{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:NBMYTEYEMEVM2J4ENRA37RUPKL","short_pith_number":"pith:NBMYTEYE","schema_version":"1.0","canonical_sha256":"6859899304612acd27846c41bfc68f52ea6c48202296dc58ab82326565489edb","source":{"kind":"arxiv","id":"cond-mat/0610605","version":2},"attestation_state":"computed","paper":{"title":"Exact perimeter generating function for a model of punctured staircase polygons","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"cond-mat.stat-mech","authors_text":"Andrew Rechnitzer, Iwan Jensen","submitted_at":"2006-10-23T01:06:04Z","abstract_excerpt":"We have derived the perimeter generating function of a model of punctured staircase polygons in which the internal staircase polygon is rotated by a 90degree angle with respect to the outer staircase polygon. In one approach we calculated a long series expansion for the problem and found that all the terms in the generating function can be reproduced from a linear Fuchsian differential equation of order 4. We then solved this ODE and found a closed form expression for the generating function. This is a highly unusual and most fortuitous result since ODEs of such high order very rarely permit a"},"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":"cond-mat/0610605","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-10-23T01:06:04Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"87f24502037282de5852b062f0d6ce70a2fc708936b170939f8601994d8c128f","abstract_canon_sha256":"64c0e2617bed4624a7d5f63484ff14748c4c4cea2c96b5b0226135dc69a9c7b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:40.583021Z","signature_b64":"35Qn8meEuNMTdhWoG2p8S0QaZJkbfW1S8Ka1HYPQKjn5+GLmqEdPhC4Wt+oUyT5flusSBsP3TodHRelD/S5lCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6859899304612acd27846c41bfc68f52ea6c48202296dc58ab82326565489edb","last_reissued_at":"2026-05-18T01:39:40.582481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:40.582481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact perimeter generating function for a model of punctured staircase polygons","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"cond-mat.stat-mech","authors_text":"Andrew Rechnitzer, Iwan Jensen","submitted_at":"2006-10-23T01:06:04Z","abstract_excerpt":"We have derived the perimeter generating function of a model of punctured staircase polygons in which the internal staircase polygon is rotated by a 90degree angle with respect to the outer staircase polygon. In one approach we calculated a long series expansion for the problem and found that all the terms in the generating function can be reproduced from a linear Fuchsian differential equation of order 4. We then solved this ODE and found a closed form expression for the generating function. This is a highly unusual and most fortuitous result since ODEs of such high order very rarely permit a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0610605","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":"cond-mat/0610605","created_at":"2026-05-18T01:39:40.582560+00:00"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0610605v2","created_at":"2026-05-18T01:39:40.582560+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0610605","created_at":"2026-05-18T01:39:40.582560+00:00"},{"alias_kind":"pith_short_12","alias_value":"NBMYTEYEMEVM","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"NBMYTEYEMEVM2J4E","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"NBMYTEYE","created_at":"2026-05-18T12:25:54.717736+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/NBMYTEYEMEVM2J4ENRA37RUPKL","json":"https://pith.science/pith/NBMYTEYEMEVM2J4ENRA37RUPKL.json","graph_json":"https://pith.science/api/pith-number/NBMYTEYEMEVM2J4ENRA37RUPKL/graph.json","events_json":"https://pith.science/api/pith-number/NBMYTEYEMEVM2J4ENRA37RUPKL/events.json","paper":"https://pith.science/paper/NBMYTEYE"},"agent_actions":{"view_html":"https://pith.science/pith/NBMYTEYEMEVM2J4ENRA37RUPKL","download_json":"https://pith.science/pith/NBMYTEYEMEVM2J4ENRA37RUPKL.json","view_paper":"https://pith.science/paper/NBMYTEYE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cond-mat/0610605&json=true","fetch_graph":"https://pith.science/api/pith-number/NBMYTEYEMEVM2J4ENRA37RUPKL/graph.json","fetch_events":"https://pith.science/api/pith-number/NBMYTEYEMEVM2J4ENRA37RUPKL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NBMYTEYEMEVM2J4ENRA37RUPKL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NBMYTEYEMEVM2J4ENRA37RUPKL/action/storage_attestation","attest_author":"https://pith.science/pith/NBMYTEYEMEVM2J4ENRA37RUPKL/action/author_attestation","sign_citation":"https://pith.science/pith/NBMYTEYEMEVM2J4ENRA37RUPKL/action/citation_signature","submit_replication":"https://pith.science/pith/NBMYTEYEMEVM2J4ENRA37RUPKL/action/replication_record"}},"created_at":"2026-05-18T01:39:40.582560+00:00","updated_at":"2026-05-18T01:39:40.582560+00:00"}