{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PIX2DAED2TRZWID7EL4AJ2XBCB","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":"d16b1079e4e3ee82396c3adf6f26d2db76cb72241f438f17d984493fe0ea9189","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-06T17:57:10Z","title_canon_sha256":"b8c19c4f9a8d1ffd37c8f245396d636e8b37315c679f025fe4937ec66e1c85c1"},"schema_version":"1.0","source":{"id":"1708.01918","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01918","created_at":"2026-05-18T00:38:20Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01918v2","created_at":"2026-05-18T00:38:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01918","created_at":"2026-05-18T00:38:20Z"},{"alias_kind":"pith_short_12","alias_value":"PIX2DAED2TRZ","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PIX2DAED2TRZWID7","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PIX2DAED","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:c951264f12bcaf7bb23daf4963c5baecf20784d7b09ea4aa47372b893094b504","target":"graph","created_at":"2026-05-18T00:38:20Z","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 long-range asymptotic behavior for an out-of-equilibrium countable one-dimensional system of Brownian particles interacting through their rank-dependent drifts. Focusing on the semi-infinite case, where only the leftmost particle gets a constant drift to the right, we derive and solve the corresponding one- sided Stefan (free-boundary) equations. Via this solution we explicitly determine the limiting particle-density profile as well as the asymptotic trajectory of the leftmost particle. While doing so we further establish stochastic domination and convergence to equilibrium result","authors_text":"Amir Dembo, Andrey Sarantsev, Manuel Cabezas, Vladas Sidoravicius","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-06T17:57:10Z","title":"Brownian Particles with Rank-Dependent Drifts: Out-of-Equilibrium Behavior"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01918","kind":"arxiv","version":2},"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":"sha256:670dfceb01901e1082908d13350c886927f58aaa21e864b701ddd9556f584c88","target":"record","created_at":"2026-05-18T00:38:20Z","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":"d16b1079e4e3ee82396c3adf6f26d2db76cb72241f438f17d984493fe0ea9189","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-06T17:57:10Z","title_canon_sha256":"b8c19c4f9a8d1ffd37c8f245396d636e8b37315c679f025fe4937ec66e1c85c1"},"schema_version":"1.0","source":{"id":"1708.01918","kind":"arxiv","version":2}},"canonical_sha256":"7a2fa18083d4e39b207f22f804eae1104dd815a4e8d26bdd4db98edebd68fa92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a2fa18083d4e39b207f22f804eae1104dd815a4e8d26bdd4db98edebd68fa92","first_computed_at":"2026-05-18T00:38:20.301761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:20.301761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B7bwaQfvHUpstlZaqj2f2wHCwnKyYVPg7ErUJts4HQOcA47sd6M49Up4tygn1K6D/NyTS1E7zDm0X6nNON85Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:20.302470Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.01918","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:670dfceb01901e1082908d13350c886927f58aaa21e864b701ddd9556f584c88","sha256:c951264f12bcaf7bb23daf4963c5baecf20784d7b09ea4aa47372b893094b504"],"state_sha256":"3ce980ec2da4d842a9e4c34f24d65b759f0f80a9df1aa198da44434651fc8594"}