{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7HWJRBZTP7FV3562UYNTDII64L","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":"dfaf926bdb3bd7ef1c3359b804771e99cb0acdd446099c36e79aa55ab6d2a7b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-17T18:04:08Z","title_canon_sha256":"86a8e55e570daa749f9c5a5b51a8a7f80804f3bbb66efaa872a0c042e88baf36"},"schema_version":"1.0","source":{"id":"1802.06268","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.06268","created_at":"2026-05-18T00:23:03Z"},{"alias_kind":"arxiv_version","alias_value":"1802.06268v1","created_at":"2026-05-18T00:23:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06268","created_at":"2026-05-18T00:23:03Z"},{"alias_kind":"pith_short_12","alias_value":"7HWJRBZTP7FV","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7HWJRBZTP7FV3562","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7HWJRBZT","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:30349a77185458e2a6b18323ae9a8f5d04ba29d57a6030beda8dd6aeda75d8c3","target":"graph","created_at":"2026-05-18T00:23:03Z","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 reformulate a general class of classical bead-spring-chain models for dilute polymeric fluids, with Hookean spring potentials, as McKean-Vlasov diffusion. This results in a coupled system of partial differential equations involving the unsteady incompressible linearized Navier-Stokes equations, referred to as the Oseen system, for the velocity and the pressure of the fluid, with a source term which is a nonlinear function of the probability density function, and a second-order degenerate parabolic Fokker-Planck equation, whose transport terms depend on the velocity field, for the probabilit","authors_text":"Endre S\\\"uli, Ghozlane Yahiaoui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-17T18:04:08Z","title":"McKean-Vlasov diffusion and the well-posedness of the Hookean bead-spring-chain model for dilute polymeric fluids: small-mass limit and equilibration in momentum space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06268","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:f88f3c4bf92bbcce8650f6204d604c247fa44e6c5756421f900635f71d58601a","target":"record","created_at":"2026-05-18T00:23:03Z","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":"dfaf926bdb3bd7ef1c3359b804771e99cb0acdd446099c36e79aa55ab6d2a7b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-17T18:04:08Z","title_canon_sha256":"86a8e55e570daa749f9c5a5b51a8a7f80804f3bbb66efaa872a0c042e88baf36"},"schema_version":"1.0","source":{"id":"1802.06268","kind":"arxiv","version":1}},"canonical_sha256":"f9ec9887337fcb5df7daa61b31a11ee2d152ec4362bbf928b6ebdec511c98db4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9ec9887337fcb5df7daa61b31a11ee2d152ec4362bbf928b6ebdec511c98db4","first_computed_at":"2026-05-18T00:23:03.864054Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:03.864054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z+5HrLSbXyiPGa2Q1VAeoA5Bq2MbOhCs/bnM552l8e2xGeR74rWlDxTaXlqB3drpSkCldGd/D+eCqWbsVwMsDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:03.864612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.06268","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f88f3c4bf92bbcce8650f6204d604c247fa44e6c5756421f900635f71d58601a","sha256:30349a77185458e2a6b18323ae9a8f5d04ba29d57a6030beda8dd6aeda75d8c3"],"state_sha256":"02cfeedb47f9c21e8743d68eee29884d86fd0176a16300075738f5ec70190168"}