{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:X6S5Q3WXJ6BOYWBP5SWBBNZ6CG","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":"ee2c5d76f6b504368679aff31bdc738273b2b11c3b1a17f3af77937527d1b4a3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-19T17:42:54Z","title_canon_sha256":"96df4fa10aab691e45e8d139e36cee38bceda10c23a2bfe274365a6bca8de84d"},"schema_version":"1.0","source":{"id":"1003.3849","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3849","created_at":"2026-05-18T02:08:25Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3849v2","created_at":"2026-05-18T02:08:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3849","created_at":"2026-05-18T02:08:25Z"},{"alias_kind":"pith_short_12","alias_value":"X6S5Q3WXJ6BO","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"X6S5Q3WXJ6BOYWBP","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"X6S5Q3WX","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:c7ddad7517b3901962ea6dce88bcb06d640c971b3db4f886a898da91c3e059f3","target":"graph","created_at":"2026-05-18T02:08:25Z","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":"We define and study on Lorentz manifolds a family of covariant diffusions in which the quadratic variation is locally determined by the curvature. This allows the interpretation of the diffusion effect on a particle by its interaction with the ambient space-time. We will focus on the case of warped products, especially Robertson-Walker manifolds, and analyse their asymptotic behaviour in the case of Einstein-de Sitter-like manifolds.","authors_text":"Jacques Franchi, Yves Le Jan","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-19T17:42:54Z","title":"Curvature Diffusions in General Relativity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3849","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:b89983c4eca1800a42fc866827390fb88d67cc8cd148afb13b3cce0023b3e21e","target":"record","created_at":"2026-05-18T02:08:25Z","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":"ee2c5d76f6b504368679aff31bdc738273b2b11c3b1a17f3af77937527d1b4a3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-19T17:42:54Z","title_canon_sha256":"96df4fa10aab691e45e8d139e36cee38bceda10c23a2bfe274365a6bca8de84d"},"schema_version":"1.0","source":{"id":"1003.3849","kind":"arxiv","version":2}},"canonical_sha256":"bfa5d86ed74f82ec582fecac10b73e11b598245c7e4f90453044399db25e94cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfa5d86ed74f82ec582fecac10b73e11b598245c7e4f90453044399db25e94cc","first_computed_at":"2026-05-18T02:08:25.190146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:08:25.190146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y/rZgBbQ2kyYIpE19wTu1+8zZcunga4+2Ik23I5q/bbdFV2bju53Uz9eYNepxx62GZiwCk7+4eLFFAa++e3CDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:08:25.190772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.3849","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b89983c4eca1800a42fc866827390fb88d67cc8cd148afb13b3cce0023b3e21e","sha256:c7ddad7517b3901962ea6dce88bcb06d640c971b3db4f886a898da91c3e059f3"],"state_sha256":"dfef0db64325747afbff4ca4e575601641c37db1f0b9ec5aa23f1642908d7cb6"}