{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:45LXPYZIEHHIWVCIHHWVENLVEV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d7b788175732191b2ab0dcbf1094ce36b8c83236107223a0f9ac7cfb20485e51","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-04-07T12:51:16Z","title_canon_sha256":"f9366cbbd3f5cfb31ccf8f8b1fc20fa70fcb6df1e487573fa10f6beccaf48340"},"schema_version":"1.0","source":{"id":"2504.05028","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.05028","created_at":"2026-07-05T10:51:35Z"},{"alias_kind":"arxiv_version","alias_value":"2504.05028v2","created_at":"2026-07-05T10:51:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.05028","created_at":"2026-07-05T10:51:35Z"},{"alias_kind":"pith_short_12","alias_value":"45LXPYZIEHHI","created_at":"2026-07-05T10:51:35Z"},{"alias_kind":"pith_short_16","alias_value":"45LXPYZIEHHIWVCI","created_at":"2026-07-05T10:51:35Z"},{"alias_kind":"pith_short_8","alias_value":"45LXPYZI","created_at":"2026-07-05T10:51:35Z"}],"graph_snapshots":[{"event_id":"sha256:4015c88f11053ff1ff993e3d2fbd79fc737ac0ef83f088359f0d6cbe299a0c8b","target":"graph","created_at":"2026-07-05T10:51:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.05028/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a version of the Lorentzian splitting theorem under a weakened Ricci curvature condition. The proof makes use of basic properties of achronal limits [19], [20], together with the geometric maximum principle for $C^0$ spacelike hypersurfaces in [1]. Our version strengthens a related result in [29] in the globally hyperbolic setting by removing a certain boundedness condition on the Ricci curvature.","authors_text":"Gregory J. Galloway","cross_cats":["gr-qc"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-04-07T12:51:16Z","title":"A note on the Lorentzian splitting theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.05028","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:32211eba80b39930e88b68328c9cd6d22ecd0a7dc21ec95a937b252801543c55","target":"record","created_at":"2026-07-05T10:51:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d7b788175732191b2ab0dcbf1094ce36b8c83236107223a0f9ac7cfb20485e51","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-04-07T12:51:16Z","title_canon_sha256":"f9366cbbd3f5cfb31ccf8f8b1fc20fa70fcb6df1e487573fa10f6beccaf48340"},"schema_version":"1.0","source":{"id":"2504.05028","kind":"arxiv","version":2}},"canonical_sha256":"e75777e32821ce8b544839ed5235752577fbd0cd4635768a00e1e9b0b82d2b04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e75777e32821ce8b544839ed5235752577fbd0cd4635768a00e1e9b0b82d2b04","first_computed_at":"2026-07-05T10:51:35.971092Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:51:35.971092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8aX1J0DFvGIaGpy6nEfi5D29zEDsoftqDjRBHqPhH/cbjZIBEb162pm0Dw/OmM6yUwm+th7hbKPFHh97LUOCAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:51:35.971609Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.05028","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32211eba80b39930e88b68328c9cd6d22ecd0a7dc21ec95a937b252801543c55","sha256:4015c88f11053ff1ff993e3d2fbd79fc737ac0ef83f088359f0d6cbe299a0c8b"],"state_sha256":"cd7a10b308a03ff2aa38e92a64bc5f656dd4e7936ddaa5b099703ba9ff7fe3cf"}