File size: 3,336 Bytes
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"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,
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]
},
"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": {
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"expected_boundary_use_occurs_once": true,
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"iff_statement_present": true,
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},
"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"
}
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