{
  "kernel": "run_sabrina_all_m_transverse_nonlocality_chain",
  "role": "post-computation assertion only",
  "schema": "ouroboros_scientific_reference_assertion_v1",
  "scientific_payload": {
    "claim_boundary": {
      "boundary_condition_analysis_complete": false,
      "capabilities_removed": [],
      "independent_second_derivation_complete": false,
      "public_replay_claim_allowed": true
    },
    "classification": "all_m_transverse_nonlocality_depth_saturation_and_distribution_order_multiplicity_exact",
    "exact_checks": {
      "all_three_public_source_archives_match": true,
      "all_three_public_source_archives_nonempty": true,
      "finite_difference_termination_identities": true,
      "finite_m3_through_m8_depth_ladder": true,
      "finite_m3_through_m8_multiplicities": true,
      "generic_nonvanishing_slice_exact": true,
      "generic_order_has_exact_Z_r_plus_2_factor": true,
      "last_order_has_exact_Z_m_plus_1_factor": true,
      "m3_m4_m5_progression": true,
      "m_minus_2_boundary_cancels_exactly": true,
      "minimal_depth_identity": true,
      "order_zero_has_exact_Z2_factor": true
    },
    "finite_exact_rows": [
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        "m": 3,
        "minimal_inverse_total_Z_depth": 0,
        "orders_at_or_above_m_vanish": true,
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        "minimal_inverse_total_Z_depth": 1,
        "orders_at_or_above_m_vanish": true,
        "rows": [
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        ]
      },
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        "m": 5,
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        "orders_at_or_above_m_vanish": true,
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        ]
      },
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        "minimal_inverse_total_Z_depth": 3,
        "orders_at_or_above_m_vanish": true,
        "rows": [
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          {
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            "r": 2,
            "total_Z_multiplicity": 4
          },
          {
            "nonzero": true,
            "r": 3,
            "total_Z_multiplicity": 5
          },
          {
            "nonzero": true,
            "r": 4,
            "total_Z_multiplicity": 6
          },
          {
            "nonzero": true,
            "r": 5,
            "total_Z_multiplicity": 7
          }
        ]
      },
      {
        "last_nonzero_order": 6,
        "m": 7,
        "minimal_inverse_total_Z_depth": 4,
        "orders_at_or_above_m_vanish": true,
        "rows": [
          {
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            "total_Z_multiplicity": 2
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            "total_Z_multiplicity": 4
          },
          {
            "nonzero": true,
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            "total_Z_multiplicity": 5
          },
          {
            "nonzero": true,
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            "total_Z_multiplicity": 6
          },
          {
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            "total_Z_multiplicity": 7
          },
          {
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            "r": 6,
            "total_Z_multiplicity": 8
          }
        ]
      },
      {
        "last_nonzero_order": 7,
        "m": 8,
        "minimal_inverse_total_Z_depth": 5,
        "orders_at_or_above_m_vanish": true,
        "rows": [
          {
            "nonzero": true,
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            "total_Z_multiplicity": 2
          },
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          },
          {
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          },
          {
            "nonzero": true,
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          },
          {
            "nonzero": true,
            "r": 4,
            "total_Z_multiplicity": 6
          },
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            "nonzero": true,
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            "total_Z_multiplicity": 7
          },
          {
            "nonzero": true,
            "r": 6,
            "total_Z_multiplicity": 8
          },
          {
            "nonzero": true,
            "r": 7,
            "total_Z_multiplicity": 9
          }
        ]
      }
    ],
    "result_version": "sabrina_all_m_transverse_nonlocality_chain_v1",
    "source_evidence": {
      "archive_sha256": {
        "arxiv_2211_14287": "1299353b9514a296786e448ec1ec7adfc430eee66d055293cb24716dc23879db",
        "arxiv_2307_16801": "98acf1e79b6d6fb929626e11f40fdb0d4a4029f174f6c493f7639e721c7424b0",
        "arxiv_2607_28718": "bfa9d2a7941ed801f874bb92b4c3e898a99900d92990403d32c4b9408c48f2a1"
      },
      "checks": {
        "all_three_public_source_archives_match": true,
        "all_three_public_source_archives_nonempty": true
      },
      "observed_sha256": {
        "arxiv_2211_14287": "1299353b9514a296786e448ec1ec7adfc430eee66d055293cb24716dc23879db",
        "arxiv_2307_16801": "98acf1e79b6d6fb929626e11f40fdb0d4a4029f174f6c493f7639e721c7424b0",
        "arxiv_2607_28718": "bfa9d2a7941ed801f874bb92b4c3e898a99900d92990403d32c4b9408c48f2a1"
      }
    },
    "sources": {
      "celestial_conformal_colliders": {
        "arxiv_id": "2211.14287",
        "title": "Celestial Conformal Colliders"
      },
      "detector_operators": {
        "arxiv_id": "2307.16801",
        "title": "Detector Operators for Celestial Symmetries"
      },
      "infinite_symmetry_algebras": {
        "arxiv_id": "2607.28718",
        "title": "Infinite Symmetry Algebras in Four-Dimensional Conformal Field Theories"
      }
    },
    "status": "complete",
    "theorem": {
      "domain": "integer m>=3 in the complex-Hermitian conformal-scalar conventions",
      "generic_distribution_orders": "for 0<=r<=m-2, R_(m,r) has exact total-Z multiplicity r+2",
      "last_nonzero_order": "r=m-1 has exact total-Z multiplicity m+1",
      "minimal_inverse_total_Z_depth": "d_min(m)=m-3",
      "progression": "m=3 -> 0, m=4 -> 1, m=5 -> 2, then the all-m proof",
      "vanishing_orders": "R_(m,r)=0 for r>=m"
    }
  },
  "scientific_payload_sha256": "6600de93b5e0dbb7dc6744cfc31499e4d84760267f62e18bc2a1c9a0e8470db5"
}