{
  "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",
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        "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",
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        "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",
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        "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,
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        "n": 2,
        "principal_mellin_real": "2",
        "stripped_amplitude": "2",
        "total_real": "-1"
      },
      {
        "D": 6,
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        "jacobian": "2",
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        "n": 3,
        "principal_mellin_real": "3",
        "stripped_amplitude": "0",
        "total_real": "-1"
      },
      {
        "D": 6,
        "cancels_to_minus_one": true,
        "jacobian": "3",
        "momentum_delta": "-6",
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        "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",
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        "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"
      },
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        "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",
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        "stripped_amplitude": "-23",
        "total_real": "-1"
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        "D": 8,
        "cancels_to_minus_one": true,
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        "D": 8,
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        "stripped_amplitude": "-1",
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        "D": 8,
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        "principal_mellin_real": "8",
        "stripped_amplitude": "-4",
        "total_real": "-1"
      },
      {
        "D": 8,
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        "principal_mellin_real": "10",
        "stripped_amplitude": "-7",
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      },
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        "D": 8,
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        "jacobian": "5",
        "momentum_delta": "-8",
        "n": 6,
        "principal_mellin_real": "12",
        "stripped_amplitude": "-10",
        "total_real": "-1"
      },
      {
        "D": 8,
        "cancels_to_minus_one": true,
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        "principal_mellin_real": "14",
        "stripped_amplitude": "-13",
        "total_real": "-1"
      },
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        "D": 8,
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        "principal_mellin_real": "16",
        "stripped_amplitude": "-16",
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      },
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        "D": 8,
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        "principal_mellin_real": "18",
        "stripped_amplitude": "-19",
        "total_real": "-1"
      },
      {
        "D": 8,
        "cancels_to_minus_one": true,
        "jacobian": "9",
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        "principal_mellin_real": "48",
        "stripped_amplitude": "-48",
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      }
    ],
    "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"
    },
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      "block_hashes": {
        "mellin_delta": "053d6a8df0aad576174dca42758bca9a0a38eede5987db0d7b3fa11b9d374f4e",
        "simplex_jacobian": "e26ade3af18e50461fef068c453c0895b8a3b1833f6c02b9862e6971447277d4",
        "simplex_result": "24194f455371e8599a13a472c41489b7a6ccdbfa6911705547e0adb3ec882a9e",
        "source_scaling": "3e7ca7bf148633f6af58ebd99e65ee9f392365e29cac93b521a91e6dc4a719e8",
        "stripped_factorization": "66664eaf805d9eeafcf7ac1d981024c7ae07ba958e2054bee8f60a1cb79a75bb"
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      "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
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      "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"
}