{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:V2DD4EP2TT5IJZ2AYJCYYDB7IS","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":"6ad8149d5755ca5684759b963aa32fdf22b09022fbb9c2b21c8fd44f104ff85f","cross_cats_sorted":["gr-qc","math-ph","math.AP","math.MG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-07-09T13:33:42Z","title_canon_sha256":"a3273be9ac78aad27c56e9b88a464543b8db91563200a83be9cb8fa98b763f97"},"schema_version":"1.0","source":{"id":"2507.06836","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.06836","created_at":"2026-07-05T11:34:23Z"},{"alias_kind":"arxiv_version","alias_value":"2507.06836v1","created_at":"2026-07-05T11:34:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.06836","created_at":"2026-07-05T11:34:23Z"},{"alias_kind":"pith_short_12","alias_value":"V2DD4EP2TT5I","created_at":"2026-07-05T11:34:23Z"},{"alias_kind":"pith_short_16","alias_value":"V2DD4EP2TT5IJZ2A","created_at":"2026-07-05T11:34:23Z"},{"alias_kind":"pith_short_8","alias_value":"V2DD4EP2","created_at":"2026-07-05T11:34:23Z"}],"graph_snapshots":[{"event_id":"sha256:f43ba8fc3ef0fe8be38686dfdfd7318ef6563e9d0ac06623fba4f5ba45b9adf9","target":"graph","created_at":"2026-07-05T11:34:23Z","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/2507.06836/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a splitting theorem for globally hyperbolic, weighted spacetimes with metrics and weights of regularity $C^1$ by combining elliptic techniques for the negative homogeneity $p$-d'Alembert operator from our recent work in the smooth setting with the concept of line-adapted curves introduced here. Our results extend the Lorentzian splitting theorem proved for smooth globally hyperbolic spacetimes by Galloway -- and variants of its weighted counterparts by Case and Woolgar--Wylie -- to this low regularity setting.","authors_text":"Argam Ohanyan, Clemens S\\\"amann, Mathias Braun, Nicola Gigli, Robert J. McCann","cross_cats":["gr-qc","math-ph","math.AP","math.MG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-07-09T13:33:42Z","title":"A Lorentzian splitting theorem for continuously differentiable metrics and weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06836","kind":"arxiv","version":1},"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":"sha256:050ce45aa91e216405f92d957541c64556180765e800e66fd4987048138fda9b","target":"record","created_at":"2026-07-05T11:34:23Z","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":"6ad8149d5755ca5684759b963aa32fdf22b09022fbb9c2b21c8fd44f104ff85f","cross_cats_sorted":["gr-qc","math-ph","math.AP","math.MG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-07-09T13:33:42Z","title_canon_sha256":"a3273be9ac78aad27c56e9b88a464543b8db91563200a83be9cb8fa98b763f97"},"schema_version":"1.0","source":{"id":"2507.06836","kind":"arxiv","version":1}},"canonical_sha256":"ae863e11fa9cfa84e740c2458c0c3f4491a392b886fe169fc1901416767d7f2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae863e11fa9cfa84e740c2458c0c3f4491a392b886fe169fc1901416767d7f2b","first_computed_at":"2026-07-05T11:34:23.901478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:34:23.901478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GulNFgwGR8IG+lGTFRDUrhfUzk/FBm1CmNuQdaca0cXmmMl8vLuJKrH+hpOmb/B1tKFeRpUi5xwa1LXn3GDhDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:34:23.901953Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.06836","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:050ce45aa91e216405f92d957541c64556180765e800e66fd4987048138fda9b","sha256:f43ba8fc3ef0fe8be38686dfdfd7318ef6563e9d0ac06623fba4f5ba45b9adf9"],"state_sha256":"ea25b0f5c676247069d5e8ab6df8166a9eb49a99fd514b3455800d4e92982b77"}