{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:H6CNHJNAJC4A2PMNFGO2XT4KYR","short_pith_number":"pith:H6CNHJNA","schema_version":"1.0","canonical_sha256":"3f84d3a5a048b80d3d8d299dabcf8ac465e728fc81e8552864458892bd56ce5c","source":{"kind":"arxiv","id":"2607.28344","version":1},"attestation_state":"computed","paper":{"title":"Reflected diffusion, no-flux continuity equations and confined Lagrangian flows in bounded domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.AP","math.PR"],"primary_cat":"math.CA","authors_text":"Rama Cont","submitted_at":"2026-07-30T15:10:59Z","abstract_excerpt":"Motivated by marginal distribution flows of reflected diffusions in bounded domains, we investigate when a density/flux pair solving a no-flux continuity equation admits a regular Lagrangian flow that remains in the closed domain and generates the prescribed density flow. We give sufficient conditions in terms of interior bounded-variation regularity, bounded-variation control on a boundary collar, a one-sided bound on an absolutely continuous divergence, and vanishing normal trace of the velocity. The proof uses the fact that tangency removes the singular boundary contribution to the divergen"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.28344","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2026-07-30T15:10:59Z","cross_cats_sorted":["cs.LG","math.AP","math.PR"],"title_canon_sha256":"41c5b99707ddc048329ceeeb84a2baff1dd2a8a8db8d90b896395455640ae110","abstract_canon_sha256":"77dd53abdb9d2f75408aff4321542cca9f5b1ae17e758e5f15da9cdb202a5164"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f84d3a5a048b80d3d8d299dabcf8ac465e728fc81e8552864458892bd56ce5c","last_reissued_at":"2026-07-31T01:37:20.553979Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-31T01:37:20.553979Z"},"graph_snapshot":{"paper":{"title":"Reflected diffusion, no-flux continuity equations and confined Lagrangian flows in bounded domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.AP","math.PR"],"primary_cat":"math.CA","authors_text":"Rama Cont","submitted_at":"2026-07-30T15:10:59Z","abstract_excerpt":"Motivated by marginal distribution flows of reflected diffusions in bounded domains, we investigate when a density/flux pair solving a no-flux continuity equation admits a regular Lagrangian flow that remains in the closed domain and generates the prescribed density flow. We give sufficient conditions in terms of interior bounded-variation regularity, bounded-variation control on a boundary collar, a one-sided bound on an absolutely continuous divergence, and vanishing normal trace of the velocity. The proof uses the fact that tangency removes the singular boundary contribution to the divergen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28344","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.28344/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.28344","created_at":"2026-07-31T01:37:20.557200+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.28344v1","created_at":"2026-07-31T01:37:20.557200+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28344","created_at":"2026-07-31T01:37:20.557200+00:00"},{"alias_kind":"pith_short_12","alias_value":"H6CNHJNAJC4A","created_at":"2026-07-31T01:37:20.557200+00:00"},{"alias_kind":"pith_short_16","alias_value":"H6CNHJNAJC4A2PMN","created_at":"2026-07-31T01:37:20.557200+00:00"},{"alias_kind":"pith_short_8","alias_value":"H6CNHJNA","created_at":"2026-07-31T01:37:20.557200+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/H6CNHJNAJC4A2PMNFGO2XT4KYR","json":"https://pith.science/pith/H6CNHJNAJC4A2PMNFGO2XT4KYR.json","graph_json":"https://pith.science/api/pith-number/H6CNHJNAJC4A2PMNFGO2XT4KYR/graph.json","events_json":"https://pith.science/api/pith-number/H6CNHJNAJC4A2PMNFGO2XT4KYR/events.json","paper":"https://pith.science/paper/H6CNHJNA"},"agent_actions":{"view_html":"https://pith.science/pith/H6CNHJNAJC4A2PMNFGO2XT4KYR","download_json":"https://pith.science/pith/H6CNHJNAJC4A2PMNFGO2XT4KYR.json","view_paper":"https://pith.science/paper/H6CNHJNA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.28344&json=true","fetch_graph":"https://pith.science/api/pith-number/H6CNHJNAJC4A2PMNFGO2XT4KYR/graph.json","fetch_events":"https://pith.science/api/pith-number/H6CNHJNAJC4A2PMNFGO2XT4KYR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H6CNHJNAJC4A2PMNFGO2XT4KYR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H6CNHJNAJC4A2PMNFGO2XT4KYR/action/storage_attestation","attest_author":"https://pith.science/pith/H6CNHJNAJC4A2PMNFGO2XT4KYR/action/author_attestation","sign_citation":"https://pith.science/pith/H6CNHJNAJC4A2PMNFGO2XT4KYR/action/citation_signature","submit_replication":"https://pith.science/pith/H6CNHJNAJC4A2PMNFGO2XT4KYR/action/replication_record"}},"created_at":"2026-07-31T01:37:20.557200+00:00","updated_at":"2026-07-31T01:37:20.557200+00:00"}