{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZRXO4KAAJG3CBS2GEV3JQWACZN","short_pith_number":"pith:ZRXO4KAA","canonical_record":{"source":{"id":"1801.01724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-05T11:51:46Z","cross_cats_sorted":[],"title_canon_sha256":"22d4b1bf34bd36694afea7355d010eb1e4f66459b23669d50b9900c707e457bb","abstract_canon_sha256":"25e383e6df2c8dc79f60c9b0665ea0c74e6151b40be7c507816e79b7637feb5e"},"schema_version":"1.0"},"canonical_sha256":"cc6eee280049b620cb462576985802cb4d19cd7ca746dec99c267ca37601f626","source":{"kind":"arxiv","id":"1801.01724","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.01724","created_at":"2026-05-18T00:26:41Z"},{"alias_kind":"arxiv_version","alias_value":"1801.01724v1","created_at":"2026-05-18T00:26:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.01724","created_at":"2026-05-18T00:26:41Z"},{"alias_kind":"pith_short_12","alias_value":"ZRXO4KAAJG3C","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZRXO4KAAJG3CBS2G","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZRXO4KAA","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZRXO4KAAJG3CBS2GEV3JQWACZN","target":"record","payload":{"canonical_record":{"source":{"id":"1801.01724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-05T11:51:46Z","cross_cats_sorted":[],"title_canon_sha256":"22d4b1bf34bd36694afea7355d010eb1e4f66459b23669d50b9900c707e457bb","abstract_canon_sha256":"25e383e6df2c8dc79f60c9b0665ea0c74e6151b40be7c507816e79b7637feb5e"},"schema_version":"1.0"},"canonical_sha256":"cc6eee280049b620cb462576985802cb4d19cd7ca746dec99c267ca37601f626","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:41.216660Z","signature_b64":"pCcQoSZ886/a0YQSS5+tJsDzlnsV4e2t4JEgRS4wpZRdk9Ch3zDv4LnTyMmdBVwEPl/ikZjzRML60A3BJCZiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc6eee280049b620cb462576985802cb4d19cd7ca746dec99c267ca37601f626","last_reissued_at":"2026-05-18T00:26:41.216005Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:41.216005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.01724","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":"2026-05-18T00:26:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uo8ZYiW4RH0ck7EDnAv5pP6NZRjNyZJK/IIxoaQxLeAGE052RkoWJwEUWeh5GjmNyK+0oZgT5TjIBhz+x9PVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:34:28.316648Z"},"content_sha256":"56e7a045102df72aec6a02f8c36f21f24d5ba92a9ac533d5c5756ced3be2de4b","schema_version":"1.0","event_id":"sha256:56e7a045102df72aec6a02f8c36f21f24d5ba92a9ac533d5c5756ced3be2de4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZRXO4KAAJG3CBS2GEV3JQWACZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Lipschitz condition along a transversal foliation implies local uniqueness for ODEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"F. Adri\\'an F. Tojo, J. \\'Angel Cid","submitted_at":"2018-01-05T11:51:46Z","abstract_excerpt":"We prove the following result: if a continuous vector field $F$ is Lipschitz when restricted to the hypersurfaces determined by a suitable foliation and a transversal condition is satisfied at the initial condition, then $F$ determines a locally unique integral curve. We also present some illustrative examples and sufficient conditions in order to apply our main result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01724","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":"2026-05-18T00:26:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QVtBOoFkV4QOiXyyl8hoex+fC8WSFHEUfFWJzRfA0RzZbY15DzFi6PYHzTXKlgaBiWmkwnSHLMMlLrhUGL0EAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:34:28.317344Z"},"content_sha256":"186d7981942e66b1b477e7272499bffd619174c4de226c9a9c1cfc5bf9f10e94","schema_version":"1.0","event_id":"sha256:186d7981942e66b1b477e7272499bffd619174c4de226c9a9c1cfc5bf9f10e94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZRXO4KAAJG3CBS2GEV3JQWACZN/bundle.json","state_url":"https://pith.science/pith/ZRXO4KAAJG3CBS2GEV3JQWACZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZRXO4KAAJG3CBS2GEV3JQWACZN/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":"2026-05-31T06:34:28Z","links":{"resolver":"https://pith.science/pith/ZRXO4KAAJG3CBS2GEV3JQWACZN","bundle":"https://pith.science/pith/ZRXO4KAAJG3CBS2GEV3JQWACZN/bundle.json","state":"https://pith.science/pith/ZRXO4KAAJG3CBS2GEV3JQWACZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZRXO4KAAJG3CBS2GEV3JQWACZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZRXO4KAAJG3CBS2GEV3JQWACZN","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":"25e383e6df2c8dc79f60c9b0665ea0c74e6151b40be7c507816e79b7637feb5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-05T11:51:46Z","title_canon_sha256":"22d4b1bf34bd36694afea7355d010eb1e4f66459b23669d50b9900c707e457bb"},"schema_version":"1.0","source":{"id":"1801.01724","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.01724","created_at":"2026-05-18T00:26:41Z"},{"alias_kind":"arxiv_version","alias_value":"1801.01724v1","created_at":"2026-05-18T00:26:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.01724","created_at":"2026-05-18T00:26:41Z"},{"alias_kind":"pith_short_12","alias_value":"ZRXO4KAAJG3C","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZRXO4KAAJG3CBS2G","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZRXO4KAA","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:186d7981942e66b1b477e7272499bffd619174c4de226c9a9c1cfc5bf9f10e94","target":"graph","created_at":"2026-05-18T00:26:41Z","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 prove the following result: if a continuous vector field $F$ is Lipschitz when restricted to the hypersurfaces determined by a suitable foliation and a transversal condition is satisfied at the initial condition, then $F$ determines a locally unique integral curve. We also present some illustrative examples and sufficient conditions in order to apply our main result.","authors_text":"F. Adri\\'an F. Tojo, J. \\'Angel Cid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-05T11:51:46Z","title":"A Lipschitz condition along a transversal foliation implies local uniqueness for ODEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01724","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":"sha256:56e7a045102df72aec6a02f8c36f21f24d5ba92a9ac533d5c5756ced3be2de4b","target":"record","created_at":"2026-05-18T00:26:41Z","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":"25e383e6df2c8dc79f60c9b0665ea0c74e6151b40be7c507816e79b7637feb5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-05T11:51:46Z","title_canon_sha256":"22d4b1bf34bd36694afea7355d010eb1e4f66459b23669d50b9900c707e457bb"},"schema_version":"1.0","source":{"id":"1801.01724","kind":"arxiv","version":1}},"canonical_sha256":"cc6eee280049b620cb462576985802cb4d19cd7ca746dec99c267ca37601f626","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc6eee280049b620cb462576985802cb4d19cd7ca746dec99c267ca37601f626","first_computed_at":"2026-05-18T00:26:41.216005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:41.216005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pCcQoSZ886/a0YQSS5+tJsDzlnsV4e2t4JEgRS4wpZRdk9Ch3zDv4LnTyMmdBVwEPl/ikZjzRML60A3BJCZiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:41.216660Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.01724","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56e7a045102df72aec6a02f8c36f21f24d5ba92a9ac533d5c5756ced3be2de4b","sha256:186d7981942e66b1b477e7272499bffd619174c4de226c9a9c1cfc5bf9f10e94"],"state_sha256":"bc8a2e0ec1fa7523e2d2259993f2440e663b210f72b0d376849e2e86eee8258e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i0fh1G0Tpokp29juUIB2ZJg6jjAzOYgtrahdtV5jAJdbv5UpJZRoRRsbGq15MQ3YUttmnnLNZR/+gDdvfj42Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:34:28.321278Z","bundle_sha256":"a96d6ab816ff0203cc61f5432fa9a1d7af317b89c4ed3a31b92129119e774f32"}}