{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DDJ7VSWIWDB6X5YOYF2EI6L2O4","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":"780385c001ac516c82962cd6fb0c0af127273316054815a67f4cd3cfa173d3c9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-02-06T11:13:34Z","title_canon_sha256":"2c1c36f882f7976384ec1ef3d877ef4ba92d0674c85d72658afad764e5612fb4"},"schema_version":"1.0","source":{"id":"1002.1356","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1356","created_at":"2026-05-18T01:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1356v2","created_at":"2026-05-18T01:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1356","created_at":"2026-05-18T01:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"DDJ7VSWIWDB6","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DDJ7VSWIWDB6X5YO","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DDJ7VSWI","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:150df9975474cff2257fd2f8fcf61311902f5a506d2e039dc25c3d45307f5427","target":"graph","created_at":"2026-05-18T01:12:23Z","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":"This paper is on tilings of polygons by rectangles. A celebrated physical interpretation of such tilings due to R.L. Brooks, C.A.B. Smith, A.H. Stone and W.T. Tutte uses direct-current circuits. The new approach of the paper is an application of alternating-current circuits.\n  The following results are obtained:\n  - a necessary condition for a rectangle to be tilable by rectangles of given shapes;\n  - a criterion for a rectangle to be tilable by rectangles similar to it but not all homothetic to it;\n  - a criterion for a generic polygon to be tilable by squares.\n  These results generalize the ","authors_text":"M. Prasolov, M. Skopenkov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-02-06T11:13:34Z","title":"Tiling by rectangles and alternating current"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1356","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":"sha256:13a06ee58b27f5cd76739544111d63fd271db69e248303a63301b042cebbc5e1","target":"record","created_at":"2026-05-18T01:12:23Z","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":"780385c001ac516c82962cd6fb0c0af127273316054815a67f4cd3cfa173d3c9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-02-06T11:13:34Z","title_canon_sha256":"2c1c36f882f7976384ec1ef3d877ef4ba92d0674c85d72658afad764e5612fb4"},"schema_version":"1.0","source":{"id":"1002.1356","kind":"arxiv","version":2}},"canonical_sha256":"18d3facac8b0c3ebf70ec17444797a772f163ad79ec1ea69f7b210b2342689e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18d3facac8b0c3ebf70ec17444797a772f163ad79ec1ea69f7b210b2342689e4","first_computed_at":"2026-05-18T01:12:23.126952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:23.126952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3QOd4ksR5C2agsZxJFaR2lRXDr+LLgS7g/lERcbGJJD2tMnfHdrT4w7VFK4MprGPcDxo9sa80LApIIojqjyCCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:23.127481Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.1356","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13a06ee58b27f5cd76739544111d63fd271db69e248303a63301b042cebbc5e1","sha256:150df9975474cff2257fd2f8fcf61311902f5a506d2e039dc25c3d45307f5427"],"state_sha256":"76e126cba31494602181e2b50cbb457837b5051ed27c6b6224f7824e914b176a"}