{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:5BQW4IJCUK3AZWY3G5Y52CXL3G","short_pith_number":"pith:5BQW4IJC","schema_version":"1.0","canonical_sha256":"e8616e2122a2b60cdb1b3771dd0aebd9908dfa360989b92cfdfc881f845daea7","source":{"kind":"arxiv","id":"1707.02539","version":2},"attestation_state":"computed","paper":{"title":"Some conditional probabilities in the TASEP with second class particles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Eunghyun Lee","submitted_at":"2017-07-09T08:09:25Z","abstract_excerpt":"In this paper we consider the TASEP with second class particles with the initial order is such that $k$ first class particles are located to the left of $N-k$ second class particles. Under this assumption of the initial state of order, we find the probability that the first class particles are at $x,x+1,\\cdots, x+k-1$ and the first class particles are still located to the left of all second class particles at later time $t$. Moreover, we obtain an explicit formula of this probability for the step initial condition. This probability generalizes a result for $k=1$ in Lee (arXiv:1705.10544)."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.02539","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-09T08:09:25Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"1aa7f440e9c82df233e843d2a35f46199309c59ecd2343392236fe4d92826e82","abstract_canon_sha256":"793007f42c4b8a9dfc995bf79074d775245b417b6ec660f1a7d5ad662e495640"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:56.714008Z","signature_b64":"13YKDCDGBofs13IvUFC/eMfFZWCc+YuFHg9SJWFfqa5NxznkmCn7Ncxpm+/ErP61TuaaVzp56GYiBPBKtDN5DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8616e2122a2b60cdb1b3771dd0aebd9908dfa360989b92cfdfc881f845daea7","last_reissued_at":"2026-05-18T00:25:56.713370Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:56.713370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some conditional probabilities in the TASEP with second class particles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Eunghyun Lee","submitted_at":"2017-07-09T08:09:25Z","abstract_excerpt":"In this paper we consider the TASEP with second class particles with the initial order is such that $k$ first class particles are located to the left of $N-k$ second class particles. Under this assumption of the initial state of order, we find the probability that the first class particles are at $x,x+1,\\cdots, x+k-1$ and the first class particles are still located to the left of all second class particles at later time $t$. Moreover, we obtain an explicit formula of this probability for the step initial condition. This probability generalizes a result for $k=1$ in Lee (arXiv:1705.10544)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02539","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.02539","created_at":"2026-05-18T00:25:56.713471+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.02539v2","created_at":"2026-05-18T00:25:56.713471+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02539","created_at":"2026-05-18T00:25:56.713471+00:00"},{"alias_kind":"pith_short_12","alias_value":"5BQW4IJCUK3A","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5BQW4IJCUK3AZWY3","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5BQW4IJC","created_at":"2026-05-18T12:31:00.734936+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5BQW4IJCUK3AZWY3G5Y52CXL3G","json":"https://pith.science/pith/5BQW4IJCUK3AZWY3G5Y52CXL3G.json","graph_json":"https://pith.science/api/pith-number/5BQW4IJCUK3AZWY3G5Y52CXL3G/graph.json","events_json":"https://pith.science/api/pith-number/5BQW4IJCUK3AZWY3G5Y52CXL3G/events.json","paper":"https://pith.science/paper/5BQW4IJC"},"agent_actions":{"view_html":"https://pith.science/pith/5BQW4IJCUK3AZWY3G5Y52CXL3G","download_json":"https://pith.science/pith/5BQW4IJCUK3AZWY3G5Y52CXL3G.json","view_paper":"https://pith.science/paper/5BQW4IJC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.02539&json=true","fetch_graph":"https://pith.science/api/pith-number/5BQW4IJCUK3AZWY3G5Y52CXL3G/graph.json","fetch_events":"https://pith.science/api/pith-number/5BQW4IJCUK3AZWY3G5Y52CXL3G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5BQW4IJCUK3AZWY3G5Y52CXL3G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5BQW4IJCUK3AZWY3G5Y52CXL3G/action/storage_attestation","attest_author":"https://pith.science/pith/5BQW4IJCUK3AZWY3G5Y52CXL3G/action/author_attestation","sign_citation":"https://pith.science/pith/5BQW4IJCUK3AZWY3G5Y52CXL3G/action/citation_signature","submit_replication":"https://pith.science/pith/5BQW4IJCUK3AZWY3G5Y52CXL3G/action/replication_record"}},"created_at":"2026-05-18T00:25:56.713471+00:00","updated_at":"2026-05-18T00:25:56.713471+00:00"}