ouroboros-pasterski-research-program / references /run_sabrina_ambidextrous_integer_prefactor_lattice.json
| { | |
| "kernel": "run_sabrina_ambidextrous_integer_prefactor_lattice", | |
| "role": "post-computation assertion only", | |
| "schema": "ouroboros_scientific_reference_assertion_v1", | |
| "scientific_payload": { | |
| "certificate_witnesses": { | |
| "integer_lattice_minus10_to_10": [ | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": null, | |
| "residue": "I*pi/9979200", | |
| "status": "pole" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": "pi**2/19958400", | |
| "residue": "0", | |
| "status": "finite_cancellation" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": -10 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": "I*pi**2/1814400", | |
| "residue": "0", | |
| "status": "finite_cancellation" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": null, | |
| "residue": "-pi/907200", | |
| "status": "pole" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": -9 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": null, | |
| "residue": "-I*pi/90720", | |
| "status": "pole" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": "-pi**2/181440", | |
| "residue": "0", | |
| "status": "finite_cancellation" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": -8 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": "-I*pi**2/20160", | |
| "residue": "0", | |
| "status": "finite_cancellation" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": null, | |
| "residue": "pi/10080", | |
| "status": "pole" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": -7 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": null, | |
| "residue": "I*pi/1260", | |
| "status": "pole" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": "pi**2/2520", | |
| "residue": "0", | |
| "status": "finite_cancellation" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": -6 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": "I*pi**2/360", | |
| "residue": "0", | |
| "status": "finite_cancellation" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": null, | |
| "residue": "-pi/180", | |
| "status": "pole" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": -5 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": null, | |
| "residue": "-I*pi/30", | |
| "status": "pole" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": "-pi**2/60", | |
| "residue": "0", | |
| "status": "finite_cancellation" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": -4 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": "-I*pi**2/12", | |
| "residue": "0", | |
| "status": "finite_cancellation" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": null, | |
| "residue": "pi/6", | |
| "status": "pole" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": -3 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": null, | |
| "residue": "2*I*pi/3", | |
| "status": "pole" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": "pi**2/3", | |
| "residue": "0", | |
| "status": "finite_cancellation" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": -2 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": "I*pi**2", | |
| "residue": "0", | |
| "status": "finite_cancellation" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": null, | |
| "residue": "-2*pi", | |
| "status": "pole" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": -1 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": null, | |
| "residue": "-4*I*pi", | |
| "status": "pole" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": "-2*pi**2", | |
| "residue": "0", | |
| "status": "finite_cancellation" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": 0 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": "-2*I*pi**2", | |
| "residue": "0", | |
| "status": "finite_cancellation" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": null, | |
| "residue": "4*pi", | |
| "status": "pole" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": 1 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": "-4*I*pi", | |
| "residue": "0", | |
| "status": "finite" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": "0", | |
| "residue": "0", | |
| "status": "zero" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": 2 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": "0", | |
| "residue": "0", | |
| "status": "zero" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": "-4*pi", | |
| "residue": "0", | |
| "status": "finite" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": 3 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": "8*I*pi", | |
| "residue": "0", | |
| "status": "finite" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": "0", | |
| "residue": "0", | |
| "status": "zero" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": 4 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": "0", | |
| "residue": "0", | |
| "status": "zero" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": "24*pi", | |
| "residue": "0", | |
| "status": "finite" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": 5 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": "-96*I*pi", | |
| "residue": "0", | |
| "status": "finite" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": "0", | |
| "residue": "0", | |
| "status": "zero" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": 6 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": "0", | |
| "residue": "0", | |
| "status": "zero" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": "-480*pi", | |
| "residue": "0", | |
| "status": "finite" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": 7 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": "2880*I*pi", | |
| "residue": "0", | |
| "status": "finite" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": "0", | |
| "residue": "0", | |
| "status": "zero" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": 8 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": "0", | |
| "residue": "0", | |
| "status": "zero" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": "20160*pi", | |
| "residue": "0", | |
| "status": "finite" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": 9 | |
| }, | |
| { | |
| "channels": { | |
| "antisymmetric": { | |
| "direct_match": true, | |
| "finite_value": "-161280*I*pi", | |
| "residue": "0", | |
| "status": "finite" | |
| }, | |
| "symmetric": { | |
| "direct_match": true, | |
| "finite_value": "0", | |
| "residue": "0", | |
| "status": "zero" | |
| } | |
| }, | |
| "complementary": true, | |
| "integer_delta": 10 | |
| } | |
| ] | |
| }, | |
| "claim_boundary": { | |
| "amplitude_residue_computed": false, | |
| "capabilities_removed": [], | |
| "contact_support_regularized": false, | |
| "full_distributional_wavefunction_classified": false | |
| }, | |
| "exact_checks": { | |
| "antisymmetric_prefactors_present": true, | |
| "archive_hash_matches": true, | |
| "closed_forms_match_direct_expansions": true, | |
| "delta_one_special_case": true, | |
| "delta_zero_special_case": true, | |
| "distributional_support_present": true, | |
| "integer_channels_are_complementary": true, | |
| "member_hash_matches": true, | |
| "positive_integer_zero_pattern": true, | |
| "source_blocks_match": true, | |
| "symmetric_prefactors_present": true | |
| }, | |
| "paper": { | |
| "arxiv_id": "2212.00962", | |
| "title": "Celestial amplitudes in an ambidextrous basis" | |
| }, | |
| "result_version": "sabrina_ambidextrous_integer_prefactor_lattice_v1", | |
| "source_evidence": { | |
| "archive_sha256": "2427287be8bd1a7795678aaa741678883d650e87fafd311bdbed06d30af1418a", | |
| "block_hashes": { | |
| "antisymmetric_light_prefactor": "f8960a1c62d8863ba211083ca3b94aa7ba02a82e3119aa7f6fbf20f34299e06f", | |
| "symmetric_light_prefactor": "c7278952c5f94673ec6bb54a4bf5bd1147b6a6c122d6d16a25f7a358b64f3546" | |
| }, | |
| "checks": { | |
| "antisymmetric_prefactors_present": true, | |
| "archive_hash_matches": true, | |
| "distributional_support_present": true, | |
| "member_hash_matches": true, | |
| "source_blocks_match": true, | |
| "symmetric_prefactors_present": true | |
| }, | |
| "member_sha256": "27eedb08d211073e0e05f79802b92b5d76ca52d12d7afe71356f10bc6123dd59" | |
| }, | |
| "status": "complete", | |
| "theorem": { | |
| "nonpositive_lattice": "at each nonpositive integer one channel has a simple pole while the complementary trigonometric zero cancels the gamma pole to a finite value", | |
| "positive_lattice": "for integer Delta>=2 exactly one channel vanishes and the other is finite", | |
| "prefactors": "C_s=4 pi Gamma(Delta-1) sin(pi Delta/2), C_a=4 pi i Gamma(Delta-1) cos(pi Delta/2)", | |
| "special_points": "at Delta=0, C_s=-2 pi^2 and Res C_a=-4 pi i; at Delta=1, Res C_s=4 pi and C_a=-2 pi^2 i" | |
| } | |
| }, | |
| "scientific_payload_sha256": "77e01bb41ab0dd463176786be21185590dc2a06da27f2585d546e2a379c2ff4f" | |
| } | |