{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BPMQN27W2ZKIRI3QMB4E7RMOPX","short_pith_number":"pith:BPMQN27W","canonical_record":{"source":{"id":"1407.7245","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-27T15:10:39Z","cross_cats_sorted":[],"title_canon_sha256":"1f483f36b36995dd8b4d0381902327ed507b68c0521047e8c6d25afebcb767b9","abstract_canon_sha256":"5dba37dc0bf0aac36f28cf51e898e9f62df9c2b5085ff604be0ecc8090f550af"},"schema_version":"1.0"},"canonical_sha256":"0bd906ebf6d65488a37060784fc58e7dc994bdcc100ffdfd6d32d02c0b99069b","source":{"kind":"arxiv","id":"1407.7245","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BPMQN27W2ZKIRI3QMB4E7RMOPX","target":"record","payload":{"canonical_record":{"source":{"id":"1407.7245","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-27T15:10:39Z","cross_cats_sorted":[],"title_canon_sha256":"1f483f36b36995dd8b4d0381902327ed507b68c0521047e8c6d25afebcb767b9","abstract_canon_sha256":"5dba37dc0bf0aac36f28cf51e898e9f62df9c2b5085ff604be0ecc8090f550af"},"schema_version":"1.0"},"canonical_sha256":"0bd906ebf6d65488a37060784fc58e7dc994bdcc100ffdfd6d32d02c0b99069b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:10.988782Z","signature_b64":"MynmDg2gN4A79WRTzarrQDLqtWAp9Ojd6ZRhoDVQF3lM/uh1t8dKEZC74gjM1m2YzH2WUzAtivdJHbgY1WlNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bd906ebf6d65488a37060784fc58e7dc994bdcc100ffdfd6d32d02c0b99069b","last_reissued_at":"2026-05-18T00:53:10.988294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:10.988294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.7245","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N+75rWFXz0TQuI68wmQ2ZTFoa4q1Y96isuuKP7MfeNpGMVF14ujo0xKivzbuzIx8xFUDYN+T8wAVpdX8LbT+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:58:48.366641Z"},"content_sha256":"0dc559b81b25dee76102bf8fc6033957804b18d4d701949408396f8e47af1771","schema_version":"1.0","event_id":"sha256:0dc559b81b25dee76102bf8fc6033957804b18d4d701949408396f8e47af1771"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BPMQN27W2ZKIRI3QMB4E7RMOPX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On tangent cones in Wasserstein space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"John Lott","submitted_at":"2014-07-27T15:10:39Z","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 $\\mu$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7245","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LqkwWDlLDxmSLAgYzGT/yaMWKp4veso5O5pS379bxRR0bK5pv3pEPoYabwR9wCDDg2ANERXrx1Ml2kunaOFLDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:58:48.367328Z"},"content_sha256":"d84311754ee6f98e460aeab532b6d0ba48b1306b46be6271aee34a30d7d2c348","schema_version":"1.0","event_id":"sha256:d84311754ee6f98e460aeab532b6d0ba48b1306b46be6271aee34a30d7d2c348"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BPMQN27W2ZKIRI3QMB4E7RMOPX/bundle.json","state_url":"https://pith.science/pith/BPMQN27W2ZKIRI3QMB4E7RMOPX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BPMQN27W2ZKIRI3QMB4E7RMOPX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T22:58:48Z","links":{"resolver":"https://pith.science/pith/BPMQN27W2ZKIRI3QMB4E7RMOPX","bundle":"https://pith.science/pith/BPMQN27W2ZKIRI3QMB4E7RMOPX/bundle.json","state":"https://pith.science/pith/BPMQN27W2ZKIRI3QMB4E7RMOPX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BPMQN27W2ZKIRI3QMB4E7RMOPX/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EEqAwDLt9UwlYWeggIbgB3HtUdfzXEwuWckH5quljErrOkt7sLfzAwCc5lhJ7UwVVw3Cdww62u1IU86QVMggDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:58:48.370903Z","bundle_sha256":"224dc67fab885be39c0d7dd8d4f1f063c55d4f0d56354044c93eafcf91d28bd4"}}