| { |
| "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" |
| } |
|
|
