File size: 3,804 Bytes
db6c8f1 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 | {
"kernel": "run_sabrina_ads_radiation_spectral_commutator",
"role": "post-computation assertion only",
"schema": "ouroboros_scientific_reference_assertion_v1",
"scientific_payload": {
"claim_boundary": {
"capabilities_removed": [],
"cotton_cft_dictionary_constructed": false,
"flat_limit_rederived": false,
"local_cut_criterion_constructed": false,
"physical_ads_radiation_criterion_rigorously_proved": false
},
"exact_checks": {
"archive_hash_matches": true,
"commutator_form_unique": true,
"cotton_alone_insufficient_stated": true,
"member_hash_matches": true,
"misaligned_pair_detected": true,
"nonzero_commuting_counterexample": true,
"rational_witnesses_all_pass": true,
"source_blocks_match": true,
"super_poynting_label_unique": true,
"symbolic_identity_exact": true,
"two_exact_solution_classes_present": true
},
"paper": {
"arxiv_id": "2404.02146",
"title": "Radiation in Holography"
},
"result_version": "sabrina_ads_radiation_spectral_commutator_v1",
"source_evidence": {
"archive_sha256": "1a1275f84b2989c1956ca93f60d06baee3e055215413dbb77fba34ba28e0fbf2",
"block_hashes": {
"ads_cft_consequence": "8e347f43f7d95be26e202ab50962119cc31c340723e94a7c8b27c02fda833d92",
"exact_solution_contrast": "c91f230530dc24dcd3655ee27a14e1be008e3ef9f1678b267ce7830d0fbbf632",
"radiation_criterion": "4061b04e420a9bda4964f1db07018893583601f910aefd40fd70cdbb2fe63816"
},
"checks": {
"archive_hash_matches": true,
"commutator_form_unique": true,
"cotton_alone_insufficient_stated": true,
"member_hash_matches": true,
"source_blocks_match": true,
"super_poynting_label_unique": true,
"two_exact_solution_classes_present": true
},
"member_sha256": "3cc6daa2e0d3520d63eb64da653fd87b39e0ef362decbd75503fd58e8cc15f3e"
},
"spectral_certificate": {
"identity": "||[C,T]||_F^2 = 2 sum_{i<j} (c_i-c_j)^2 T_ij^2",
"misaligned_pair": {
"commutator_nonzero": true,
"frobenius_norm_squared": "18"
},
"nonzero_commuting_pair": {
"both_nonzero": true,
"commutator_zero": true,
"degenerate_block_mixing_nonzero": true
},
"rational_witness_count": 96,
"rational_witness_failures": [],
"selection_rules": {
"coordinate_free": "real symmetric C and T commute if and only if they are simultaneously orthogonally diagonalizable",
"degenerate_spectrum": "stress may mix vectors only within equal-Cotton-eigenvalue blocks",
"distinct_spectrum": "zero commutator forces every off-diagonal stress component to vanish in the Cotton eigenbasis"
},
"symbolic_lhs": "2*c1**2*t12**2 + 2*c1**2*t13**2 - 4*c1*c2*t12**2 - 4*c1*c3*t13**2 + 2*c2**2*t12**2 + 2*c2**2*t23**2 - 4*c2*c3*t23**2 + 2*c3**2*t13**2 + 2*c3**2*t23**2",
"symbolic_residual": "0",
"symbolic_rhs": "2*c1**2*t12**2 + 2*c1**2*t13**2 - 4*c1*c2*t12**2 - 4*c1*c3*t13**2 + 2*c2**2*t12**2 + 2*c2**2*t23**2 - 4*c2*c3*t23**2 + 2*c3**2*t13**2 + 2*c3**2*t23**2"
},
"status": "complete",
"theorem": {
"interpretation": "the criterion measures eigenframe misalignment, weighted by Cotton eigenvalue gaps",
"no_radiation_algebraic_condition": "the proposed super-Poynting criterion vanishes exactly when Cotton-York and stress commute",
"nonzero_not_sufficient": "nonzero Cotton-York and nonzero stress are necessary but not sufficient for a nonzero commutator",
"spectral_identity": "||[C,T]||_F^2 = 2 sum_{i<j} (c_i-c_j)^2 T_ij^2"
}
},
"scientific_payload_sha256": "241d637afce046d817e7a3107063956a87e7581ccc4ccb9230959c16a846ff1d"
}
|