{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MFSQJEG4F56EMTCOOXO2FMUTSK","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":"a5caffaaee40b990bdb6cb066ee55b29045425f893681bc97754ba4266dba78c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-14T20:26:28Z","title_canon_sha256":"3022f5893830260667f05b340c89345798dd7809985de29078d2738cec5d51c9"},"schema_version":"1.0","source":{"id":"1507.04016","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04016","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04016v3","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04016","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"pith_short_12","alias_value":"MFSQJEG4F56E","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MFSQJEG4F56EMTCO","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MFSQJEG4","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:aa6f56ff8ba94a9d1e0c972d42794be30d07ed5373ba99bcfb49774236b80e46","target":"graph","created_at":"2026-05-18T01:21:23Z","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":"In this paper, we study flows associated to Sobolev vector fields with subexponentially integrable divergence. Our approach is based on the transport equation following DiPerna-Lions [DPL89]. A key ingredient is to use a quantitative estimate of solutions to the Cauchy problem of transport equation to obtain the regularity of density functions.","authors_text":"Albert Clop, Joan Mateu, Joan Orobitg, Renjin Jiang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-14T20:26:28Z","title":"Flows for non-smooth vector fields with subexponentially integrable divergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04016","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:b30b765b4f7c85c67c8e9d91b3b7c9ac7424eacc2b05bf8f6556af6fb884a50b","target":"record","created_at":"2026-05-18T01:21:23Z","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":"a5caffaaee40b990bdb6cb066ee55b29045425f893681bc97754ba4266dba78c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-14T20:26:28Z","title_canon_sha256":"3022f5893830260667f05b340c89345798dd7809985de29078d2738cec5d51c9"},"schema_version":"1.0","source":{"id":"1507.04016","kind":"arxiv","version":3}},"canonical_sha256":"61650490dc2f7c464c4e75dda2b29392b5308f86b3a83c9ebb6e0ecc97f42c23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61650490dc2f7c464c4e75dda2b29392b5308f86b3a83c9ebb6e0ecc97f42c23","first_computed_at":"2026-05-18T01:21:23.009255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:23.009255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z5BCqJq7zu0pWy6o9Rv3OuuRKKTsLT9mBn51tfM61oT67lEFp5Vwd3SMu+uQlCcJz/XGDB5cRfkwCJNUQGdmBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:23.009984Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04016","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b30b765b4f7c85c67c8e9d91b3b7c9ac7424eacc2b05bf8f6556af6fb884a50b","sha256:aa6f56ff8ba94a9d1e0c972d42794be30d07ed5373ba99bcfb49774236b80e46"],"state_sha256":"e3f942584d26b2703770c0a9517bd675461ef585f1a65d73249ee46782ede94d"}