{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HOENEMCXDZGCZU2LQ2BHPUAOLW","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":"6cf42851390aea96cebe36a87a3ceb235ba4692c9ce9a7787b34859216ed2ea8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-19T10:09:22Z","title_canon_sha256":"a36ee50b90cc6be972cbed0a291098de278a42d43c9ef394080028a2543fb0e3"},"schema_version":"1.0","source":{"id":"2505.12926","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.12926","created_at":"2026-06-03T01:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"2505.12926v4","created_at":"2026-06-03T01:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.12926","created_at":"2026-06-03T01:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"HOENEMCXDZGC","created_at":"2026-06-03T01:05:04Z"},{"alias_kind":"pith_short_16","alias_value":"HOENEMCXDZGCZU2L","created_at":"2026-06-03T01:05:04Z"},{"alias_kind":"pith_short_8","alias_value":"HOENEMCX","created_at":"2026-06-03T01:05:04Z"}],"graph_snapshots":[{"event_id":"sha256:8c8edbe334d66d3f547be4e2e5d5aeade66d46b9d5132769e532b7e0ab58e83c","target":"graph","created_at":"2026-06-03T01:05:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.12926/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the convergence to (quasi--)equilibrium of a density dependent Markov chain in~${\\mathbb Z}^d$, whose drift satisfies a system of ordinary differential equations having an attractive fixed point. For a sequence of such processes~${\\mathbb X}^N$, indexed by a size parameter~$N$, the time taken until the distribution of~${\\mathbb X}^N$, started in some given state, approaches its (quasi--)equilibrium distribution~$\\pi^N$ typically increases with~$N$. To first order, it corresponds to the time~$t_N$ at which the solution to the drift equations reaches a distance of~$\\sqrt N$ from t","authors_text":"Andrew Barbour, Graham Brightwell, Malwina Luczak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-19T10:09:22Z","title":"Convergence to equilibrium for density dependent Markov jump processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.12926","kind":"arxiv","version":4},"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:dccdec3c98598ec490971f8ac1b9d2cbd0278c2bdb83335a5f3eee15f9f611df","target":"record","created_at":"2026-06-03T01:05:04Z","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":"6cf42851390aea96cebe36a87a3ceb235ba4692c9ce9a7787b34859216ed2ea8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-19T10:09:22Z","title_canon_sha256":"a36ee50b90cc6be972cbed0a291098de278a42d43c9ef394080028a2543fb0e3"},"schema_version":"1.0","source":{"id":"2505.12926","kind":"arxiv","version":4}},"canonical_sha256":"3b88d230571e4c2cd34b868277d00e5da097197d3b38357b9930ef1588511fc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b88d230571e4c2cd34b868277d00e5da097197d3b38357b9930ef1588511fc8","first_computed_at":"2026-06-03T01:05:04.485421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:05:04.485421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LYkzlPOBVWUP0bNKsLByJK6n6UiLve8sFaSXdJlPxIrACsbszFvwJOsVdA3PHD3YW3smLTwj4VrrlNBvkPwvDg==","signature_status":"signed_v1","signed_at":"2026-06-03T01:05:04.485832Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.12926","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dccdec3c98598ec490971f8ac1b9d2cbd0278c2bdb83335a5f3eee15f9f611df","sha256:8c8edbe334d66d3f547be4e2e5d5aeade66d46b9d5132769e532b7e0ab58e83c"],"state_sha256":"290cb5ebf60785eecffd5cc21956c2aa39eaed00bfbbe046002888fdccd779f6"}