{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:OVXEITZSZLOOWREZP6J6DVIPSY","short_pith_number":"pith:OVXEITZS","schema_version":"1.0","canonical_sha256":"756e444f32cadceb44997f93e1d50f9607a13251fb26d2b68c3beb78fe7a60d4","source":{"kind":"arxiv","id":"1309.2894","version":1},"attestation_state":"computed","paper":{"title":"Occupation Probabilities and Fluctuations in the Asymmetric Simple Inclusion Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Iddo Eliazar, Ori Hirschberg, Shlomi Reuveni, Uri Yechiali","submitted_at":"2013-09-11T17:15:41Z","abstract_excerpt":"The Asymmetric Simple Inclusion Process (ASIP), a lattice-gas model of unidirectional transport and aggregation, was recently proposed as an `inclusion' counterpart of the Asymmetric Simple Exclusion Process (ASEP). In this paper we present an exact closed-form expression for the probability that a given number of particles occupies a given set of consecutive lattice sites. Our results are expressed in terms of the entries of Catalan's trapezoids --- number arrays which generalize Catalan's numbers and Catalan's triangle. We further prove that the ASIP is asymptotically governed by: (i) an inv"},"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":"1309.2894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-11T17:15:41Z","cross_cats_sorted":[],"title_canon_sha256":"4800779513fe3d0e1d82c27dcdd2aadefdda674c88c82038ced418c5a42e650b","abstract_canon_sha256":"bec626d64fc735144522e88b4b6ef6df8a5bcfdf3a262e9a0dfeba84c346a755"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:47:43.156891Z","signature_b64":"D/N2zUc1a0jIbAi4SUUXxzmlWHQ184TtkdYkuMI7E4lztpHepmWYL6ga2gh0+YINOP4e2OfepjtKaMLO1AKnBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"756e444f32cadceb44997f93e1d50f9607a13251fb26d2b68c3beb78fe7a60d4","last_reissued_at":"2026-05-18T01:47:43.156394Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:47:43.156394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Occupation Probabilities and Fluctuations in the Asymmetric Simple Inclusion Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Iddo Eliazar, Ori Hirschberg, Shlomi Reuveni, Uri Yechiali","submitted_at":"2013-09-11T17:15:41Z","abstract_excerpt":"The Asymmetric Simple Inclusion Process (ASIP), a lattice-gas model of unidirectional transport and aggregation, was recently proposed as an `inclusion' counterpart of the Asymmetric Simple Exclusion Process (ASEP). In this paper we present an exact closed-form expression for the probability that a given number of particles occupies a given set of consecutive lattice sites. Our results are expressed in terms of the entries of Catalan's trapezoids --- number arrays which generalize Catalan's numbers and Catalan's triangle. We further prove that the ASIP is asymptotically governed by: (i) an inv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2894","kind":"arxiv","version":1},"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":"1309.2894","created_at":"2026-05-18T01:47:43.156475+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.2894v1","created_at":"2026-05-18T01:47:43.156475+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2894","created_at":"2026-05-18T01:47:43.156475+00:00"},{"alias_kind":"pith_short_12","alias_value":"OVXEITZSZLOO","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OVXEITZSZLOOWREZ","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OVXEITZS","created_at":"2026-05-18T12:27:54.935989+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/OVXEITZSZLOOWREZP6J6DVIPSY","json":"https://pith.science/pith/OVXEITZSZLOOWREZP6J6DVIPSY.json","graph_json":"https://pith.science/api/pith-number/OVXEITZSZLOOWREZP6J6DVIPSY/graph.json","events_json":"https://pith.science/api/pith-number/OVXEITZSZLOOWREZP6J6DVIPSY/events.json","paper":"https://pith.science/paper/OVXEITZS"},"agent_actions":{"view_html":"https://pith.science/pith/OVXEITZSZLOOWREZP6J6DVIPSY","download_json":"https://pith.science/pith/OVXEITZSZLOOWREZP6J6DVIPSY.json","view_paper":"https://pith.science/paper/OVXEITZS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.2894&json=true","fetch_graph":"https://pith.science/api/pith-number/OVXEITZSZLOOWREZP6J6DVIPSY/graph.json","fetch_events":"https://pith.science/api/pith-number/OVXEITZSZLOOWREZP6J6DVIPSY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OVXEITZSZLOOWREZP6J6DVIPSY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OVXEITZSZLOOWREZP6J6DVIPSY/action/storage_attestation","attest_author":"https://pith.science/pith/OVXEITZSZLOOWREZP6J6DVIPSY/action/author_attestation","sign_citation":"https://pith.science/pith/OVXEITZSZLOOWREZP6J6DVIPSY/action/citation_signature","submit_replication":"https://pith.science/pith/OVXEITZSZLOOWREZP6J6DVIPSY/action/replication_record"}},"created_at":"2026-05-18T01:47:43.156475+00:00","updated_at":"2026-05-18T01:47:43.156475+00:00"}