{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UKDWLZCVOC5TDW52JOX5YQO6QN","short_pith_number":"pith:UKDWLZCV","canonical_record":{"source":{"id":"1803.04387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-03-12T17:27:12Z","cross_cats_sorted":[],"title_canon_sha256":"8364c95bdfe7e4bbc2cbb3a1201ee06a6dcc9bb2ac6459ccec86e2571244a39f","abstract_canon_sha256":"56152314178e585268d569d4644aadf2117c9c48f8a82e16ec9a2dcd03c54e1d"},"schema_version":"1.0"},"canonical_sha256":"a28765e45570bb31dbba4bafdc41de835e8e44d51cd350a33723509e9d2f769a","source":{"kind":"arxiv","id":"1803.04387","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.04387","created_at":"2026-05-18T00:21:29Z"},{"alias_kind":"arxiv_version","alias_value":"1803.04387v1","created_at":"2026-05-18T00:21:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04387","created_at":"2026-05-18T00:21:29Z"},{"alias_kind":"pith_short_12","alias_value":"UKDWLZCVOC5T","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UKDWLZCVOC5TDW52","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UKDWLZCV","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UKDWLZCVOC5TDW52JOX5YQO6QN","target":"record","payload":{"canonical_record":{"source":{"id":"1803.04387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-03-12T17:27:12Z","cross_cats_sorted":[],"title_canon_sha256":"8364c95bdfe7e4bbc2cbb3a1201ee06a6dcc9bb2ac6459ccec86e2571244a39f","abstract_canon_sha256":"56152314178e585268d569d4644aadf2117c9c48f8a82e16ec9a2dcd03c54e1d"},"schema_version":"1.0"},"canonical_sha256":"a28765e45570bb31dbba4bafdc41de835e8e44d51cd350a33723509e9d2f769a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:29.820067Z","signature_b64":"O3i1iF7OocwnOAkfz33LQfK9spUvsLClo78fBZpVzOlVqYA2vReeR9HM7rmf1zPaZJOoLRH4JJfP1UDx7yh4Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a28765e45570bb31dbba4bafdc41de835e8e44d51cd350a33723509e9d2f769a","last_reissued_at":"2026-05-18T00:21:29.819480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:29.819480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.04387","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:21:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o0OFFam0kVjyP0nIn6iyhhIrkjdbQmaG1z5L0D2+uVQBUIv0pi4Jyn9TslfSHQydA4UcgsD339IgO+WSYheDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T00:14:40.482649Z"},"content_sha256":"f11ef405b3c05ca8b2948e8eff95a093bbea48e1e1d10257003f5f92eaac2a7c","schema_version":"1.0","event_id":"sha256:f11ef405b3c05ca8b2948e8eff95a093bbea48e1e1d10257003f5f92eaac2a7c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UKDWLZCVOC5TDW52JOX5YQO6QN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity of Lagrangian flows over $RCD^*(K,N)$ spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Daniele Semola, Elia Bru\\`e","submitted_at":"2018-03-12T17:27:12Z","abstract_excerpt":"The aim of this note is to provide regularity results for Regular Lagrangian flows of Sobolev vector fields over compact metric measure spaces verifying the Riemannian curvature dimension condition. We first prove, borrowing some ideas already present in the literature, that flows generated by vector fields with bounded symmetric derivative are Lipschitz, providing the natural extension of the standard Cauchy-Lipschitz theorem to this setting. Then we prove a Lusin-type regularity result in the Sobolev case (under the additional assumption that the m.m.s. is Ahlfors regular) therefore extendin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04387","kind":"arxiv","version":1},"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":"2026-05-18T00:21:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bKcJLjDLypRgYgkiQ8U5YgPEl2qmVT0uhYZzl9WhWvTNf6UzRj2jKRm/1xYb8EmcHsTe8kGkTwmkxXudC+pDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T00:14:40.482990Z"},"content_sha256":"b1610f3b9b8c9e5fd515ea414e4bbaa25a87bfacf9474bbea1c74d68e7238c37","schema_version":"1.0","event_id":"sha256:b1610f3b9b8c9e5fd515ea414e4bbaa25a87bfacf9474bbea1c74d68e7238c37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UKDWLZCVOC5TDW52JOX5YQO6QN/bundle.json","state_url":"https://pith.science/pith/UKDWLZCVOC5TDW52JOX5YQO6QN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UKDWLZCVOC5TDW52JOX5YQO6QN/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":"2026-06-22T00:14:40Z","links":{"resolver":"https://pith.science/pith/UKDWLZCVOC5TDW52JOX5YQO6QN","bundle":"https://pith.science/pith/UKDWLZCVOC5TDW52JOX5YQO6QN/bundle.json","state":"https://pith.science/pith/UKDWLZCVOC5TDW52JOX5YQO6QN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UKDWLZCVOC5TDW52JOX5YQO6QN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UKDWLZCVOC5TDW52JOX5YQO6QN","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":"56152314178e585268d569d4644aadf2117c9c48f8a82e16ec9a2dcd03c54e1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-03-12T17:27:12Z","title_canon_sha256":"8364c95bdfe7e4bbc2cbb3a1201ee06a6dcc9bb2ac6459ccec86e2571244a39f"},"schema_version":"1.0","source":{"id":"1803.04387","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.04387","created_at":"2026-05-18T00:21:29Z"},{"alias_kind":"arxiv_version","alias_value":"1803.04387v1","created_at":"2026-05-18T00:21:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04387","created_at":"2026-05-18T00:21:29Z"},{"alias_kind":"pith_short_12","alias_value":"UKDWLZCVOC5T","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UKDWLZCVOC5TDW52","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UKDWLZCV","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:b1610f3b9b8c9e5fd515ea414e4bbaa25a87bfacf9474bbea1c74d68e7238c37","target":"graph","created_at":"2026-05-18T00:21:29Z","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":"The aim of this note is to provide regularity results for Regular Lagrangian flows of Sobolev vector fields over compact metric measure spaces verifying the Riemannian curvature dimension condition. We first prove, borrowing some ideas already present in the literature, that flows generated by vector fields with bounded symmetric derivative are Lipschitz, providing the natural extension of the standard Cauchy-Lipschitz theorem to this setting. Then we prove a Lusin-type regularity result in the Sobolev case (under the additional assumption that the m.m.s. is Ahlfors regular) therefore extendin","authors_text":"Daniele Semola, Elia Bru\\`e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-03-12T17:27:12Z","title":"Regularity of Lagrangian flows over $RCD^*(K,N)$ spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04387","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:f11ef405b3c05ca8b2948e8eff95a093bbea48e1e1d10257003f5f92eaac2a7c","target":"record","created_at":"2026-05-18T00:21:29Z","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":"56152314178e585268d569d4644aadf2117c9c48f8a82e16ec9a2dcd03c54e1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-03-12T17:27:12Z","title_canon_sha256":"8364c95bdfe7e4bbc2cbb3a1201ee06a6dcc9bb2ac6459ccec86e2571244a39f"},"schema_version":"1.0","source":{"id":"1803.04387","kind":"arxiv","version":1}},"canonical_sha256":"a28765e45570bb31dbba4bafdc41de835e8e44d51cd350a33723509e9d2f769a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a28765e45570bb31dbba4bafdc41de835e8e44d51cd350a33723509e9d2f769a","first_computed_at":"2026-05-18T00:21:29.819480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:29.819480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O3i1iF7OocwnOAkfz33LQfK9spUvsLClo78fBZpVzOlVqYA2vReeR9HM7rmf1zPaZJOoLRH4JJfP1UDx7yh4Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:29.820067Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.04387","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f11ef405b3c05ca8b2948e8eff95a093bbea48e1e1d10257003f5f92eaac2a7c","sha256:b1610f3b9b8c9e5fd515ea414e4bbaa25a87bfacf9474bbea1c74d68e7238c37"],"state_sha256":"29da5579ab13b5f1b4fe476761042dc0ddf8b5ce2f12565d1e0d81d167dda559"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y4A62Re/gpigXOkiibtj7SMsVLKVIDAjAJOpzodgXPpHEG4S0EyGCAvqRD/oc2QxwtQLBm0Ne+pXPwBcBJZuDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T00:14:40.484878Z","bundle_sha256":"d82cb4a0b8cffc51185ae03b5fe6e24b1e396177a82abcd009dd2ff7f9400050"}}