{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SIPJVDYDNUIHTA3Q7BF45LQFAV","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":"2cfc81188b94a929e01d692d0e4db5f5c6e87bfac7261f5449c6be8dcbdd38b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-09T01:49:58Z","title_canon_sha256":"d49c49c24f22782f796bc864963183fbfe40b13abf4f23f474dac29ae3332f4d"},"schema_version":"1.0","source":{"id":"1509.02599","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02599","created_at":"2026-05-18T01:33:34Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02599v1","created_at":"2026-05-18T01:33:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02599","created_at":"2026-05-18T01:33:34Z"},{"alias_kind":"pith_short_12","alias_value":"SIPJVDYDNUIH","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SIPJVDYDNUIHTA3Q","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SIPJVDYD","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:016f7fda8457177e38ea10714deb18a4bbdb2125896ab1a5ac2d290b0e184e91","target":"graph","created_at":"2026-05-18T01:33:34Z","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 consider the so-called spatially homogenous Kolmogorov-Vicsek model, a non-linear Fokker-Planck equation of self-driven stochastic particles with orientation interaction under the space-homogeneity. We prove the global existence and uniqueness of weak solutions to the equation. We also show that weak solutions exponentially converge to a steady state, which has the form of the Fisher-von Mises distribution.","authors_text":"Alessio Figalli, Javier Morales, Moon-Jin Kang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-09T01:49:58Z","title":"Global well-posedness of the spatially homogeneous Kolmogorov-Vicsek model as a gradient flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02599","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":"sha256:99d944b29641f6888b3c6ce2940f5d5fce0e8b124adbfd7be58f6cfa76d69500","target":"record","created_at":"2026-05-18T01:33:34Z","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":"2cfc81188b94a929e01d692d0e4db5f5c6e87bfac7261f5449c6be8dcbdd38b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-09T01:49:58Z","title_canon_sha256":"d49c49c24f22782f796bc864963183fbfe40b13abf4f23f474dac29ae3332f4d"},"schema_version":"1.0","source":{"id":"1509.02599","kind":"arxiv","version":1}},"canonical_sha256":"921e9a8f036d10798370f84bceae05056e7b58025dddeb595099e5b187e94a13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"921e9a8f036d10798370f84bceae05056e7b58025dddeb595099e5b187e94a13","first_computed_at":"2026-05-18T01:33:34.608721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:34.608721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OfvhCe4OQs+dYFpj8gNdt30B9XVX2UjpIfxTkAwgwCh/lppGsYZmaovcAjKAUa0NbIRpl0JT+9FDRCeohDeYDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:34.609561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02599","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99d944b29641f6888b3c6ce2940f5d5fce0e8b124adbfd7be58f6cfa76d69500","sha256:016f7fda8457177e38ea10714deb18a4bbdb2125896ab1a5ac2d290b0e184e91"],"state_sha256":"25fd4e02b24de18b031bf2162a09a8323f8e84460c4eed53acfe7c9da634846f"}