{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NJOIGVMEM5IU5D7ZYCVCUDTNXY","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":"8e90925e913b6c866677b6980f7d8ad84fe168f03a42b7170e3007dacfa3b253","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-25T19:33:23Z","title_canon_sha256":"ad572cb89f237da58cbfc1a942a5f48d37eb2ac4de207be35e0fad426ded6051"},"schema_version":"1.0","source":{"id":"1204.5734","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5734","created_at":"2026-05-18T03:45:55Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5734v2","created_at":"2026-05-18T03:45:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5734","created_at":"2026-05-18T03:45:55Z"},{"alias_kind":"pith_short_12","alias_value":"NJOIGVMEM5IU","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NJOIGVMEM5IU5D7Z","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NJOIGVME","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:2bf47394d0388bbc8020489d785594ba1b8a37dba22f79dc912c533418aae238","target":"graph","created_at":"2026-05-18T03:45:55Z","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 develop a recursive formula for counting the number of rectangulations of a square, i.e the number of combinatorially distinct tilings of a square by rectangles. Our formula specializes to give a formula counting generic rectangulations, as analyzed by Reading in [5]. Our computations agree with [5] as far as was calculated and extend to the non-generic case. An interesting feature of the number of rectangulations is that it appears to have an 8-fold periodicity modulo 2. We verify this periodicity for small values of n, but the general result remains elusive, perhaps hinting at some unseen","authors_text":"Jim Conant, Tim Michaels","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-25T19:33:23Z","title":"On the number of tilings of a square by rectangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5734","kind":"arxiv","version":2},"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":"sha256:575774068abe7047ed7383d6afb827bdaf3124f7a7f415856c989123dde8518a","target":"record","created_at":"2026-05-18T03:45:55Z","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":"8e90925e913b6c866677b6980f7d8ad84fe168f03a42b7170e3007dacfa3b253","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-25T19:33:23Z","title_canon_sha256":"ad572cb89f237da58cbfc1a942a5f48d37eb2ac4de207be35e0fad426ded6051"},"schema_version":"1.0","source":{"id":"1204.5734","kind":"arxiv","version":2}},"canonical_sha256":"6a5c83558467514e8ff9c0aa2a0e6dbe338338eb3b82ee9ccf6621dae8f85258","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a5c83558467514e8ff9c0aa2a0e6dbe338338eb3b82ee9ccf6621dae8f85258","first_computed_at":"2026-05-18T03:45:55.319265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:55.319265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iNRNO6Cqz+ScwNATxFJNP7Mn2vJo+WwWGVBPpdzjrWkuvqyu6j1+61ZMKvFWnWCNfHH5ZqWu/JcJF7YNJdukAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:55.319849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5734","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:575774068abe7047ed7383d6afb827bdaf3124f7a7f415856c989123dde8518a","sha256:2bf47394d0388bbc8020489d785594ba1b8a37dba22f79dc912c533418aae238"],"state_sha256":"9fb36a6ac658f704b5f5b7b6e187fd91a666fc861dc32be3a096fa5e4378d89a"}