{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:JDBK36CABJ4ICLUF6JVOXBNFRF","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":"804a755f71688fd782b5ed529e99d420027ea542824deef6248ade8dc6360be5","cross_cats_sorted":["cs.CC","cs.LO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-12-21T19:05:40Z","title_canon_sha256":"e26460a0af779cb4c76dade157d59f3eb5b245de6348c59a83402ced91aa5e54"},"schema_version":"1.0","source":{"id":"2112.11487","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.11487","created_at":"2026-07-05T12:05:55Z"},{"alias_kind":"arxiv_version","alias_value":"2112.11487v7","created_at":"2026-07-05T12:05:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.11487","created_at":"2026-07-05T12:05:55Z"},{"alias_kind":"pith_short_12","alias_value":"JDBK36CABJ4I","created_at":"2026-07-05T12:05:55Z"},{"alias_kind":"pith_short_16","alias_value":"JDBK36CABJ4ICLUF","created_at":"2026-07-05T12:05:55Z"},{"alias_kind":"pith_short_8","alias_value":"JDBK36CA","created_at":"2026-07-05T12:05:55Z"}],"graph_snapshots":[{"event_id":"sha256:9122cb0f457e833dfc37ef087ddca685e287590fbda43ef0138c86f73039ca86","target":"graph","created_at":"2026-07-05T12:05:55Z","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/2112.11487/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we show that the constant-dimensional Weisfeiler-Leman algorithm for groups (Brachter & Schweitzer, LICS 2020) can be fruitfully used to improve parallel complexity upper bounds on isomorphism testing for several families of groups. In particular, we show:\n  - Groups with an Abelian normal Hall subgroup whose complement is $O(1)$-generated are identified by constant-dimensional Weisfeiler-Leman using only a constant number of rounds. This places isomorphism testing for this family of groups into $\\textsf{L}$; the previous upper bound for isomorphism testing was $\\textsf{P}$ (Qia","authors_text":"Joshua A. Grochow, Michael Levet","cross_cats":["cs.CC","cs.LO","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-12-21T19:05:40Z","title":"On the Parallel Complexity of Group Isomorphism via Weisfeiler-Leman"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.11487","kind":"arxiv","version":7},"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":"sha256:2064fe161854cd46330aaf57f488338614ae2c3d3ed79fefc8530cf2015e0bf8","target":"record","created_at":"2026-07-05T12:05:55Z","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":"804a755f71688fd782b5ed529e99d420027ea542824deef6248ade8dc6360be5","cross_cats_sorted":["cs.CC","cs.LO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-12-21T19:05:40Z","title_canon_sha256":"e26460a0af779cb4c76dade157d59f3eb5b245de6348c59a83402ced91aa5e54"},"schema_version":"1.0","source":{"id":"2112.11487","kind":"arxiv","version":7}},"canonical_sha256":"48c2adf8400a78812e85f26aeb85a58955dae8e1d3ffcac969b9ba51bbc1ea82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48c2adf8400a78812e85f26aeb85a58955dae8e1d3ffcac969b9ba51bbc1ea82","first_computed_at":"2026-07-05T12:05:55.704139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:05:55.704139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xhWpS44X5yZqhiEylFfSRuzaK7haUHo/o+uflA+iRBrLwJYCne8XAMpAqLiVzxgo9aTAifTAg+JqUGg+zQzPDw==","signature_status":"signed_v1","signed_at":"2026-07-05T12:05:55.704833Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.11487","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2064fe161854cd46330aaf57f488338614ae2c3d3ed79fefc8530cf2015e0bf8","sha256:9122cb0f457e833dfc37ef087ddca685e287590fbda43ef0138c86f73039ca86"],"state_sha256":"23e45d710aa80d7099b81e39a2a0081aabfa7e4b9dd2e066ec0b7884a5093966"}