{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:W7R4CL6CF4PRXK6A57AFHPVXDY","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":"ef52e7069d964efd2e8948f8d5f98151ec96e4cedbeafd1a36e26c66ea7e5b19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-15T12:04:32Z","title_canon_sha256":"cef9755aea9fdaac9974fb9150c0ac70d3c8d52bb36e73be4f629f04162a9075"},"schema_version":"1.0","source":{"id":"1510.04486","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04486","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04486v1","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04486","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"pith_short_12","alias_value":"W7R4CL6CF4PR","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W7R4CL6CF4PRXK6A","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W7R4CL6C","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:09db6c0a50add9c9b208863fb7aff8a9000823caf43d4bbf0df029aff2e6e50c","target":"graph","created_at":"2026-05-18T01:30:07Z","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"},"paper":{"abstract_excerpt":"We generalize a special case of a theorem of Proctor on the enumeration of lozenge tilings of a hexagon with a maximal staircase removed, using Kuo's graphical condensation method. Additionally, we prove a formula for a weighted version of the given region. The result also extends work of Ciucu and Fischer. By applying the factorization theorem of Ciucu, we are also able to generalize a special case of MacMahon's boxed plane partition formula.","authors_text":"Ranjan Rohatgi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-15T12:04:32Z","title":"Enumeration of lozenge tilings of halved hexagons with a boundary defect"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04486","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:cea6dfce60226ed90bd0150d16b9344e1da8823d32642b7835e272205b1de912","target":"record","created_at":"2026-05-18T01:30:07Z","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":"ef52e7069d964efd2e8948f8d5f98151ec96e4cedbeafd1a36e26c66ea7e5b19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-15T12:04:32Z","title_canon_sha256":"cef9755aea9fdaac9974fb9150c0ac70d3c8d52bb36e73be4f629f04162a9075"},"schema_version":"1.0","source":{"id":"1510.04486","kind":"arxiv","version":1}},"canonical_sha256":"b7e3c12fc22f1f1babc0efc053beb71e0907ffe6604fdc5bba55f4f35b33bbef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7e3c12fc22f1f1babc0efc053beb71e0907ffe6604fdc5bba55f4f35b33bbef","first_computed_at":"2026-05-18T01:30:07.018409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:07.018409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zABh1xbJwfRvOmV7Cap9bmsXwnOedu3FqA/MLNxeMbM5aa4ErCUuLyBBdDIO2HZwEhKmzQtYyrBa/ZOgU/inCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:07.018929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04486","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cea6dfce60226ed90bd0150d16b9344e1da8823d32642b7835e272205b1de912","sha256:09db6c0a50add9c9b208863fb7aff8a9000823caf43d4bbf0df029aff2e6e50c"],"state_sha256":"6fcb752d82fa26c8dc4d9ab966e4285dcf3b9946d17870dca3e5270b202bd1f1"}