{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XZREVX7TBW456SBTXTX3XNW4ER","short_pith_number":"pith:XZREVX7T","schema_version":"1.0","canonical_sha256":"be624adff30db9df4833bcefbbb6dc24412e4d901d628f2555f611cf97c6d0d7","source":{"kind":"arxiv","id":"1510.04498","version":1},"attestation_state":"computed","paper":{"title":"Enumeration of lozenge tilings of a hexagon with a maximal staircase and a unit triangle removed","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ranjan Rohatgi","submitted_at":"2015-10-15T12:28:25Z","abstract_excerpt":"Proctor proved a formula for the number of lozenge tilings of a hexagon with side-lengths $a,b,c,a,b,c$ after removing a \"maximal staircase.\" Ciucu then presented a weighted version of Proctor's result. Here we present weighted and unweighted formulas for a similar region which has an additional unit triangle removed. We use Kuo's graphical condensation method to prove the results. By applying the factorization theorem of Ciucu, we obtain a formula for the number of lozenge tilings of a hexagon with three holes on consecutive edges."},"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":"1510.04498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-15T12:28:25Z","cross_cats_sorted":[],"title_canon_sha256":"b995ee1e2249126c13543ff3258f9255723bc2eabf66e9d7b95b597ed6da23c4","abstract_canon_sha256":"97fcf0f8fd51189305f34e8900a296873573fc651015627b78161ab62564c95d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:06.979440Z","signature_b64":"51MCuPEonig2XTEYyy2g3kuuNXwHqvLwXDndc41zYIwWZADmLvswDb4FUjcU3/RqkV0eeLU8g+RGsdX3we4lDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be624adff30db9df4833bcefbbb6dc24412e4d901d628f2555f611cf97c6d0d7","last_reissued_at":"2026-05-18T01:30:06.978757Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:06.978757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Enumeration of lozenge tilings of a hexagon with a maximal staircase and a unit triangle removed","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ranjan Rohatgi","submitted_at":"2015-10-15T12:28:25Z","abstract_excerpt":"Proctor proved a formula for the number of lozenge tilings of a hexagon with side-lengths $a,b,c,a,b,c$ after removing a \"maximal staircase.\" Ciucu then presented a weighted version of Proctor's result. Here we present weighted and unweighted formulas for a similar region which has an additional unit triangle removed. We use Kuo's graphical condensation method to prove the results. By applying the factorization theorem of Ciucu, we obtain a formula for the number of lozenge tilings of a hexagon with three holes on consecutive edges."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04498","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":"1510.04498","created_at":"2026-05-18T01:30:06.978851+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.04498v1","created_at":"2026-05-18T01:30:06.978851+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04498","created_at":"2026-05-18T01:30:06.978851+00:00"},{"alias_kind":"pith_short_12","alias_value":"XZREVX7TBW45","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XZREVX7TBW456SBT","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XZREVX7T","created_at":"2026-05-18T12:29:50.041715+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/XZREVX7TBW456SBTXTX3XNW4ER","json":"https://pith.science/pith/XZREVX7TBW456SBTXTX3XNW4ER.json","graph_json":"https://pith.science/api/pith-number/XZREVX7TBW456SBTXTX3XNW4ER/graph.json","events_json":"https://pith.science/api/pith-number/XZREVX7TBW456SBTXTX3XNW4ER/events.json","paper":"https://pith.science/paper/XZREVX7T"},"agent_actions":{"view_html":"https://pith.science/pith/XZREVX7TBW456SBTXTX3XNW4ER","download_json":"https://pith.science/pith/XZREVX7TBW456SBTXTX3XNW4ER.json","view_paper":"https://pith.science/paper/XZREVX7T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.04498&json=true","fetch_graph":"https://pith.science/api/pith-number/XZREVX7TBW456SBTXTX3XNW4ER/graph.json","fetch_events":"https://pith.science/api/pith-number/XZREVX7TBW456SBTXTX3XNW4ER/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XZREVX7TBW456SBTXTX3XNW4ER/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XZREVX7TBW456SBTXTX3XNW4ER/action/storage_attestation","attest_author":"https://pith.science/pith/XZREVX7TBW456SBTXTX3XNW4ER/action/author_attestation","sign_citation":"https://pith.science/pith/XZREVX7TBW456SBTXTX3XNW4ER/action/citation_signature","submit_replication":"https://pith.science/pith/XZREVX7TBW456SBTXTX3XNW4ER/action/replication_record"}},"created_at":"2026-05-18T01:30:06.978851+00:00","updated_at":"2026-05-18T01:30:06.978851+00:00"}