{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:LLKCEFC2JQIMCPX3DTWSJFJ2NX","short_pith_number":"pith:LLKCEFC2","schema_version":"1.0","canonical_sha256":"5ad422145a4c10c13efb1ced24953a6dd8f37eccc462ce982dc47acccdd2c8a3","source":{"kind":"arxiv","id":"2405.09457","version":1},"attestation_state":"computed","paper":{"title":"Recurrence solution of monomer-polymer models on two-dimensional rectangular lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO"],"primary_cat":"cond-mat.stat-mech","authors_text":"Yong Kong","submitted_at":"2024-05-15T15:51:35Z","abstract_excerpt":"The problem of counting polymer coverings on the rectangular lattices is investigated. In this model, a linear rigid polymer covers $k$ adjacent lattice sites such that no two polymers occupy a common site. Those unoccupied lattice sites are considered as monomers. We prove that for a given number of polymers ($k$-mers), the number of arrangements for the polymers on two-dimensional rectangular lattices satisfies simple recurrence relations. These recurrence relations are quite general and apply for arbitrary polymer length ($k$) and the width of the lattices ($n$). The well-studied monomer-di"},"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":"2405.09457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2024-05-15T15:51:35Z","cross_cats_sorted":["cs.CC","math.CO"],"title_canon_sha256":"2180821eda1c7dac2d7a69e6d509dc7ea2281043264599de5860ee02e7f950c4","abstract_canon_sha256":"6e8e63b0ec14764d3a84de1dca52648bc69eb3fd0a258f47e0ace45a40b98eb3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:05:25.334033Z","signature_b64":"M7gn1jxB5xBazcRd4yNqPE/g+Y8UULvFD2lWTVY2Oe1lXreI6YAbRbiHYxjGCej/u6tgop7sJJxfbDqd+VmFCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ad422145a4c10c13efb1ced24953a6dd8f37eccc462ce982dc47acccdd2c8a3","last_reissued_at":"2026-05-20T00:05:25.333203Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:05:25.333203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recurrence solution of monomer-polymer models on two-dimensional rectangular lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO"],"primary_cat":"cond-mat.stat-mech","authors_text":"Yong Kong","submitted_at":"2024-05-15T15:51:35Z","abstract_excerpt":"The problem of counting polymer coverings on the rectangular lattices is investigated. In this model, a linear rigid polymer covers $k$ adjacent lattice sites such that no two polymers occupy a common site. Those unoccupied lattice sites are considered as monomers. We prove that for a given number of polymers ($k$-mers), the number of arrangements for the polymers on two-dimensional rectangular lattices satisfies simple recurrence relations. These recurrence relations are quite general and apply for arbitrary polymer length ($k$) and the width of the lattices ($n$). The well-studied monomer-di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.09457","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.09457/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2405.09457","created_at":"2026-05-20T00:05:25.333339+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.09457v1","created_at":"2026-05-20T00:05:25.333339+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.09457","created_at":"2026-05-20T00:05:25.333339+00:00"},{"alias_kind":"pith_short_12","alias_value":"LLKCEFC2JQIM","created_at":"2026-05-20T00:05:25.333339+00:00"},{"alias_kind":"pith_short_16","alias_value":"LLKCEFC2JQIMCPX3","created_at":"2026-05-20T00:05:25.333339+00:00"},{"alias_kind":"pith_short_8","alias_value":"LLKCEFC2","created_at":"2026-05-20T00:05:25.333339+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/LLKCEFC2JQIMCPX3DTWSJFJ2NX","json":"https://pith.science/pith/LLKCEFC2JQIMCPX3DTWSJFJ2NX.json","graph_json":"https://pith.science/api/pith-number/LLKCEFC2JQIMCPX3DTWSJFJ2NX/graph.json","events_json":"https://pith.science/api/pith-number/LLKCEFC2JQIMCPX3DTWSJFJ2NX/events.json","paper":"https://pith.science/paper/LLKCEFC2"},"agent_actions":{"view_html":"https://pith.science/pith/LLKCEFC2JQIMCPX3DTWSJFJ2NX","download_json":"https://pith.science/pith/LLKCEFC2JQIMCPX3DTWSJFJ2NX.json","view_paper":"https://pith.science/paper/LLKCEFC2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.09457&json=true","fetch_graph":"https://pith.science/api/pith-number/LLKCEFC2JQIMCPX3DTWSJFJ2NX/graph.json","fetch_events":"https://pith.science/api/pith-number/LLKCEFC2JQIMCPX3DTWSJFJ2NX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LLKCEFC2JQIMCPX3DTWSJFJ2NX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LLKCEFC2JQIMCPX3DTWSJFJ2NX/action/storage_attestation","attest_author":"https://pith.science/pith/LLKCEFC2JQIMCPX3DTWSJFJ2NX/action/author_attestation","sign_citation":"https://pith.science/pith/LLKCEFC2JQIMCPX3DTWSJFJ2NX/action/citation_signature","submit_replication":"https://pith.science/pith/LLKCEFC2JQIMCPX3DTWSJFJ2NX/action/replication_record"}},"created_at":"2026-05-20T00:05:25.333339+00:00","updated_at":"2026-05-20T00:05:25.333339+00:00"}