{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LLKCEFC2JQIMCPX3DTWSJFJ2NX","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":"6e8e63b0ec14764d3a84de1dca52648bc69eb3fd0a258f47e0ace45a40b98eb3","cross_cats_sorted":["cs.CC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2024-05-15T15:51:35Z","title_canon_sha256":"2180821eda1c7dac2d7a69e6d509dc7ea2281043264599de5860ee02e7f950c4"},"schema_version":"1.0","source":{"id":"2405.09457","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.09457","created_at":"2026-05-20T00:05:25Z"},{"alias_kind":"arxiv_version","alias_value":"2405.09457v1","created_at":"2026-05-20T00:05:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.09457","created_at":"2026-05-20T00:05:25Z"},{"alias_kind":"pith_short_12","alias_value":"LLKCEFC2JQIM","created_at":"2026-05-20T00:05:25Z"},{"alias_kind":"pith_short_16","alias_value":"LLKCEFC2JQIMCPX3","created_at":"2026-05-20T00:05:25Z"},{"alias_kind":"pith_short_8","alias_value":"LLKCEFC2","created_at":"2026-05-20T00:05:25Z"}],"graph_snapshots":[{"event_id":"sha256:b0fd4c65f6d5334d09f9c0969ee001ae11d678bea959587e34562056c5fc0480","target":"graph","created_at":"2026-05-20T00:05:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2405.09457/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Yong Kong","cross_cats":["cs.CC","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2024-05-15T15:51:35Z","title":"Recurrence solution of monomer-polymer models on two-dimensional rectangular lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.09457","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:d2c647c1769ede7e2b03eea65c2dc01025d795ed9ccdbcd348554fc9cf189911","target":"record","created_at":"2026-05-20T00:05:25Z","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":"6e8e63b0ec14764d3a84de1dca52648bc69eb3fd0a258f47e0ace45a40b98eb3","cross_cats_sorted":["cs.CC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2024-05-15T15:51:35Z","title_canon_sha256":"2180821eda1c7dac2d7a69e6d509dc7ea2281043264599de5860ee02e7f950c4"},"schema_version":"1.0","source":{"id":"2405.09457","kind":"arxiv","version":1}},"canonical_sha256":"5ad422145a4c10c13efb1ced24953a6dd8f37eccc462ce982dc47acccdd2c8a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ad422145a4c10c13efb1ced24953a6dd8f37eccc462ce982dc47acccdd2c8a3","first_computed_at":"2026-05-20T00:05:25.333203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:05:25.333203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M7gn1jxB5xBazcRd4yNqPE/g+Y8UULvFD2lWTVY2Oe1lXreI6YAbRbiHYxjGCej/u6tgop7sJJxfbDqd+VmFCA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:05:25.334033Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.09457","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2c647c1769ede7e2b03eea65c2dc01025d795ed9ccdbcd348554fc9cf189911","sha256:b0fd4c65f6d5334d09f9c0969ee001ae11d678bea959587e34562056c5fc0480"],"state_sha256":"8c70f40911e01ac17fa05f2d3c5dc6338fa484f2e1c3e36c26df66c2b77d623f"}