{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BPMQN27W2ZKIRI3QMB4E7RMOPX","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":"5dba37dc0bf0aac36f28cf51e898e9f62df9c2b5085ff604be0ecc8090f550af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-27T15:10:39Z","title_canon_sha256":"1f483f36b36995dd8b4d0381902327ed507b68c0521047e8c6d25afebcb767b9"},"schema_version":"1.0","source":{"id":"1407.7245","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7245","created_at":"2026-05-18T00:53:10Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7245v3","created_at":"2026-05-18T00:53:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7245","created_at":"2026-05-18T00:53:10Z"},{"alias_kind":"pith_short_12","alias_value":"BPMQN27W2ZKI","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BPMQN27W2ZKIRI3Q","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BPMQN27W","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:d84311754ee6f98e460aeab532b6d0ba48b1306b46be6271aee34a30d7d2c348","target":"graph","created_at":"2026-05-18T00:53:10Z","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 Riemannian manifold, let P(M) denote the Wasserstein space of probability measures on M. If S is an embedded submanifold of M, and $\\mu$ is an absolutely continuous measure on S, then we compute the tangent cone of P(M) at $\\mu$.","authors_text":"John Lott","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-27T15:10:39Z","title":"On tangent cones in Wasserstein space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7245","kind":"arxiv","version":3},"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":"sha256:0dc559b81b25dee76102bf8fc6033957804b18d4d701949408396f8e47af1771","target":"record","created_at":"2026-05-18T00:53:10Z","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":"5dba37dc0bf0aac36f28cf51e898e9f62df9c2b5085ff604be0ecc8090f550af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-27T15:10:39Z","title_canon_sha256":"1f483f36b36995dd8b4d0381902327ed507b68c0521047e8c6d25afebcb767b9"},"schema_version":"1.0","source":{"id":"1407.7245","kind":"arxiv","version":3}},"canonical_sha256":"0bd906ebf6d65488a37060784fc58e7dc994bdcc100ffdfd6d32d02c0b99069b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bd906ebf6d65488a37060784fc58e7dc994bdcc100ffdfd6d32d02c0b99069b","first_computed_at":"2026-05-18T00:53:10.988294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:10.988294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MynmDg2gN4A79WRTzarrQDLqtWAp9Ojd6ZRhoDVQF3lM/uh1t8dKEZC74gjM1m2YzH2WUzAtivdJHbgY1WlNBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:10.988782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.7245","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0dc559b81b25dee76102bf8fc6033957804b18d4d701949408396f8e47af1771","sha256:d84311754ee6f98e460aeab532b6d0ba48b1306b46be6271aee34a30d7d2c348"],"state_sha256":"0f14bec4c73a4fe0f52b37e46307d84b4ddeed16a80f98d848fe01774c1b2a35"}