| { |
| "kernel": "run_sabrina_soft_mellin_residue_identity", |
| "role": "post-computation assertion only", |
| "schema": "ouroboros_scientific_reference_assertion_v1", |
| "scientific_payload": { |
| "claim_boundary": { |
| "capabilities_removed": [], |
| "distributional_endpoint_convention": "symmetric half-line delta weight", |
| "paper_leading_and_subleading_results_challenged": false, |
| "scope": "The source immediately applies n=0 and n=1; both are exact because n!=1.", |
| "smoothness_assumption": "g(omega)=omega a(omega) is smooth at omega=0", |
| "unqualified_n_ge_2_extension_challenged": true |
| }, |
| "classification": "physical_n0_n1_exact_unqualified_all_n_extension_requires_factorial", |
| "exact_checks": { |
| "archive_hash_matches": true, |
| "corrected_identity_passes_n0_through_n8": true, |
| "fourier_annihilation_phase": true, |
| "fourier_creation_phase": true, |
| "mellin_residue_is_derivative_over_factorial": true, |
| "member_hash_matches": true, |
| "n0_source_identity_exact": true, |
| "n1_source_identity_exact": true, |
| "n2_is_exact_counterexample_to_unqualified_all_n_extension": true, |
| "n2_mismatch_factor_is_two": true, |
| "source_blocks_match": true, |
| "source_equation_labels_unique": true |
| }, |
| "finite_exact_rows": [ |
| { |
| "annihilation_coefficient": "pi", |
| "creation_coefficient": "pi", |
| "displayed_identity_matches": true, |
| "endpoint_derivative": "1", |
| "factorial_corrected_identity_matches": true, |
| "mellin_residue": "1", |
| "mellin_test_function": "a(omega)=omega^-1 exp(-omega)", |
| "n": 0, |
| "source_formula_ratio": "1" |
| }, |
| { |
| "annihilation_coefficient": "-I*pi", |
| "creation_coefficient": "I*pi", |
| "displayed_identity_matches": true, |
| "endpoint_derivative": "1", |
| "factorial_corrected_identity_matches": true, |
| "mellin_residue": "1", |
| "mellin_test_function": "a(omega)=omega^0 exp(-omega)", |
| "n": 1, |
| "source_formula_ratio": "1" |
| }, |
| { |
| "annihilation_coefficient": "-2*pi", |
| "creation_coefficient": "-2*pi", |
| "displayed_identity_matches": false, |
| "endpoint_derivative": "2", |
| "factorial_corrected_identity_matches": true, |
| "mellin_residue": "1", |
| "mellin_test_function": "a(omega)=omega^1 exp(-omega)", |
| "n": 2, |
| "source_formula_ratio": "2" |
| }, |
| { |
| "annihilation_coefficient": "6*I*pi", |
| "creation_coefficient": "-6*I*pi", |
| "displayed_identity_matches": false, |
| "endpoint_derivative": "6", |
| "factorial_corrected_identity_matches": true, |
| "mellin_residue": "1", |
| "mellin_test_function": "a(omega)=omega^2 exp(-omega)", |
| "n": 3, |
| "source_formula_ratio": "6" |
| }, |
| { |
| "annihilation_coefficient": "24*pi", |
| "creation_coefficient": "24*pi", |
| "displayed_identity_matches": false, |
| "endpoint_derivative": "24", |
| "factorial_corrected_identity_matches": true, |
| "mellin_residue": "1", |
| "mellin_test_function": "a(omega)=omega^3 exp(-omega)", |
| "n": 4, |
| "source_formula_ratio": "24" |
| }, |
| { |
| "annihilation_coefficient": "-120*I*pi", |
| "creation_coefficient": "120*I*pi", |
| "displayed_identity_matches": false, |
| "endpoint_derivative": "120", |
| "factorial_corrected_identity_matches": true, |
| "mellin_residue": "1", |
| "mellin_test_function": "a(omega)=omega^4 exp(-omega)", |
| "n": 5, |
| "source_formula_ratio": "120" |
| }, |
| { |
| "annihilation_coefficient": "-720*pi", |
| "creation_coefficient": "-720*pi", |
| "displayed_identity_matches": false, |
| "endpoint_derivative": "720", |
| "factorial_corrected_identity_matches": true, |
| "mellin_residue": "1", |
| "mellin_test_function": "a(omega)=omega^5 exp(-omega)", |
| "n": 6, |
| "source_formula_ratio": "720" |
| }, |
| { |
| "annihilation_coefficient": "5040*I*pi", |
| "creation_coefficient": "-5040*I*pi", |
| "displayed_identity_matches": false, |
| "endpoint_derivative": "5040", |
| "factorial_corrected_identity_matches": true, |
| "mellin_residue": "1", |
| "mellin_test_function": "a(omega)=omega^6 exp(-omega)", |
| "n": 7, |
| "source_formula_ratio": "5040" |
| }, |
| { |
| "annihilation_coefficient": "40320*pi", |
| "creation_coefficient": "40320*pi", |
| "displayed_identity_matches": false, |
| "endpoint_derivative": "40320", |
| "factorial_corrected_identity_matches": true, |
| "mellin_residue": "1", |
| "mellin_test_function": "a(omega)=omega^7 exp(-omega)", |
| "n": 8, |
| "source_formula_ratio": "40320" |
| } |
| ], |
| "paper": { |
| "arxiv_id": "2105.09792", |
| "source_equations": [ |
| "Mellin", |
| "mellinmode", |
| "eq:IDDelta1", |
| "eq:IDDelta2" |
| ], |
| "title": "Revisiting the Conformally Soft Sector with Celestial Diamonds" |
| }, |
| "result_version": "sabrina_soft_mellin_residue_scope_theorem_v1", |
| "source_evidence": { |
| "archive_sha256": "96fe817814bf7bfc432df67f49f60ea0afa72f6eeb335e93624b6d8bb54359f3", |
| "block_hashes": { |
| "Mellin": "6bceb4357552b5aa5e81879be46ef7a2bca646b1766392f58887007fa4ffb310", |
| "eq:IDDelta1": "4972b66bb470f919154ab6fd3324c373869538b172947c553b8508ce4fcdaddf", |
| "eq:IDDelta2": "c7e9d17afa4c3d9719ddce22c97340c3be4facd874f86d1bb519cc51c8902c5c", |
| "mellinmode": "e019183a7f11f077ce6d9e78ace905c0e421de10bd9940f9b6d1036b3f242122" |
| }, |
| "checks": { |
| "archive_hash_matches": true, |
| "member_hash_matches": true, |
| "source_blocks_match": true, |
| "source_equation_labels_unique": true |
| } |
| }, |
| "status": "complete", |
| "theorem": { |
| "corrected_annihilation_identity": "LHS=(-i)^n pi n! Res_{Delta=1-n}[a_Delta] (1+z zbar)^(-1-n).", |
| "corrected_creation_identity": "LHS=(+i)^n pi n! Res_{Delta=1-n}[a_Delta^dagger] (1+z zbar)^(-1-n).", |
| "equivalent_source_form": "Replace u_pm^n on the left by u_pm^n/n!.", |
| "fourier_endpoint_rule": "Integral_0^infinity g(omega) delta^(n)(c omega) d omega =(-1)^n g^(n)(0)/(2 c^(n+1)) under the symmetric endpoint convention.", |
| "mellin_residue_rule": "Res_{Delta=1-n} Integral_0^infinity omega^(Delta-2) g(omega) d omega = g^(n)(0)/n!." |
| } |
| }, |
| "scientific_payload_sha256": "2bac79f473b925a796d826a6c2d4fdd4003b5c269b8843d9f37dd83ed0e4d58f" |
| } |
|
|
