{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:S7HWDRIEXBFPYV5LMW5ZOT7RJL","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":"18de4df907a45b6fe648bcf1396de1c92543ec2483d7b2e767158bcc499d20b6","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-03T19:00:05Z","title_canon_sha256":"51e0a0913a756c66f3367f2480b0da6f8e884aedcab5e334e4cc7cb6971cafb7"},"schema_version":"1.0","source":{"id":"1508.00531","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00531","created_at":"2026-05-18T00:49:34Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00531v2","created_at":"2026-05-18T00:49:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00531","created_at":"2026-05-18T00:49:34Z"},{"alias_kind":"pith_short_12","alias_value":"S7HWDRIEXBFP","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"S7HWDRIEXBFPYV5L","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"S7HWDRIE","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:08c903486b63dbea2065795f50d3f313c2582b92b42022e9c73d9d6d718682b1","target":"graph","created_at":"2026-05-18T00:49:34Z","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"},"paper":{"abstract_excerpt":"Given a time function $\\tau$ on a spacetime $M$, we define a `null distance function', $\\hat{d}_\\tau$, built from and closely related to the causal structure of $M$. In basic models with timelike $\\nabla \\tau$, we show that 1) $\\hat{d}_\\tau$ is a definite distance function, which induces the manifold topology, 2) the causal structure of $M$ is completely encoded in $\\hat{d}_\\tau$ and $\\tau$. In general, $\\hat{d}_\\tau$ is a conformally invariant pseudometric, which may be indefinite. We give an `anti-Lipschitz' condition on $\\tau$, which ensures that $\\hat{d}_\\tau$ is definite, and show this co","authors_text":"Carlos Vega, Christina Sormani","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-03T19:00:05Z","title":"Null distance on a spacetime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00531","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":"sha256:3142543b96cbb33fccdf7e18ce28a00cf45d442a58d1664b6fdb03cd11b24c66","target":"record","created_at":"2026-05-18T00:49:34Z","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":"18de4df907a45b6fe648bcf1396de1c92543ec2483d7b2e767158bcc499d20b6","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-03T19:00:05Z","title_canon_sha256":"51e0a0913a756c66f3367f2480b0da6f8e884aedcab5e334e4cc7cb6971cafb7"},"schema_version":"1.0","source":{"id":"1508.00531","kind":"arxiv","version":2}},"canonical_sha256":"97cf61c504b84afc57ab65bb974ff14ae0ad30d78f7467b53abdc9fb1bcc37cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97cf61c504b84afc57ab65bb974ff14ae0ad30d78f7467b53abdc9fb1bcc37cb","first_computed_at":"2026-05-18T00:49:34.968951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:34.968951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KCmrJG4iMapa4orlD0k7B7QOE9CCO49ZP8HCBqLaJoYD8PQ9IqlyYKnF/0cLpornhbnh+IiKXz85Q7GDRoM0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:34.969641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00531","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3142543b96cbb33fccdf7e18ce28a00cf45d442a58d1664b6fdb03cd11b24c66","sha256:08c903486b63dbea2065795f50d3f313c2582b92b42022e9c73d9d6d718682b1"],"state_sha256":"909e03e6dddeed2eb416f21be0fbc53ad79259c0cb4d5eafe8dcb2f508947169"}