{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IKECK537CSZENJ6G6UGUR2YIB7","short_pith_number":"pith:IKECK537","canonical_record":{"source":{"id":"1511.03043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-10T10:03:00Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"8c80b4e76917a57394dafd691d9f9d3f18d876a9d09db92b70d0e862c9ca9dab","abstract_canon_sha256":"1d17853b5339bb48154934243876b608c8286ee32e5d3972744a1b2f05a11b00"},"schema_version":"1.0"},"canonical_sha256":"428825777f14b246a7c6f50d48eb080fe6bc260a3a4fd67647052633544c6e9c","source":{"kind":"arxiv","id":"1511.03043","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03043","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03043v1","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03043","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"pith_short_12","alias_value":"IKECK537CSZE","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IKECK537CSZENJ6G","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IKECK537","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IKECK537CSZENJ6G6UGUR2YIB7","target":"record","payload":{"canonical_record":{"source":{"id":"1511.03043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-10T10:03:00Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"8c80b4e76917a57394dafd691d9f9d3f18d876a9d09db92b70d0e862c9ca9dab","abstract_canon_sha256":"1d17853b5339bb48154934243876b608c8286ee32e5d3972744a1b2f05a11b00"},"schema_version":"1.0"},"canonical_sha256":"428825777f14b246a7c6f50d48eb080fe6bc260a3a4fd67647052633544c6e9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:17.132809Z","signature_b64":"eUpRuQMko9L/BQp/ak4un9Ya7UV7csWjtOg7QnT9tXbyH4m+DPcVwZYqha0wun+OVmRtOhnAQkxFw7xeBhVjAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"428825777f14b246a7c6f50d48eb080fe6bc260a3a4fd67647052633544c6e9c","last_reissued_at":"2026-05-18T01:27:17.132187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:17.132187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.03043","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":"2026-05-18T01:27:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ckDCbKJ0kcqSmCuAItAX4IO76wzFVXhdrkGDf2EWDd4jF3vYhx6olN3+XC1Fc21KoyKbpvRo37In+9uVIfhfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:39:18.810406Z"},"content_sha256":"dcbf4a4300629e154d5baba1799f2bec9417d53c3d0f9b06bd42ca8d47c4fed4","schema_version":"1.0","event_id":"sha256:dcbf4a4300629e154d5baba1799f2bec9417d53c3d0f9b06bd42ca8d47c4fed4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IKECK537CSZENJ6G6UGUR2YIB7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tiling with Small Tiles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anne Kenyon, Martin Tassy","submitted_at":"2015-11-10T10:03:00Z","abstract_excerpt":"We look at sets of tiles that can tile any region of size greater than 1 on the square grid. This is not the typical tiling question, but relates closely to it and therefore can help solve other tiling problems -- we give an example of this. We also present a result to a more classic tiling question with dominoes and L-shape tiles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03043","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":"2026-05-18T01:27:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JvDacCIXhb0uNYEXcLEzLG4doGhrTjpeWt0wQXGwJHbCHgdoqD5T6KDKAB6ficznOjude1ifeTqh3IUOySbIDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:39:18.811119Z"},"content_sha256":"060fb4f1257c48a4ea57f72b79cba1d9a12f5e68e2072d0f84119a31ccc5eab3","schema_version":"1.0","event_id":"sha256:060fb4f1257c48a4ea57f72b79cba1d9a12f5e68e2072d0f84119a31ccc5eab3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IKECK537CSZENJ6G6UGUR2YIB7/bundle.json","state_url":"https://pith.science/pith/IKECK537CSZENJ6G6UGUR2YIB7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IKECK537CSZENJ6G6UGUR2YIB7/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":"2026-06-10T18:39:18Z","links":{"resolver":"https://pith.science/pith/IKECK537CSZENJ6G6UGUR2YIB7","bundle":"https://pith.science/pith/IKECK537CSZENJ6G6UGUR2YIB7/bundle.json","state":"https://pith.science/pith/IKECK537CSZENJ6G6UGUR2YIB7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IKECK537CSZENJ6G6UGUR2YIB7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IKECK537CSZENJ6G6UGUR2YIB7","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":"1d17853b5339bb48154934243876b608c8286ee32e5d3972744a1b2f05a11b00","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-10T10:03:00Z","title_canon_sha256":"8c80b4e76917a57394dafd691d9f9d3f18d876a9d09db92b70d0e862c9ca9dab"},"schema_version":"1.0","source":{"id":"1511.03043","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03043","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03043v1","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03043","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"pith_short_12","alias_value":"IKECK537CSZE","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IKECK537CSZENJ6G","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IKECK537","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:060fb4f1257c48a4ea57f72b79cba1d9a12f5e68e2072d0f84119a31ccc5eab3","target":"graph","created_at":"2026-05-18T01:27:17Z","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 look at sets of tiles that can tile any region of size greater than 1 on the square grid. This is not the typical tiling question, but relates closely to it and therefore can help solve other tiling problems -- we give an example of this. We also present a result to a more classic tiling question with dominoes and L-shape tiles.","authors_text":"Anne Kenyon, Martin Tassy","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-10T10:03:00Z","title":"Tiling with Small Tiles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03043","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:dcbf4a4300629e154d5baba1799f2bec9417d53c3d0f9b06bd42ca8d47c4fed4","target":"record","created_at":"2026-05-18T01:27:17Z","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":"1d17853b5339bb48154934243876b608c8286ee32e5d3972744a1b2f05a11b00","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-10T10:03:00Z","title_canon_sha256":"8c80b4e76917a57394dafd691d9f9d3f18d876a9d09db92b70d0e862c9ca9dab"},"schema_version":"1.0","source":{"id":"1511.03043","kind":"arxiv","version":1}},"canonical_sha256":"428825777f14b246a7c6f50d48eb080fe6bc260a3a4fd67647052633544c6e9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"428825777f14b246a7c6f50d48eb080fe6bc260a3a4fd67647052633544c6e9c","first_computed_at":"2026-05-18T01:27:17.132187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:17.132187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eUpRuQMko9L/BQp/ak4un9Ya7UV7csWjtOg7QnT9tXbyH4m+DPcVwZYqha0wun+OVmRtOhnAQkxFw7xeBhVjAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:17.132809Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.03043","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcbf4a4300629e154d5baba1799f2bec9417d53c3d0f9b06bd42ca8d47c4fed4","sha256:060fb4f1257c48a4ea57f72b79cba1d9a12f5e68e2072d0f84119a31ccc5eab3"],"state_sha256":"b5ea19313058e240c007076d080b0d3df0ea3dd036e6ec2ae8604c75c82cc339"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aDYSQPVVZ8oYSg+wLoO3/qLOI+TCJ3vcTcFb3p13p2Cj/Z702v30zkdYv8DOu+Xch/oeQqInhyC+mQ3/I2YGCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T18:39:18.814200Z","bundle_sha256":"86e231d6a2a57314146101488c12e0b2ad3160ad26d5769f4dd6f4552ecf6cc1"}}