{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:75DAGXK63GDTOTCMBOFHBVML5N","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":"58a470350983f8ca782e4d42eeac8be0872687212312b1a545b1e37da8092da6","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2017-02-17T17:48:41Z","title_canon_sha256":"0e1299bdf88834411c41ef8848711f43881fc284220d0cc3d273dfa536d06407"},"schema_version":"1.0","source":{"id":"1702.05456","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05456","created_at":"2026-05-18T00:43:45Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05456v2","created_at":"2026-05-18T00:43:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05456","created_at":"2026-05-18T00:43:45Z"},{"alias_kind":"pith_short_12","alias_value":"75DAGXK63GDT","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"75DAGXK63GDTOTCM","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"75DAGXK6","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:a7b28b37ecbb4d6e8116563fa835cd170e2197c3dda37ffa0ccb512e0eac7bd2","target":"graph","created_at":"2026-05-18T00:43:45Z","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":"LCLs or locally checkable labelling problems (e.g. maximal independent set, maximal matching, and vertex colouring) in the LOCAL model of computation are very well-understood in cycles (toroidal 1-dimensional grids): every problem has a complexity of $O(1)$, $\\Theta(\\log^* n)$, or $\\Theta(n)$, and the design of optimal algorithms can be fully automated.\n  This work develops the complexity theory of LCL problems for toroidal 2-dimensional grids. The complexity classes are the same as in the 1-dimensional case: $O(1)$, $\\Theta(\\log^* n)$, and $\\Theta(n)$. However, given an LCL problem it is unde","authors_text":"Christopher Purcell, Janne H. Korhonen, Joel Rybicki, Juho Hirvonen, Jukka Suomela, Patric R. J. \\\"Osterg{\\aa}rd, Przemys{\\l}aw Uzna\\'nski, Sebastian Brandt, Tuomo Lempi\\\"ainen","cross_cats":["cs.CC","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2017-02-17T17:48:41Z","title":"LCL problems on grids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05456","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":"sha256:15f94c358bccb05d8e3e6e2d369e6824d1f0ad0a151d9ec29e352ac70a9ef1a8","target":"record","created_at":"2026-05-18T00:43:45Z","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":"58a470350983f8ca782e4d42eeac8be0872687212312b1a545b1e37da8092da6","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2017-02-17T17:48:41Z","title_canon_sha256":"0e1299bdf88834411c41ef8848711f43881fc284220d0cc3d273dfa536d06407"},"schema_version":"1.0","source":{"id":"1702.05456","kind":"arxiv","version":2}},"canonical_sha256":"ff46035d5ed987374c4c0b8a70d58beb5cac15e7247dace558a72c473e9701b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff46035d5ed987374c4c0b8a70d58beb5cac15e7247dace558a72c473e9701b0","first_computed_at":"2026-05-18T00:43:45.060817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:45.060817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DDJ/V7dI9knShbihyIdmvZWvzAUaQvJ+y/4sHtIj578F4rWicyPPtGVW3qaUNRvt+f6L6n2X6eXamK4h4YZYAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:45.061488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.05456","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15f94c358bccb05d8e3e6e2d369e6824d1f0ad0a151d9ec29e352ac70a9ef1a8","sha256:a7b28b37ecbb4d6e8116563fa835cd170e2197c3dda37ffa0ccb512e0eac7bd2"],"state_sha256":"a45fdac9201d48cd26713ce9275bd741bf1730d2211d0132417c463f830e8236"}