| { |
| "kernel": "run_sabrina_projective_mellin_scale_theorem", |
| "role": "post-computation assertion only", |
| "schema": "ouroboros_scientific_reference_assertion_v1", |
| "scientific_payload": { |
| "claim_boundary": { |
| "capabilities_removed": [], |
| "extra_physical_scales_included": false, |
| "massive_amplitudes_included": false, |
| "massless_canonical_external_scaling_required": true, |
| "noncanonical_external_dimensions_included": false, |
| "physical_theorem_dimension_scope": "D>=3; D=2 retained only as a formal algebraic boundary check", |
| "scale_anomalies_included": false, |
| "source_error_claimed": false |
| }, |
| "classification": "all_D_all_n_projective_mellin_radial_scale_cancellation_exact_under_canonical_scaling", |
| "exact_checks": { |
| "D2_through_D12_n2_through_n12_all_cancel": true, |
| "D4_principal_mellin_real_weight_vanishes": true, |
| "archive_hash_matches": true, |
| "finite_grid_has_121_points": true, |
| "member_hash_matches": true, |
| "source_blocks_match": true, |
| "source_markers_are_unique": true, |
| "source_states_four_dimensional_delta_scaling": true, |
| "source_states_full_amplitude_degree_minus_n": true, |
| "symbolic_all_D_all_n_total_is_minus_one": true, |
| "symbolic_full_amplitude_degree_specializes_to_minus_n_at_D4": true, |
| "symbolic_stripped_degree_specializes_to_4_minus_n": true |
| }, |
| "finite_exact_grid": [ |
| { |
| "D": 2, |
| "cancels_to_minus_one": true, |
| "jacobian": "1", |
| "momentum_delta": "-2", |
| "n": 2, |
| "principal_mellin_real": "-2", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 2, |
| "cancels_to_minus_one": true, |
| "jacobian": "2", |
| "momentum_delta": "-2", |
| "n": 3, |
| "principal_mellin_real": "-3", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 2, |
| "cancels_to_minus_one": true, |
| "jacobian": "3", |
| "momentum_delta": "-2", |
| "n": 4, |
| "principal_mellin_real": "-4", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 2, |
| "cancels_to_minus_one": true, |
| "jacobian": "4", |
| "momentum_delta": "-2", |
| "n": 5, |
| "principal_mellin_real": "-5", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 2, |
| "cancels_to_minus_one": true, |
| "jacobian": "5", |
| "momentum_delta": "-2", |
| "n": 6, |
| "principal_mellin_real": "-6", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 2, |
| "cancels_to_minus_one": true, |
| "jacobian": "6", |
| "momentum_delta": "-2", |
| "n": 7, |
| "principal_mellin_real": "-7", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 2, |
| "cancels_to_minus_one": true, |
| "jacobian": "7", |
| "momentum_delta": "-2", |
| "n": 8, |
| "principal_mellin_real": "-8", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 2, |
| "cancels_to_minus_one": true, |
| "jacobian": "8", |
| "momentum_delta": "-2", |
| "n": 9, |
| "principal_mellin_real": "-9", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 2, |
| "cancels_to_minus_one": true, |
| "jacobian": "9", |
| "momentum_delta": "-2", |
| "n": 10, |
| "principal_mellin_real": "-10", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 2, |
| "cancels_to_minus_one": true, |
| "jacobian": "10", |
| "momentum_delta": "-2", |
| "n": 11, |
| "principal_mellin_real": "-11", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 2, |
| "cancels_to_minus_one": true, |
| "jacobian": "11", |
| "momentum_delta": "-2", |
| "n": 12, |
| "principal_mellin_real": "-12", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 3, |
| "cancels_to_minus_one": true, |
| "jacobian": "1", |
| "momentum_delta": "-3", |
| "n": 2, |
| "principal_mellin_real": "-1", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 3, |
| "cancels_to_minus_one": true, |
| "jacobian": "2", |
| "momentum_delta": "-3", |
| "n": 3, |
| "principal_mellin_real": "-3/2", |
| "stripped_amplitude": "3/2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 3, |
| "cancels_to_minus_one": true, |
| "jacobian": "3", |
| "momentum_delta": "-3", |
| "n": 4, |
| "principal_mellin_real": "-2", |
| "stripped_amplitude": "1", |
| "total_real": "-1" |
| }, |
| { |
| "D": 3, |
| "cancels_to_minus_one": true, |
| "jacobian": "4", |
| "momentum_delta": "-3", |
| "n": 5, |
| "principal_mellin_real": "-5/2", |
| "stripped_amplitude": "1/2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 3, |
| "cancels_to_minus_one": true, |
| "jacobian": "5", |
| "momentum_delta": "-3", |
| "n": 6, |
| "principal_mellin_real": "-3", |
| "stripped_amplitude": "0", |
| "total_real": "-1" |
| }, |
| { |
| "D": 3, |
| "cancels_to_minus_one": true, |
| "jacobian": "6", |
| "momentum_delta": "-3", |
| "n": 7, |
| "principal_mellin_real": "-7/2", |
| "stripped_amplitude": "-1/2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 3, |
| "cancels_to_minus_one": true, |
| "jacobian": "7", |
| "momentum_delta": "-3", |
| "n": 8, |
| "principal_mellin_real": "-4", |
| "stripped_amplitude": "-1", |
| "total_real": "-1" |
| }, |
| { |
| "D": 3, |
| "cancels_to_minus_one": true, |
| "jacobian": "8", |
| "momentum_delta": "-3", |
| "n": 9, |
| "principal_mellin_real": "-9/2", |
| "stripped_amplitude": "-3/2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 3, |
| "cancels_to_minus_one": true, |
| "jacobian": "9", |
| "momentum_delta": "-3", |
| "n": 10, |
| "principal_mellin_real": "-5", |
| "stripped_amplitude": "-2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 3, |
| "cancels_to_minus_one": true, |
| "jacobian": "10", |
| "momentum_delta": "-3", |
| "n": 11, |
| "principal_mellin_real": "-11/2", |
| "stripped_amplitude": "-5/2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 3, |
| "cancels_to_minus_one": true, |
| "jacobian": "11", |
| "momentum_delta": "-3", |
| "n": 12, |
| "principal_mellin_real": "-6", |
| "stripped_amplitude": "-3", |
| "total_real": "-1" |
| }, |
| { |
| "D": 4, |
| "cancels_to_minus_one": true, |
| "jacobian": "1", |
| "momentum_delta": "-4", |
| "n": 2, |
| "principal_mellin_real": "0", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 4, |
| "cancels_to_minus_one": true, |
| "jacobian": "2", |
| "momentum_delta": "-4", |
| "n": 3, |
| "principal_mellin_real": "0", |
| "stripped_amplitude": "1", |
| "total_real": "-1" |
| }, |
| { |
| "D": 4, |
| "cancels_to_minus_one": true, |
| "jacobian": "3", |
| "momentum_delta": "-4", |
| "n": 4, |
| "principal_mellin_real": "0", |
| "stripped_amplitude": "0", |
| "total_real": "-1" |
| }, |
| { |
| "D": 4, |
| "cancels_to_minus_one": true, |
| "jacobian": "4", |
| "momentum_delta": "-4", |
| "n": 5, |
| "principal_mellin_real": "0", |
| "stripped_amplitude": "-1", |
| "total_real": "-1" |
| }, |
| { |
| "D": 4, |
| "cancels_to_minus_one": true, |
| "jacobian": "5", |
| "momentum_delta": "-4", |
| "n": 6, |
| "principal_mellin_real": "0", |
| "stripped_amplitude": "-2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 4, |
| "cancels_to_minus_one": true, |
| "jacobian": "6", |
| "momentum_delta": "-4", |
| "n": 7, |
| "principal_mellin_real": "0", |
| "stripped_amplitude": "-3", |
| "total_real": "-1" |
| }, |
| { |
| "D": 4, |
| "cancels_to_minus_one": true, |
| "jacobian": "7", |
| "momentum_delta": "-4", |
| "n": 8, |
| "principal_mellin_real": "0", |
| "stripped_amplitude": "-4", |
| "total_real": "-1" |
| }, |
| { |
| "D": 4, |
| "cancels_to_minus_one": true, |
| "jacobian": "8", |
| "momentum_delta": "-4", |
| "n": 9, |
| "principal_mellin_real": "0", |
| "stripped_amplitude": "-5", |
| "total_real": "-1" |
| }, |
| { |
| "D": 4, |
| "cancels_to_minus_one": true, |
| "jacobian": "9", |
| "momentum_delta": "-4", |
| "n": 10, |
| "principal_mellin_real": "0", |
| "stripped_amplitude": "-6", |
| "total_real": "-1" |
| }, |
| { |
| "D": 4, |
| "cancels_to_minus_one": true, |
| "jacobian": "10", |
| "momentum_delta": "-4", |
| "n": 11, |
| "principal_mellin_real": "0", |
| "stripped_amplitude": "-7", |
| "total_real": "-1" |
| }, |
| { |
| "D": 4, |
| "cancels_to_minus_one": true, |
| "jacobian": "11", |
| "momentum_delta": "-4", |
| "n": 12, |
| "principal_mellin_real": "0", |
| "stripped_amplitude": "-8", |
| "total_real": "-1" |
| }, |
| { |
| "D": 5, |
| "cancels_to_minus_one": true, |
| "jacobian": "1", |
| "momentum_delta": "-5", |
| "n": 2, |
| "principal_mellin_real": "1", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 5, |
| "cancels_to_minus_one": true, |
| "jacobian": "2", |
| "momentum_delta": "-5", |
| "n": 3, |
| "principal_mellin_real": "3/2", |
| "stripped_amplitude": "1/2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 5, |
| "cancels_to_minus_one": true, |
| "jacobian": "3", |
| "momentum_delta": "-5", |
| "n": 4, |
| "principal_mellin_real": "2", |
| "stripped_amplitude": "-1", |
| "total_real": "-1" |
| }, |
| { |
| "D": 5, |
| "cancels_to_minus_one": true, |
| "jacobian": "4", |
| "momentum_delta": "-5", |
| "n": 5, |
| "principal_mellin_real": "5/2", |
| "stripped_amplitude": "-5/2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 5, |
| "cancels_to_minus_one": true, |
| "jacobian": "5", |
| "momentum_delta": "-5", |
| "n": 6, |
| "principal_mellin_real": "3", |
| "stripped_amplitude": "-4", |
| "total_real": "-1" |
| }, |
| { |
| "D": 5, |
| "cancels_to_minus_one": true, |
| "jacobian": "6", |
| "momentum_delta": "-5", |
| "n": 7, |
| "principal_mellin_real": "7/2", |
| "stripped_amplitude": "-11/2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 5, |
| "cancels_to_minus_one": true, |
| "jacobian": "7", |
| "momentum_delta": "-5", |
| "n": 8, |
| "principal_mellin_real": "4", |
| "stripped_amplitude": "-7", |
| "total_real": "-1" |
| }, |
| { |
| "D": 5, |
| "cancels_to_minus_one": true, |
| "jacobian": "8", |
| "momentum_delta": "-5", |
| "n": 9, |
| "principal_mellin_real": "9/2", |
| "stripped_amplitude": "-17/2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 5, |
| "cancels_to_minus_one": true, |
| "jacobian": "9", |
| "momentum_delta": "-5", |
| "n": 10, |
| "principal_mellin_real": "5", |
| "stripped_amplitude": "-10", |
| "total_real": "-1" |
| }, |
| { |
| "D": 5, |
| "cancels_to_minus_one": true, |
| "jacobian": "10", |
| "momentum_delta": "-5", |
| "n": 11, |
| "principal_mellin_real": "11/2", |
| "stripped_amplitude": "-23/2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 5, |
| "cancels_to_minus_one": true, |
| "jacobian": "11", |
| "momentum_delta": "-5", |
| "n": 12, |
| "principal_mellin_real": "6", |
| "stripped_amplitude": "-13", |
| "total_real": "-1" |
| }, |
| { |
| "D": 6, |
| "cancels_to_minus_one": true, |
| "jacobian": "1", |
| "momentum_delta": "-6", |
| "n": 2, |
| "principal_mellin_real": "2", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 6, |
| "cancels_to_minus_one": true, |
| "jacobian": "2", |
| "momentum_delta": "-6", |
| "n": 3, |
| "principal_mellin_real": "3", |
| "stripped_amplitude": "0", |
| "total_real": "-1" |
| }, |
| { |
| "D": 6, |
| "cancels_to_minus_one": true, |
| "jacobian": "3", |
| "momentum_delta": "-6", |
| "n": 4, |
| "principal_mellin_real": "4", |
| "stripped_amplitude": "-2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 6, |
| "cancels_to_minus_one": true, |
| "jacobian": "4", |
| "momentum_delta": "-6", |
| "n": 5, |
| "principal_mellin_real": "5", |
| "stripped_amplitude": "-4", |
| "total_real": "-1" |
| }, |
| { |
| "D": 6, |
| "cancels_to_minus_one": true, |
| "jacobian": "5", |
| "momentum_delta": "-6", |
| "n": 6, |
| "principal_mellin_real": "6", |
| "stripped_amplitude": "-6", |
| "total_real": "-1" |
| }, |
| { |
| "D": 6, |
| "cancels_to_minus_one": true, |
| "jacobian": "6", |
| "momentum_delta": "-6", |
| "n": 7, |
| "principal_mellin_real": "7", |
| "stripped_amplitude": "-8", |
| "total_real": "-1" |
| }, |
| { |
| "D": 6, |
| "cancels_to_minus_one": true, |
| "jacobian": "7", |
| "momentum_delta": "-6", |
| "n": 8, |
| "principal_mellin_real": "8", |
| "stripped_amplitude": "-10", |
| "total_real": "-1" |
| }, |
| { |
| "D": 6, |
| "cancels_to_minus_one": true, |
| "jacobian": "8", |
| "momentum_delta": "-6", |
| "n": 9, |
| "principal_mellin_real": "9", |
| "stripped_amplitude": "-12", |
| "total_real": "-1" |
| }, |
| { |
| "D": 6, |
| "cancels_to_minus_one": true, |
| "jacobian": "9", |
| "momentum_delta": "-6", |
| "n": 10, |
| "principal_mellin_real": "10", |
| "stripped_amplitude": "-14", |
| "total_real": "-1" |
| }, |
| { |
| "D": 6, |
| "cancels_to_minus_one": true, |
| "jacobian": "10", |
| "momentum_delta": "-6", |
| "n": 11, |
| "principal_mellin_real": "11", |
| "stripped_amplitude": "-16", |
| "total_real": "-1" |
| }, |
| { |
| "D": 6, |
| "cancels_to_minus_one": true, |
| "jacobian": "11", |
| "momentum_delta": "-6", |
| "n": 12, |
| "principal_mellin_real": "12", |
| "stripped_amplitude": "-18", |
| "total_real": "-1" |
| }, |
| { |
| "D": 7, |
| "cancels_to_minus_one": true, |
| "jacobian": "1", |
| "momentum_delta": "-7", |
| "n": 2, |
| "principal_mellin_real": "3", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 7, |
| "cancels_to_minus_one": true, |
| "jacobian": "2", |
| "momentum_delta": "-7", |
| "n": 3, |
| "principal_mellin_real": "9/2", |
| "stripped_amplitude": "-1/2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 7, |
| "cancels_to_minus_one": true, |
| "jacobian": "3", |
| "momentum_delta": "-7", |
| "n": 4, |
| "principal_mellin_real": "6", |
| "stripped_amplitude": "-3", |
| "total_real": "-1" |
| }, |
| { |
| "D": 7, |
| "cancels_to_minus_one": true, |
| "jacobian": "4", |
| "momentum_delta": "-7", |
| "n": 5, |
| "principal_mellin_real": "15/2", |
| "stripped_amplitude": "-11/2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 7, |
| "cancels_to_minus_one": true, |
| "jacobian": "5", |
| "momentum_delta": "-7", |
| "n": 6, |
| "principal_mellin_real": "9", |
| "stripped_amplitude": "-8", |
| "total_real": "-1" |
| }, |
| { |
| "D": 7, |
| "cancels_to_minus_one": true, |
| "jacobian": "6", |
| "momentum_delta": "-7", |
| "n": 7, |
| "principal_mellin_real": "21/2", |
| "stripped_amplitude": "-21/2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 7, |
| "cancels_to_minus_one": true, |
| "jacobian": "7", |
| "momentum_delta": "-7", |
| "n": 8, |
| "principal_mellin_real": "12", |
| "stripped_amplitude": "-13", |
| "total_real": "-1" |
| }, |
| { |
| "D": 7, |
| "cancels_to_minus_one": true, |
| "jacobian": "8", |
| "momentum_delta": "-7", |
| "n": 9, |
| "principal_mellin_real": "27/2", |
| "stripped_amplitude": "-31/2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 7, |
| "cancels_to_minus_one": true, |
| "jacobian": "9", |
| "momentum_delta": "-7", |
| "n": 10, |
| "principal_mellin_real": "15", |
| "stripped_amplitude": "-18", |
| "total_real": "-1" |
| }, |
| { |
| "D": 7, |
| "cancels_to_minus_one": true, |
| "jacobian": "10", |
| "momentum_delta": "-7", |
| "n": 11, |
| "principal_mellin_real": "33/2", |
| "stripped_amplitude": "-41/2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 7, |
| "cancels_to_minus_one": true, |
| "jacobian": "11", |
| "momentum_delta": "-7", |
| "n": 12, |
| "principal_mellin_real": "18", |
| "stripped_amplitude": "-23", |
| "total_real": "-1" |
| }, |
| { |
| "D": 8, |
| "cancels_to_minus_one": true, |
| "jacobian": "1", |
| "momentum_delta": "-8", |
| "n": 2, |
| "principal_mellin_real": "4", |
| "stripped_amplitude": "2", |
| "total_real": "-1" |
| }, |
| { |
| "D": 8, |
| "cancels_to_minus_one": true, |
| "jacobian": "2", |
| "momentum_delta": "-8", |
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| }, |
| { |
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| "jacobian": "8", |
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| "stripped_amplitude": "-33", |
| "total_real": "-1" |
| }, |
| { |
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| "jacobian": "9", |
| "momentum_delta": "-12", |
| "n": 10, |
| "principal_mellin_real": "40", |
| "stripped_amplitude": "-38", |
| "total_real": "-1" |
| }, |
| { |
| "D": 12, |
| "cancels_to_minus_one": true, |
| "jacobian": "10", |
| "momentum_delta": "-12", |
| "n": 11, |
| "principal_mellin_real": "44", |
| "stripped_amplitude": "-43", |
| "total_real": "-1" |
| }, |
| { |
| "D": 12, |
| "cancels_to_minus_one": true, |
| "jacobian": "11", |
| "momentum_delta": "-12", |
| "n": 12, |
| "principal_mellin_real": "48", |
| "stripped_amplitude": "-48", |
| "total_real": "-1" |
| } |
| ], |
| "paper": { |
| "arxiv_id": "1706.03917", |
| "title": "Gluon Amplitudes as 2d Conformal Correlators" |
| }, |
| "result_version": "sabrina_projective_mellin_scale_theorem_v1", |
| "source_D4_specialization": { |
| "full_amplitude": "-n", |
| "jacobian": "n - 1", |
| "momentum_delta": "-4", |
| "principal_mellin_real": "0", |
| "stripped_amplitude": "4 - n", |
| "total_real": "-1" |
| }, |
| "source_evidence": { |
| "archive_sha256": "af2756072965c969be2a74c492fe25a797fe9f85e24d61605cf088e355d06244", |
| "block_hashes": { |
| "mellin_delta": "053d6a8df0aad576174dca42758bca9a0a38eede5987db0d7b3fa11b9d374f4e", |
| "simplex_jacobian": "e26ade3af18e50461fef068c453c0895b8a3b1833f6c02b9862e6971447277d4", |
| "simplex_result": "24194f455371e8599a13a472c41489b7a6ccdbfa6911705547e0adb3ec882a9e", |
| "source_scaling": "3e7ca7bf148633f6af58ebd99e65ee9f392365e29cac93b521a91e6dc4a719e8", |
| "stripped_factorization": "66664eaf805d9eeafcf7ac1d981024c7ae07ba958e2054bee8f60a1cb79a75bb" |
| }, |
| "checks": { |
| "archive_hash_matches": true, |
| "member_hash_matches": true, |
| "source_blocks_match": true, |
| "source_markers_are_unique": true, |
| "source_states_four_dimensional_delta_scaling": true, |
| "source_states_full_amplitude_degree_minus_n": true |
| }, |
| "member_sha256": "88253eb755b1b2418d0ac3480c1d4b67d9bb3985f8f6f6c3b0f79c85784f4bfe" |
| }, |
| "status": "complete", |
| "theorem": { |
| "canonical_stripped_amplitude_degree": "D-n(D-2)/2", |
| "mellin_real_weight_degree": "n(D-4)/2", |
| "momentum_delta_degree": "-D", |
| "principal_series_dimension": "Delta_i=(D-2)/2+i lambda_i", |
| "projective_jacobian_degree": "n-1", |
| "radial_distribution": "integral_0^infinity ds s^(-1+i Lambda)=2 pi delta(Lambda)", |
| "radial_exponent": "-1+i sum_i lambda_i", |
| "symbolic_real_residual": "-1" |
| } |
| }, |
| "scientific_payload_sha256": "bb866693a5cac8a1a30c7d4d3dec8feea3e6911173eca33cae0c27c503449354" |
| } |
|
|
