{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5L5AZ4FOX2GSEL5KN5RMQ6GFRO","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":"08b18f275d33ca073de09a041d636d0b8c87b15bda779c83a6f72fbf2867a680","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-10T22:39:13Z","title_canon_sha256":"e2583107589b1f1bbd659b082031c9e238db2857bbef5d21e3f405ec1d6231c9"},"schema_version":"1.0","source":{"id":"1008.1812","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1812","created_at":"2026-05-18T04:42:22Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1812v1","created_at":"2026-05-18T04:42:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1812","created_at":"2026-05-18T04:42:22Z"},{"alias_kind":"pith_short_12","alias_value":"5L5AZ4FOX2GS","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5L5AZ4FOX2GSEL5K","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5L5AZ4FO","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:a04ff412ae7ad90e664f988ce8d0d5ef9ecc63866bb5ad600b9fac710a1faf1e","target":"graph","created_at":"2026-05-18T04:42:22Z","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":"In this paper we will show how the results found in Cator and Pimentel 2009, about the Busemann functions in last-passage percolation, can be used to calculate the asymptotic distribution of the speed of a single second class particle starting from an arbitrary deterministic configuration which has a rarefaction fan, in either the totally asymetric exclusion process, or the Hammersley interacting particle process. The method will be to use the well known last-passage percolation description of the exclusion process and of the Hammersley process, and then the well known connection between secon","authors_text":"Eric Cator, Leandro P. R. Pimentel","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-10T22:39:13Z","title":"Busemann functions and the speed of a second class particle in the rarefaction fan"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1812","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":"sha256:3a2fe035f1170613273d01d5997208d105cf39eaaf12aa08e6047fb7b11f182b","target":"record","created_at":"2026-05-18T04:42:22Z","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":"08b18f275d33ca073de09a041d636d0b8c87b15bda779c83a6f72fbf2867a680","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-10T22:39:13Z","title_canon_sha256":"e2583107589b1f1bbd659b082031c9e238db2857bbef5d21e3f405ec1d6231c9"},"schema_version":"1.0","source":{"id":"1008.1812","kind":"arxiv","version":1}},"canonical_sha256":"eafa0cf0aebe8d222faa6f62c878c58b83f190d77897a733a20b67cc5ccbaa36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eafa0cf0aebe8d222faa6f62c878c58b83f190d77897a733a20b67cc5ccbaa36","first_computed_at":"2026-05-18T04:42:22.910236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:22.910236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dplwDuzga+3u/VihC+2UQ10LKZC1fvX98Ib8xW0ylXKNN2Aj/pJ6Uh5SZeM3OqbAGJhZmjiARG1qxGO/Ys3sBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:22.910768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1812","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a2fe035f1170613273d01d5997208d105cf39eaaf12aa08e6047fb7b11f182b","sha256:a04ff412ae7ad90e664f988ce8d0d5ef9ecc63866bb5ad600b9fac710a1faf1e"],"state_sha256":"bcc38579aafb0246140baf645d6e39971f54858dfb52b9410cda2fb18a05eaa0"}