{
  "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"
}