{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:I5KPHEAMBTAGQHSTXJCG7F7XIZ","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":"ae8a773716e2bd09fdc88220834aea0617b392a20777135dac376f7811125fe3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-01-09T18:44:15Z","title_canon_sha256":"34373187892c5400854100e726684ef53a8e87324c0fb79450afc705a627525b"},"schema_version":"1.0","source":{"id":"1701.02297","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02297","created_at":"2026-05-18T00:53:11Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02297v1","created_at":"2026-05-18T00:53:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02297","created_at":"2026-05-18T00:53:11Z"},{"alias_kind":"pith_short_12","alias_value":"I5KPHEAMBTAG","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"I5KPHEAMBTAGQHST","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"I5KPHEAM","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:7c357c05b4e9357b625b9970e588f18c32654df9c505bc05d58683a66e2cab32","target":"graph","created_at":"2026-05-18T00:53:11Z","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":"If M is a smooth compact connected Riemannian manifold, let P(M) denote the Wasserstein space of probability measures on M. We describe a geometric construction of parallel transport of some tangent cones along geodesics in P(M). We show that when everything is smooth, the geometric parallel transport agrees with earlier formal calculations.","authors_text":"John Lott","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-01-09T18:44:15Z","title":"An intrinsic parallel transport in Wasserstein space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02297","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":"sha256:97602de65124a3b9c839d85f8bf8c13c1cf5083c10152d5ce9a9d9c06caa9f6d","target":"record","created_at":"2026-05-18T00:53:11Z","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":"ae8a773716e2bd09fdc88220834aea0617b392a20777135dac376f7811125fe3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-01-09T18:44:15Z","title_canon_sha256":"34373187892c5400854100e726684ef53a8e87324c0fb79450afc705a627525b"},"schema_version":"1.0","source":{"id":"1701.02297","kind":"arxiv","version":1}},"canonical_sha256":"4754f3900c0cc0681e53ba446f97f746757ccaf53961d10be3c5025c34bd2b18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4754f3900c0cc0681e53ba446f97f746757ccaf53961d10be3c5025c34bd2b18","first_computed_at":"2026-05-18T00:53:11.280699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:11.280699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yEUxSLO/CYNsWUSI3VkNMUVchcLKMlWiTBIg+xME335XYYvsp8BJLHiualOtWf+ThZwnNKsbA6OvpjVj9qYnDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:11.281061Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02297","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97602de65124a3b9c839d85f8bf8c13c1cf5083c10152d5ce9a9d9c06caa9f6d","sha256:7c357c05b4e9357b625b9970e588f18c32654df9c505bc05d58683a66e2cab32"],"state_sha256":"35098076e348172c558684762766c23dbe10ee4703b923b3958b747a87414fd5"}