{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UIC4BIDOTGNWL73OLYUGYC6PY3","short_pith_number":"pith:UIC4BIDO","canonical_record":{"source":{"id":"1406.7788","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-30T16:00:50Z","cross_cats_sorted":[],"title_canon_sha256":"4cf7d9b598b8d16efd97ea2caaab3aa935be88ca318fc0686dd0ba80aca7f568","abstract_canon_sha256":"b7cf3197dbdad4ebc8622f3d6d76e326a4b705bd95e2e0ce2085f9a67e89fe7d"},"schema_version":"1.0"},"canonical_sha256":"a205c0a06e999b65ff6e5e286c0bcfc6dce02ed69bd864945be4acc61a9f4fea","source":{"kind":"arxiv","id":"1406.7788","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7788","created_at":"2026-05-18T02:48:44Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7788v1","created_at":"2026-05-18T02:48:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7788","created_at":"2026-05-18T02:48:44Z"},{"alias_kind":"pith_short_12","alias_value":"UIC4BIDOTGNW","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UIC4BIDOTGNWL73O","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UIC4BIDO","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UIC4BIDOTGNWL73OLYUGYC6PY3","target":"record","payload":{"canonical_record":{"source":{"id":"1406.7788","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-30T16:00:50Z","cross_cats_sorted":[],"title_canon_sha256":"4cf7d9b598b8d16efd97ea2caaab3aa935be88ca318fc0686dd0ba80aca7f568","abstract_canon_sha256":"b7cf3197dbdad4ebc8622f3d6d76e326a4b705bd95e2e0ce2085f9a67e89fe7d"},"schema_version":"1.0"},"canonical_sha256":"a205c0a06e999b65ff6e5e286c0bcfc6dce02ed69bd864945be4acc61a9f4fea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:44.184843Z","signature_b64":"ppcLIvwWJm0t1I2zLGcAZSeiUU6aoyVv+whlBdzNraRVGFSiLyLQU0JBR+chw5HR122UGntePTVLvllM4+shDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a205c0a06e999b65ff6e5e286c0bcfc6dce02ed69bd864945be4acc61a9f4fea","last_reissued_at":"2026-05-18T02:48:44.184278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:44.184278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.7788","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:48:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9fr+VCLi0g57filFu9y7W9PS2iK8u3HIYcRV/i2pMAaBs9TfxmFbIxYmQtUn3wkD6X4+OiETMRwcVzwtdl+HDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T13:38:44.738837Z"},"content_sha256":"3dc95ce9f12c727a95717a9be6ad63a871fa3c994a0954b230d2060d76200081","schema_version":"1.0","event_id":"sha256:3dc95ce9f12c727a95717a9be6ad63a871fa3c994a0954b230d2060d76200081"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UIC4BIDOTGNWL73OLYUGYC6PY3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tilings of Rectangular Regions by Rectangular Tiles: Counts Derived from Transfer Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Richard J. Mathar","submitted_at":"2014-06-30T16:00:50Z","abstract_excerpt":"Step by step completion of a left-to-right tiling of a rectangular floor with tiles of a single shape starts from one edge of the floor, considers the possible ways of inserting a tile at the leftmost uncovered square, passes through a sequence of rugged shapes of the front line between covered and uncovered regions of the floor, and finishes with a straight front line at the opposite edge. We count the tilings by mapping the front shapes to nodes in a digraph, then counting closed walks on that digraph with the transfer matrix method.\n  Generating functions are detailed for tiles of shape 1 x"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7788","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:48:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V0jW9vDPFfzZVt0uIcpLT0I7hKsDKr3dmQzeXKeYDX+Cm+AW9W01WP6TCvtViGAZWkvzyEYKfbPDRidRVzRcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T13:38:44.739172Z"},"content_sha256":"c41a015d910df7342d8bfcce53f88a61606b8b698d2ccce229f80dea4dc9c6bb","schema_version":"1.0","event_id":"sha256:c41a015d910df7342d8bfcce53f88a61606b8b698d2ccce229f80dea4dc9c6bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UIC4BIDOTGNWL73OLYUGYC6PY3/bundle.json","state_url":"https://pith.science/pith/UIC4BIDOTGNWL73OLYUGYC6PY3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UIC4BIDOTGNWL73OLYUGYC6PY3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T13:38:44Z","links":{"resolver":"https://pith.science/pith/UIC4BIDOTGNWL73OLYUGYC6PY3","bundle":"https://pith.science/pith/UIC4BIDOTGNWL73OLYUGYC6PY3/bundle.json","state":"https://pith.science/pith/UIC4BIDOTGNWL73OLYUGYC6PY3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UIC4BIDOTGNWL73OLYUGYC6PY3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UIC4BIDOTGNWL73OLYUGYC6PY3","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":"b7cf3197dbdad4ebc8622f3d6d76e326a4b705bd95e2e0ce2085f9a67e89fe7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-30T16:00:50Z","title_canon_sha256":"4cf7d9b598b8d16efd97ea2caaab3aa935be88ca318fc0686dd0ba80aca7f568"},"schema_version":"1.0","source":{"id":"1406.7788","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7788","created_at":"2026-05-18T02:48:44Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7788v1","created_at":"2026-05-18T02:48:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7788","created_at":"2026-05-18T02:48:44Z"},{"alias_kind":"pith_short_12","alias_value":"UIC4BIDOTGNW","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UIC4BIDOTGNWL73O","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UIC4BIDO","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:c41a015d910df7342d8bfcce53f88a61606b8b698d2ccce229f80dea4dc9c6bb","target":"graph","created_at":"2026-05-18T02:48:44Z","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":"Step by step completion of a left-to-right tiling of a rectangular floor with tiles of a single shape starts from one edge of the floor, considers the possible ways of inserting a tile at the leftmost uncovered square, passes through a sequence of rugged shapes of the front line between covered and uncovered regions of the floor, and finishes with a straight front line at the opposite edge. We count the tilings by mapping the front shapes to nodes in a digraph, then counting closed walks on that digraph with the transfer matrix method.\n  Generating functions are detailed for tiles of shape 1 x","authors_text":"Richard J. Mathar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-30T16:00:50Z","title":"Tilings of Rectangular Regions by Rectangular Tiles: Counts Derived from Transfer Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7788","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":"sha256:3dc95ce9f12c727a95717a9be6ad63a871fa3c994a0954b230d2060d76200081","target":"record","created_at":"2026-05-18T02:48:44Z","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":"b7cf3197dbdad4ebc8622f3d6d76e326a4b705bd95e2e0ce2085f9a67e89fe7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-30T16:00:50Z","title_canon_sha256":"4cf7d9b598b8d16efd97ea2caaab3aa935be88ca318fc0686dd0ba80aca7f568"},"schema_version":"1.0","source":{"id":"1406.7788","kind":"arxiv","version":1}},"canonical_sha256":"a205c0a06e999b65ff6e5e286c0bcfc6dce02ed69bd864945be4acc61a9f4fea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a205c0a06e999b65ff6e5e286c0bcfc6dce02ed69bd864945be4acc61a9f4fea","first_computed_at":"2026-05-18T02:48:44.184278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:44.184278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ppcLIvwWJm0t1I2zLGcAZSeiUU6aoyVv+whlBdzNraRVGFSiLyLQU0JBR+chw5HR122UGntePTVLvllM4+shDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:44.184843Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.7788","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3dc95ce9f12c727a95717a9be6ad63a871fa3c994a0954b230d2060d76200081","sha256:c41a015d910df7342d8bfcce53f88a61606b8b698d2ccce229f80dea4dc9c6bb"],"state_sha256":"94d2d6b25f6f6c8ab09e620edad581567a4357bd56a9cd14faca01caafff1357"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mrcpei9yZZwcxvH5r7QNOFEvMQhKJROKzVq5wR+nqIx0F+jcxCuF9yyOgWNQJA9YtLZ3mATzyNaKqECs93leBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T13:38:44.740967Z","bundle_sha256":"580c128894183dd4dd8cdb2b385a6b016346aeb7436b7ca1d21bb00574bde448"}}