{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1999:GH3AK4T7AETGFJ4YCKRYKB5LWV","short_pith_number":"pith:GH3AK4T7","schema_version":"1.0","canonical_sha256":"31f605727f012662a79812a38507abb56adf9f101573a3052d08b8d6b29a7ec9","source":{"kind":"arxiv","id":"math/9905012","version":1},"attestation_state":"computed","paper":{"title":"Some Polyomino Tilings of the Plane","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cristopher Moore","submitted_at":"1999-05-03T19:31:20Z","abstract_excerpt":"We calculate the generating functions for the number of tilings of rectangles of various widths by the right tromino, the $L$ tetromino, and the $T$ tetromino. This allows us to place lower bounds on the entropy of tilings of the plane by each of these. For the $T$ tetromino, we also derive a lower bound from the solution of the Ising model in two dimensions."},"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":"math/9905012","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"1999-05-03T19:31:20Z","cross_cats_sorted":[],"title_canon_sha256":"43718f2c9b3e0ed801ccbf9654942127800373ec6b9f72b5dd4cd635064e9443","abstract_canon_sha256":"013e5286e5ff3f7671d429571e55b9ef1de457b01e095e7e79f7d60e99f457c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:41:08.568879Z","signature_b64":"ufIE1fhrPTfIxDkDVROnHGAhdkzoWRaWQh1m6CKQEVidSvqhjyPOfDSrl4eFSIZNckZzSIJr54yuRUp9iiTrDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31f605727f012662a79812a38507abb56adf9f101573a3052d08b8d6b29a7ec9","last_reissued_at":"2026-07-04T14:41:08.568518Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:41:08.568518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Polyomino Tilings of the Plane","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cristopher Moore","submitted_at":"1999-05-03T19:31:20Z","abstract_excerpt":"We calculate the generating functions for the number of tilings of rectangles of various widths by the right tromino, the $L$ tetromino, and the $T$ tetromino. This allows us to place lower bounds on the entropy of tilings of the plane by each of these. For the $T$ tetromino, we also derive a lower bound from the solution of the Ising model in two dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9905012","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/math/9905012/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":"math/9905012","created_at":"2026-07-04T14:41:08.568580+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9905012v1","created_at":"2026-07-04T14:41:08.568580+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9905012","created_at":"2026-07-04T14:41:08.568580+00:00"},{"alias_kind":"pith_short_12","alias_value":"GH3AK4T7AETG","created_at":"2026-07-04T14:41:08.568580+00:00"},{"alias_kind":"pith_short_16","alias_value":"GH3AK4T7AETGFJ4Y","created_at":"2026-07-04T14:41:08.568580+00:00"},{"alias_kind":"pith_short_8","alias_value":"GH3AK4T7","created_at":"2026-07-04T14:41:08.568580+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2504.17734","citing_title":"Signed puzzles for Schubert coefficients","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GH3AK4T7AETGFJ4YCKRYKB5LWV","json":"https://pith.science/pith/GH3AK4T7AETGFJ4YCKRYKB5LWV.json","graph_json":"https://pith.science/api/pith-number/GH3AK4T7AETGFJ4YCKRYKB5LWV/graph.json","events_json":"https://pith.science/api/pith-number/GH3AK4T7AETGFJ4YCKRYKB5LWV/events.json","paper":"https://pith.science/paper/GH3AK4T7"},"agent_actions":{"view_html":"https://pith.science/pith/GH3AK4T7AETGFJ4YCKRYKB5LWV","download_json":"https://pith.science/pith/GH3AK4T7AETGFJ4YCKRYKB5LWV.json","view_paper":"https://pith.science/paper/GH3AK4T7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9905012&json=true","fetch_graph":"https://pith.science/api/pith-number/GH3AK4T7AETGFJ4YCKRYKB5LWV/graph.json","fetch_events":"https://pith.science/api/pith-number/GH3AK4T7AETGFJ4YCKRYKB5LWV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GH3AK4T7AETGFJ4YCKRYKB5LWV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GH3AK4T7AETGFJ4YCKRYKB5LWV/action/storage_attestation","attest_author":"https://pith.science/pith/GH3AK4T7AETGFJ4YCKRYKB5LWV/action/author_attestation","sign_citation":"https://pith.science/pith/GH3AK4T7AETGFJ4YCKRYKB5LWV/action/citation_signature","submit_replication":"https://pith.science/pith/GH3AK4T7AETGFJ4YCKRYKB5LWV/action/replication_record"}},"created_at":"2026-07-04T14:41:08.568580+00:00","updated_at":"2026-07-04T14:41:08.568580+00:00"}