{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MXUGTB3CE35NEOKBUQVNQORWHW","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":"f064d67e10bc1080bc67f6e592fdacb95a0a74883e7485ddab57ab613f02f578","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-25T01:09:10Z","title_canon_sha256":"ff1f7636cf5fd011d4b96207840e71a54d5536d5e88724c788029e83416d5373"},"schema_version":"1.0","source":{"id":"1210.6712","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6712","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6712v1","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6712","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"MXUGTB3CE35N","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MXUGTB3CE35NEOKB","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MXUGTB3C","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:e8472e9818d83d2536fcf786076086b8d9757eb8e48fd74048b03c4074163c47","target":"graph","created_at":"2026-05-18T03:42:23Z","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 investigation studies the decidability problem of plane edge coloring with three symbols. In the edge coloring (or Wang tiles) of a plane, unit squares with colored edges that have one of $p$ colors are arranged side by side such that the touching edges of the adjacent tiles have the same colors. Given a basic set $B$ of Wang tiles, the decision problem is to find an algorithm to determine whether or not $\\Sigma(B)\\neq\\emptyset$, where $\\Sigma(B)$ is the set of all global patterns on $\\mathbb{Z}^{2}$ that can be constructed from the Wang tiles in $B$.\n  When $p\\geq 5$, the problem is know","authors_text":"De-Jan Lai, Hung-Hsun Chen, Song-Sun Lin, Wen-Guei Hu","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-25T01:09:10Z","title":"Decidability of plane edge coloring with three colors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6712","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:cf9e8bd0fc4aa500eebd067066391fa30d5214eb811c956b4613a9dafc2b926c","target":"record","created_at":"2026-05-18T03:42:23Z","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":"f064d67e10bc1080bc67f6e592fdacb95a0a74883e7485ddab57ab613f02f578","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-25T01:09:10Z","title_canon_sha256":"ff1f7636cf5fd011d4b96207840e71a54d5536d5e88724c788029e83416d5373"},"schema_version":"1.0","source":{"id":"1210.6712","kind":"arxiv","version":1}},"canonical_sha256":"65e869876226fad23941a42ad83a363d9c32e9ce3998bf366503373aa9458502","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65e869876226fad23941a42ad83a363d9c32e9ce3998bf366503373aa9458502","first_computed_at":"2026-05-18T03:42:23.317783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:23.317783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3tykept9v6sw+kTbs5CoTMoKN/xW/6hxv0RKDI2Hxm0fPUpZGA57tWgOkVqDrvE0lz0k1iq9nre+5x15UZPICw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:23.318283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6712","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf9e8bd0fc4aa500eebd067066391fa30d5214eb811c956b4613a9dafc2b926c","sha256:e8472e9818d83d2536fcf786076086b8d9757eb8e48fd74048b03c4074163c47"],"state_sha256":"c8fec03c724b6ae6b50297a7641a3fd9dfb1da35143698ae315ef0aca2897813"}