{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4M4L25KHO6XLX3AWBMZPIKHZO7","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":"10652feffc684a2f338b10b0f73838b217dbc3c804da0019434f67b5ac5eee8d","cross_cats_sorted":["math.MP","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-05-30T07:53:55Z","title_canon_sha256":"9a9c51d992d15995847c45dc3ce4f121d953b8ddf9f5e355c4449341c76317f2"},"schema_version":"1.0","source":{"id":"1905.12901","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.12901","created_at":"2026-05-17T23:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"1905.12901v1","created_at":"2026-05-17T23:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.12901","created_at":"2026-05-17T23:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"4M4L25KHO6XL","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4M4L25KHO6XLX3AW","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4M4L25KH","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:9ad0e99dce8760435b7894d5298786930b6bbbc46dd2db12c3c495ac20d5b887","target":"graph","created_at":"2026-05-17T23:44:39Z","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 study the rate of convergence to equilibrium of the solution of a Fokker--Planck type equation introduced by one of the authors in 2006 to describe opinion formation in a multi-agent system. The main feature of this Fokker--Planck equation is the presence of a variable diffusion coefficient and boundaries, which introduce new challenging mathematical problems in the study of its long-time behavior.","authors_text":"Ada Pulvirenti, Elide Terraneo, Giulia Furioli, Giuseppe Toscani","cross_cats":["math.MP","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-05-30T07:53:55Z","title":"Wright-Fisher-type equations for opinion formation, large time behavior and weighted logarithmic-Sobolev inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12901","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:acb30b3114177aa428dc442499edb9584c616f2cc1222fb2d6cbea90e0f6c019","target":"record","created_at":"2026-05-17T23:44:39Z","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":"10652feffc684a2f338b10b0f73838b217dbc3c804da0019434f67b5ac5eee8d","cross_cats_sorted":["math.MP","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-05-30T07:53:55Z","title_canon_sha256":"9a9c51d992d15995847c45dc3ce4f121d953b8ddf9f5e355c4449341c76317f2"},"schema_version":"1.0","source":{"id":"1905.12901","kind":"arxiv","version":1}},"canonical_sha256":"e338bd754777aebbec160b32f428f977db94e8cf4c7e04775a245ec2c5a05d3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e338bd754777aebbec160b32f428f977db94e8cf4c7e04775a245ec2c5a05d3b","first_computed_at":"2026-05-17T23:44:39.374133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:39.374133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xjgqyg8kyfyoae9ihRNCcnuZEdrGk+Uza31ju9551Q6clU5LGM3USxBxbuWV/hJXiYtd16qu12GkNLizAb7rCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:39.374587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.12901","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acb30b3114177aa428dc442499edb9584c616f2cc1222fb2d6cbea90e0f6c019","sha256:9ad0e99dce8760435b7894d5298786930b6bbbc46dd2db12c3c495ac20d5b887"],"state_sha256":"76dcefc29d13332a996dd8eec941986352bd4353c6b66bc2b6960a6677b02086"}