{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FV7L5DBZX4P5FM7V7AMZ4GQSWD","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":"2bd21f989e4165fc9a971f8ce59eb7b7995a7ec31b2db3d555887480da30c608","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-10-08T09:42:09Z","title_canon_sha256":"1eaf936b442245fac3d02ac4948875e5e434497387f6f55c966c929025595d67"},"schema_version":"1.0","source":{"id":"1110.1715","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1715","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1715v1","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1715","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"FV7L5DBZX4P5","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FV7L5DBZX4P5FM7V","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FV7L5DBZ","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:8a61e26a508416416279fa633efb459460c8fb2756ac44b8f7ffc255b09c17e8","target":"graph","created_at":"2026-05-18T03:42:44Z","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":"A universal tiler is a convex polyhedron whose every cross-section tiles the plane. In this paper, we introduce a certain slight-rotating operation for cross-sections of pentahedra. Based on a selected initial cross-section and by applying the slight-rotating operation suitably, we prove that a convex polyhedron is a universal tiler if and only if it is a tetrahedron or a triangular prism.","authors_text":"David G. L. Wang","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-10-08T09:42:09Z","title":"Determining All Universal Tilers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1715","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:a5db72fe4fdcf993e35bbc34e4c3d77ff788e7625057b34c0c1b39b43bab3e7f","target":"record","created_at":"2026-05-18T03:42:44Z","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":"2bd21f989e4165fc9a971f8ce59eb7b7995a7ec31b2db3d555887480da30c608","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-10-08T09:42:09Z","title_canon_sha256":"1eaf936b442245fac3d02ac4948875e5e434497387f6f55c966c929025595d67"},"schema_version":"1.0","source":{"id":"1110.1715","kind":"arxiv","version":1}},"canonical_sha256":"2d7ebe8c39bf1fd2b3f5f8199e1a12b0ffb288a3151d5515950487fbb3ec404f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d7ebe8c39bf1fd2b3f5f8199e1a12b0ffb288a3151d5515950487fbb3ec404f","first_computed_at":"2026-05-18T03:42:44.722055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:44.722055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QPorXFaX3kNt/OMpVJtBtcb6jpRCkGBoXXPYOtsdMeSTNbe/5mwz+0iRCKWUEGtrL9xE61Ol6qdrdZ1nw3FXAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:44.722773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1715","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5db72fe4fdcf993e35bbc34e4c3d77ff788e7625057b34c0c1b39b43bab3e7f","sha256:8a61e26a508416416279fa633efb459460c8fb2756ac44b8f7ffc255b09c17e8"],"state_sha256":"b9e018ab5c3887c728a8d94a3ace6e7c2d7484118c08d143a0ab3087c186a55e"}