{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PIX2DAED2TRZWID7EL4AJ2XBCB","short_pith_number":"pith:PIX2DAED","canonical_record":{"source":{"id":"1708.01918","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-06T17:57:10Z","cross_cats_sorted":[],"title_canon_sha256":"b8c19c4f9a8d1ffd37c8f245396d636e8b37315c679f025fe4937ec66e1c85c1","abstract_canon_sha256":"d16b1079e4e3ee82396c3adf6f26d2db76cb72241f438f17d984493fe0ea9189"},"schema_version":"1.0"},"canonical_sha256":"7a2fa18083d4e39b207f22f804eae1104dd815a4e8d26bdd4db98edebd68fa92","source":{"kind":"arxiv","id":"1708.01918","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PIX2DAED2TRZWID7EL4AJ2XBCB","target":"record","payload":{"canonical_record":{"source":{"id":"1708.01918","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-06T17:57:10Z","cross_cats_sorted":[],"title_canon_sha256":"b8c19c4f9a8d1ffd37c8f245396d636e8b37315c679f025fe4937ec66e1c85c1","abstract_canon_sha256":"d16b1079e4e3ee82396c3adf6f26d2db76cb72241f438f17d984493fe0ea9189"},"schema_version":"1.0"},"canonical_sha256":"7a2fa18083d4e39b207f22f804eae1104dd815a4e8d26bdd4db98edebd68fa92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:20.302470Z","signature_b64":"B7bwaQfvHUpstlZaqj2f2wHCwnKyYVPg7ErUJts4HQOcA47sd6M49Up4tygn1K6D/NyTS1E7zDm0X6nNON85Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a2fa18083d4e39b207f22f804eae1104dd815a4e8d26bdd4db98edebd68fa92","last_reissued_at":"2026-05-18T00:38:20.301761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:20.301761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.01918","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"maiPhpMgJwNnE3HmLM68D5+NFcg/JuObvimUUU8p10VVEDNLFs3CVzLa28PKzOrhvqX+ifcecZEHcwZlGlOPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:15:17.932246Z"},"content_sha256":"670dfceb01901e1082908d13350c886927f58aaa21e864b701ddd9556f584c88","schema_version":"1.0","event_id":"sha256:670dfceb01901e1082908d13350c886927f58aaa21e864b701ddd9556f584c88"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PIX2DAED2TRZWID7EL4AJ2XBCB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Brownian Particles with Rank-Dependent Drifts: Out-of-Equilibrium Behavior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amir Dembo, Andrey Sarantsev, Manuel Cabezas, Vladas Sidoravicius","submitted_at":"2017-08-06T17:57:10Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01918","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jgOpOC9UVwGwo/nhs+SwqCv6CHdlPA84fDXAum6i3SnaOmom13LOCJxTs8XOvAV6IGmdt4YfRCBcHIGp+0jNAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:15:17.932601Z"},"content_sha256":"c951264f12bcaf7bb23daf4963c5baecf20784d7b09ea4aa47372b893094b504","schema_version":"1.0","event_id":"sha256:c951264f12bcaf7bb23daf4963c5baecf20784d7b09ea4aa47372b893094b504"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PIX2DAED2TRZWID7EL4AJ2XBCB/bundle.json","state_url":"https://pith.science/pith/PIX2DAED2TRZWID7EL4AJ2XBCB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PIX2DAED2TRZWID7EL4AJ2XBCB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T06:15:17Z","links":{"resolver":"https://pith.science/pith/PIX2DAED2TRZWID7EL4AJ2XBCB","bundle":"https://pith.science/pith/PIX2DAED2TRZWID7EL4AJ2XBCB/bundle.json","state":"https://pith.science/pith/PIX2DAED2TRZWID7EL4AJ2XBCB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PIX2DAED2TRZWID7EL4AJ2XBCB/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FAkQGQ6F2sWPF4P8iSuNZpCHsB8K4LP49JX8hOyNXe1M/sYDpEFL/ZZcak5DTldZWB8uHqKoewD8uIf8aOuJCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:15:17.934531Z","bundle_sha256":"4d2c82eb177e8ceb38467b111fea829759f30dfa5705ac8e7a7c0d4f4fed5b22"}}