{
  "kernel": "run_sabrina_causal_interior_inclusion_lemma",
  "role": "post-computation assertion only",
  "schema": "ouroboros_scientific_reference_assertion_v1",
  "scientific_payload": {
    "claim_boundary": {
      "capabilities_removed": [],
      "closedness_automatic_without_causal_assumption": false,
      "conformal_boundary_extension_proved": false,
      "full_connected_wedge_theorem_reproved": false,
      "mixed_state_extension_proved": false,
      "n_to_n_extension_proved": false,
      "source_error_claimed": false
    },
    "exact_checks": {
      "archive_hash_matches": true,
      "countermodel_failure_is_reflexive_point": true,
      "dropping_interior_has_countermodel": true,
      "expected_boundary_use_occurs_once": true,
      "expected_inclusion_occurs_once": true,
      "finite_push_up_models_all_pass": true,
      "finite_push_up_models_nonempty": true,
      "iff_statement_present": true,
      "member_hash_matches": true,
      "source_blocks_match": true
    },
    "paper": {
      "arxiv_id": "2509.26264",
      "title": "On sufficient conditions for holographic scattering"
    },
    "relation_certificate": {
      "dropped_interior_countermodel": {
        "A_equals_B": [
          1
        ],
        "both_inclusions_fail": true,
        "future_missing_points": [
          1
        ],
        "past_missing_points": [
          1
        ],
        "universe": [
          0,
          1,
          2
        ]
      },
      "finite_chain_models_checked": 2472,
      "models_per_size": {
        "3": 8,
        "4": 22,
        "5": 63,
        "6": 185,
        "7": 550,
        "8": 1644
      },
      "violation_count": 0,
      "violations": []
    },
    "result_version": "sabrina_causal_interior_inclusion_lemma_v1",
    "source_evidence": {
      "archive_sha256": "17edb31380f6f0e8856d0f3541a36ab4a6023551894698a45dbf44e7a37991e0",
      "block_hashes": {
        "connected_wedge_interior_step": "0acd2ad7d5f826b3491f5a93434815a10221b0c36a1e3d3ba717f8a5032bd280",
        "future_directions": "991b34fb34ee0d068b2e68a8486d9ee42faca7752e729f0e2defa0f5d90e54e5",
        "iff_summary": "b3c1294ca9af051db3b58680b34f87e19b3321c273f3196054d1e1532e65a0bc"
      },
      "checks": {
        "archive_hash_matches": true,
        "expected_boundary_use_occurs_once": true,
        "expected_inclusion_occurs_once": true,
        "iff_statement_present": true,
        "member_hash_matches": true,
        "source_blocks_match": true
      },
      "member_sha256": "0a4c40bb1e3e38c2da8a3c2ad0ced1f39e9071d9c9ec31dcab1ffd848f4ee9cb"
    },
    "status": "complete",
    "theorem": {
      "boundary_corollary": "if J^+(A) (respectively J^-(A)) is closed, then its boundary lies in that causal set and is disjoint from the boundary of J^+(B) (respectively J^-(B))",
      "future": "J^+(A) is contained in I^+(B), hence in the interior of J^+(B)",
      "hypotheses": "M is a time-oriented spacetime and A is a subset of the manifold interior of B",
      "past": "J^-(A) is contained in I^-(B), hence in the interior of J^-(B)",
      "proof": "for a in A choose b_- << a and b_+ >> a inside B; push-up gives b_- << y from a <= y and y << b_+ from y <= a"
    }
  },
  "scientific_payload_sha256": "d99b817c432380bbff4836ba0a169029b609c9519bb2ee813a581878f4ac7531"
}