{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:5M6BEBBY3M6S2SPQDRSNMCZUZ4","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":"58b2f87cd49224f38e8aec87f1fff6d121fffe94b6f9d5a43da48c249334b104","cross_cats_sorted":["cond-mat.soft"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-05-31T08:09:51Z","title_canon_sha256":"53b81a96c60682db0abe142a017b5ef14272865a143d1666d3bf2d40f28aedee"},"schema_version":"1.0","source":{"id":"cond-mat/0505745","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0505745","created_at":"2026-05-18T03:24:32Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0505745v1","created_at":"2026-05-18T03:24:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0505745","created_at":"2026-05-18T03:24:32Z"},{"alias_kind":"pith_short_12","alias_value":"5M6BEBBY3M6S","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"5M6BEBBY3M6S2SPQ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"5M6BEBBY","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:948b1bb03a6f3bd52cce104c76483f544451e3b190df9cdc08eaa881d6b384b8","target":"graph","created_at":"2026-05-18T03:24:32Z","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":"A lattice version of the Fokker-Planck equation (FPE), accounting for dissipative interactions, not resolved on the molecular scale, is introduced. The lattice FPE is applied to the study of electrorheological transport of a one-dimensional charged fluid, and found to yield quantitative agreement with a recent analytical solution. Future extensions, including inelastic ion-ion collisions, are also outlined.","authors_text":"J.-P. Hansen, S. Melchionna, S. Succi","cross_cats":["cond-mat.soft"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-05-31T08:09:51Z","title":"Lattice formulation of the Fokker-Planck equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0505745","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:b07da3a4743d23e539e78d8e1dc6387edeb43c7b3d2e1df2b3e2605142ed7383","target":"record","created_at":"2026-05-18T03:24:32Z","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":"58b2f87cd49224f38e8aec87f1fff6d121fffe94b6f9d5a43da48c249334b104","cross_cats_sorted":["cond-mat.soft"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-05-31T08:09:51Z","title_canon_sha256":"53b81a96c60682db0abe142a017b5ef14272865a143d1666d3bf2d40f28aedee"},"schema_version":"1.0","source":{"id":"cond-mat/0505745","kind":"arxiv","version":1}},"canonical_sha256":"eb3c120438db3d2d49f01c64d60b34cf08a9a861554732fcc55c6f78265b5805","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb3c120438db3d2d49f01c64d60b34cf08a9a861554732fcc55c6f78265b5805","first_computed_at":"2026-05-18T03:24:32.021212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:32.021212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9nyyYV7OML6W6VoPTur7UOYCit6P3/mgbMdhcxmJuIFg/MmOK9oswMvSEvY6h+z0JdEL4Yy0iHSSfwpwahmTAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:32.021613Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0505745","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b07da3a4743d23e539e78d8e1dc6387edeb43c7b3d2e1df2b3e2605142ed7383","sha256:948b1bb03a6f3bd52cce104c76483f544451e3b190df9cdc08eaa881d6b384b8"],"state_sha256":"e5ec8e6d1c0569f0fb06c1362ca365da9b8b3114fbd659dabda2f76b1b0ff95f"}