{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:B4I7MYQI5P2YW272H74JOFLSBH","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":"d88bd8b0754990de83a6a68c47e7ef69dd716181e171baf27439bddcb23e9a62","cross_cats_sorted":["cs.DS","math.CO","math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-01-31T19:17:52Z","title_canon_sha256":"a2f2dde893cae17622cd93cd9d8dfbee8dd77f3564d18bc4521bfb924bce4ce3"},"schema_version":"1.0","source":{"id":"2402.00133","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.00133","created_at":"2026-07-05T11:59:04Z"},{"alias_kind":"arxiv_version","alias_value":"2402.00133v5","created_at":"2026-07-05T11:59:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.00133","created_at":"2026-07-05T11:59:04Z"},{"alias_kind":"pith_short_12","alias_value":"B4I7MYQI5P2Y","created_at":"2026-07-05T11:59:04Z"},{"alias_kind":"pith_short_16","alias_value":"B4I7MYQI5P2YW272","created_at":"2026-07-05T11:59:04Z"},{"alias_kind":"pith_short_8","alias_value":"B4I7MYQI","created_at":"2026-07-05T11:59:04Z"}],"graph_snapshots":[{"event_id":"sha256:ac855fed41a7c023c8d12eedcb67319fdceef7f1317bf67c26a6aecc1eab4302","target":"graph","created_at":"2026-07-05T11:59:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2402.00133/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the constant-depth circuit complexity of the Isomorphism Problem, Minimum Generating Set Problem (MGS), and Sub(quasi)group Membership Problem (Membership) for groups and quasigroups (=Latin squares), given as input in terms of their multiplication (Cayley) tables. Despite decades of research on these problems, lower bounds for these problems even against depth-$2$ AC circuits remain unknown. Perhaps surprisingly, Chattopadhyay, Tor\\'an, and Wagner (FSTTCS 2010; ACM Trans. Comput. Theory, 2013) showed that Quasigroup Isomorphism could be solved by AC circuits of depth $O(\\log \\l","authors_text":"Armin Wei{\\ss}, Joshua A. Grochow, Michael Levet, Nathaniel A. Collins","cross_cats":["cs.DS","math.CO","math.GR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-01-31T19:17:52Z","title":"On the Constant-Depth Circuit Complexity of Generating Quasigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.00133","kind":"arxiv","version":5},"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:bddb249febfec40fee14e83e6b9f1a221bf2b6fbec4a43d19c763ba942013f0a","target":"record","created_at":"2026-07-05T11:59:04Z","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":"d88bd8b0754990de83a6a68c47e7ef69dd716181e171baf27439bddcb23e9a62","cross_cats_sorted":["cs.DS","math.CO","math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-01-31T19:17:52Z","title_canon_sha256":"a2f2dde893cae17622cd93cd9d8dfbee8dd77f3564d18bc4521bfb924bce4ce3"},"schema_version":"1.0","source":{"id":"2402.00133","kind":"arxiv","version":5}},"canonical_sha256":"0f11f66208ebf58b6bfa3ff897157209f4c90428d2eb7a1a2491e5cd1d2cc6b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f11f66208ebf58b6bfa3ff897157209f4c90428d2eb7a1a2491e5cd1d2cc6b4","first_computed_at":"2026-07-05T11:59:04.501811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:59:04.501811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qoo7BDtkM85Xfh+KM4OA/OUFqtbfqZs1AsBJhez6iQuYLU9JgZBGRGxiqpUyPdq+rfzbc0VX51vYajDI6+VeBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:59:04.502264Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.00133","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bddb249febfec40fee14e83e6b9f1a221bf2b6fbec4a43d19c763ba942013f0a","sha256:ac855fed41a7c023c8d12eedcb67319fdceef7f1317bf67c26a6aecc1eab4302"],"state_sha256":"7760d8577bd74dd86e00833a996b99192baa4bc1dc42a4500ea0769da2474438"}