefficient": "0", |
| "commutator_zero": true, |
| "formula_exact": true, |
| "m": 0, |
| "n": 1 |
| }, |
| { |
| "coefficient": "-2", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 0, |
| "n": 2 |
| }, |
| { |
| "coefficient": "-6*z", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 0, |
| "n": 3 |
| }, |
| { |
| "coefficient": "-12*z**2", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 0, |
| "n": 4 |
| }, |
| { |
| "coefficient": "-20*z**3", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 0, |
| "n": 5 |
| }, |
| { |
| "coefficient": "-30*z**4", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 0, |
| "n": 6 |
| }, |
| { |
| "coefficient": "0", |
| "commutator_zero": true, |
| "formula_exact": true, |
| "m": 1, |
| "n": 0 |
| }, |
| { |
| "coefficient": "0", |
| "commutator_zero": true, |
| "formula_exact": true, |
| "m": 1, |
| "n": 1 |
| }, |
| { |
| "coefficient": "-2*z", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 1, |
| "n": 2 |
| }, |
| { |
| "coefficient": "-6*z**2", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 1, |
| "n": 3 |
| }, |
| { |
| "coefficient": "-12*z**3", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 1, |
| "n": 4 |
| }, |
| { |
| "coefficient": "-20*z**4", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 1, |
| "n": 5 |
| }, |
| { |
| "coefficient": "-30*z**5", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 1, |
| "n": 6 |
| }, |
| { |
| "coefficient": "2", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 2, |
| "n": 0 |
| }, |
| { |
| "coefficient": "2*z", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 2, |
| "n": 1 |
| }, |
| { |
| "coefficient": "0", |
| "commutator_zero": true, |
| "formula_exact": true, |
| "m": 2, |
| "n": 2 |
| }, |
| { |
| "coefficient": "-4*z**3", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 2, |
| "n": 3 |
| }, |
| { |
| "coefficient": "-10*z**4", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 2, |
| "n": 4 |
| }, |
| { |
| "coefficient": "-18*z**5", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 2, |
| "n": 5 |
| }, |
| { |
| "coefficient": "-28*z**6", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 2, |
| "n": 6 |
| }, |
| { |
| "coefficient": "6*z", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 3, |
| "n": 0 |
| }, |
| { |
| "coefficient": "6*z**2", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 3, |
| "n": 1 |
| }, |
| { |
| "coefficient": "4*z**3", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 3, |
| "n": 2 |
| }, |
| { |
| "coefficient": "0", |
| "commutator_zero": true, |
| "formula_exact": true, |
| "m": 3, |
| "n": 3 |
| }, |
| { |
| "coefficient": "-6*z**5", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 3, |
| "n": 4 |
| }, |
| { |
| "coefficient": "-14*z**6", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 3, |
| "n": 5 |
| }, |
| { |
| "coefficient": "-24*z**7", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 3, |
| "n": 6 |
| }, |
| { |
| "coefficient": "12*z**2", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 4, |
| "n": 0 |
| }, |
| { |
| "coefficient": "12*z**3", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 4, |
| "n": 1 |
| }, |
| { |
| "coefficient": "10*z**4", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 4, |
| "n": 2 |
| }, |
| { |
| "coefficient": "6*z**5", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 4, |
| "n": 3 |
| }, |
| { |
| "coefficient": "0", |
| "commutator_zero": true, |
| "formula_exact": true, |
| "m": 4, |
| "n": 4 |
| }, |
| { |
| "coefficient": "-8*z**7", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 4, |
| "n": 5 |
| }, |
| { |
| "coefficient": "-18*z**8", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 4, |
| "n": 6 |
| }, |
| { |
| "coefficient": "20*z**3", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 5, |
| "n": 0 |
| }, |
| { |
| "coefficient": "20*z**4", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 5, |
| "n": 1 |
| }, |
| { |
| "coefficient": "18*z**5", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 5, |
| "n": 2 |
| }, |
| { |
| "coefficient": "14*z**6", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 5, |
| "n": 3 |
| }, |
| { |
| "coefficient": "8*z**7", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 5, |
| "n": 4 |
| }, |
| { |
| "coefficient": "0", |
| "commutator_zero": true, |
| "formula_exact": true, |
| "m": 5, |
| "n": 5 |
| }, |
| { |
| "coefficient": "-10*z**9", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 5, |
| "n": 6 |
| }, |
| { |
| "coefficient": "30*z**4", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 6, |
| "n": 0 |
| }, |
| { |
| "coefficient": "30*z**5", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 6, |
| "n": 1 |
| }, |
| { |
| "coefficient": "28*z**6", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 6, |
| "n": 2 |
| }, |
| { |
| "coefficient": "24*z**7", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 6, |
| "n": 3 |
| }, |
| { |
| "coefficient": "18*z**8", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 6, |
| "n": 4 |
| }, |
| { |
| "coefficient": "10*z**9", |
| "commutator_zero": false, |
| "formula_exact": true, |
| "m": 6, |
| "n": 5 |
| }, |
| { |
| "coefficient": "0", |
| "commutator_zero": true, |
| "formula_exact": true, |
| "m": 6, |
| "n": 6 |
| } |
| ], |
| "zero_pairs": [ |
| [ |
| 0, |
| 0 |
| ], |
| [ |
| 0, |
| 1 |
| ], |
| [ |
| 1, |
| 0 |
| ], |
| [ |
| 1, |
| 1 |
| ], |
| [ |
| 2, |
| 2 |
| ], |
| [ |
| 3, |
| 3 |
| ], |
| [ |
| 4, |
| 4 |
| ], |
| [ |
| 5, |
| 5 |
| ], |
| [ |
| 6, |
| 6 |
| ] |
| ] |
| }, |
| "paper": { |
| "arxiv_id": "1407.3814", |
| "title": "Low's Subleading Soft Theorem as a Symmetry of QED" |
| }, |
| "result_version": "sabrina_low_hard_generator_nonclosure_v1", |
| "source_evidence": { |
| "archive_sha256": "56dd48c217761e4cfc914fc3480831c01049a5e34b6ed4ef11893fc445964043", |
| "block_hashes": { |
| "soft_to_symmetry_hard_generator": "a85fe5207d3e2b66985bb44637b1ec1e6a838b5729964b31b85ec5f077e3430c" |
| }, |
| "checks": { |
| "archive_hash_matches": true, |
| "decompressed_member_hash_matches": true, |
| "incoming_hard_charge_present": true, |
| "outgoing_hard_charge_present": true, |
| "scalar_hard_operator_present": true, |
| "soft_plus_hard_completion_present": true, |
| "source_blocks_match": true, |
| "ward_identity_present": true |
| }, |
| "member_sha256": "b136e79a81fe707dac8d99c8bc5e9c72fe7162ba771dd2887cd878305aadce66" |
| }, |
| "status": "complete", |
| "theorem": { |
| "angular_component": "zero", |
| "closure_obstruction": "the commutator is in the same X_U family only when the displayed covariant derivative vanishes", |
| "commutator": "[X_Y,X_Z]=-E^-1 D_z(Y partial_z Z-Z partial_z Y) partial_E", |
| "monomial_modes": "for Y=z^m,Z=z^n and Gamma=0, the coefficient is -(n-m)(m+n-1)z^(m+n-2)/E" |
| } |
| }, |
| "scientific_payload_sha256": "923662d26ef1703e8e9b20da3584065e853328708a7abc6c4e522e16abb2d9b5" |
| } |
|
|
