{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TKI6K4IIEDZGAKPM4M53PD5VJJ","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":"a7a122169dba4f1bf91eaa918c4a41dc447e5bd0c45fd2166bdae99feaf47d86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-02T14:49:25Z","title_canon_sha256":"9c44d0213c2ff09ee21e506065e17530ad60c4ca491d6739601c85666cbb23b1"},"schema_version":"1.0","source":{"id":"1305.0454","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0454","created_at":"2026-05-18T03:26:40Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0454v1","created_at":"2026-05-18T03:26:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0454","created_at":"2026-05-18T03:26:40Z"},{"alias_kind":"pith_short_12","alias_value":"TKI6K4IIEDZG","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TKI6K4IIEDZGAKPM","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TKI6K4II","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:fa4862f52e366348a63c6716e2d55900d806d01829336d317bce4d8697ee5c0b","target":"graph","created_at":"2026-05-18T03:26:40Z","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 martingales on manifolds with time-dependent connection, extending in this way the theory of stochastic processes on manifolds with time-changing geometry initiated by Arnaudon, Coulibaly and Thalmaier (2008). We show that some, but not all properties of martingales on manifolds with a fixed connection extend to this more general setting.","authors_text":"Anton Thalmaier, Hongxin Guo, Robert Philipowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-02T14:49:25Z","title":"Martingales on manifolds with time-dependent connection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0454","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":"sha256:1923277956f15b2984eb8d61df47654895d37938c4ea0a3ef2a7f29a722e39c1","target":"record","created_at":"2026-05-18T03:26:40Z","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":"a7a122169dba4f1bf91eaa918c4a41dc447e5bd0c45fd2166bdae99feaf47d86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-02T14:49:25Z","title_canon_sha256":"9c44d0213c2ff09ee21e506065e17530ad60c4ca491d6739601c85666cbb23b1"},"schema_version":"1.0","source":{"id":"1305.0454","kind":"arxiv","version":1}},"canonical_sha256":"9a91e5710820f26029ece33bb78fb54a50c3086b04d28f0b1d88a702325afd1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a91e5710820f26029ece33bb78fb54a50c3086b04d28f0b1d88a702325afd1f","first_computed_at":"2026-05-18T03:26:40.261288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:40.261288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ceqacT46QnS3YvvSTFyBjn9LIA2Qt0Nri5EMlan8bMtXAUhcbLhcnnM0BRtLZYTZX9a0qwcp61GTGqiROiOCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:40.261814Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0454","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1923277956f15b2984eb8d61df47654895d37938c4ea0a3ef2a7f29a722e39c1","sha256:fa4862f52e366348a63c6716e2d55900d806d01829336d317bce4d8697ee5c0b"],"state_sha256":"06180788c21de9ed95c9e6637b6f0bdf05de0d083f6edf5e4c5f8cd4c73d08eb"}