{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2YPT5IU2OZKP7QSXDRZYKEJIPW","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":"17ac1d4f47fe696fcbf99b88c027753eff3c15b5c93ac45d7f040ebd73e3d332","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-08-11T19:28:17Z","title_canon_sha256":"74840fdc3eebb3f83d93dfa3968758f3cb80b5f7095c854a425ac5773e8e5d4e"},"schema_version":"1.0","source":{"id":"1608.03572","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03572","created_at":"2026-05-18T00:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03572v2","created_at":"2026-05-18T00:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03572","created_at":"2026-05-18T00:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"2YPT5IU2OZKP","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2YPT5IU2OZKP7QSX","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2YPT5IU2","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:07b9be78ad85b9c5b47c9cfccd58afc418503b3e714889bb8413443b265f1bee","target":"graph","created_at":"2026-05-18T00:42:02Z","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":"Suppose that $(W,S)$ is a Coxeter system with associated Artin group $A$ and with a simplicial complex $L$ as its nerve. We define the notion of a \"standard abelian subgroup\" in $A$. The poset of such subgroups in $A$ is parameterized by the poset of simplices in a certain subdivision $L_\\oslash$ of $L$. This complex of standard abelian subgroups is used to generalize an earlier result from the case of right-angled Artin groups to case of general Artin groups, by calculating, in many instances, the smallest dimension of a manifold model for $BA$. (This is the \"action dimension\" of $A$ denoted ","authors_text":"Jingyin Huang, Michael W. Davis","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-08-11T19:28:17Z","title":"Determining the action dimension of an Artin group by using its complex of abelian subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03572","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":"sha256:71ccef8d5d011424973da1e5d1fb793ef03247d074049901f73c3fe91924b3e0","target":"record","created_at":"2026-05-18T00:42:02Z","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":"17ac1d4f47fe696fcbf99b88c027753eff3c15b5c93ac45d7f040ebd73e3d332","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-08-11T19:28:17Z","title_canon_sha256":"74840fdc3eebb3f83d93dfa3968758f3cb80b5f7095c854a425ac5773e8e5d4e"},"schema_version":"1.0","source":{"id":"1608.03572","kind":"arxiv","version":2}},"canonical_sha256":"d61f3ea29a7654ffc2571c738511287daf744fc38c41f82ae36c6408802d6add","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d61f3ea29a7654ffc2571c738511287daf744fc38c41f82ae36c6408802d6add","first_computed_at":"2026-05-18T00:42:02.673292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:02.673292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LASmtyVfJJxUl9x4QmB/aB2lwdRI8a68BXSRVMVu4VEJGLSpLTPmHzXagfB+Ks+tTJXgfXtKYAF1q7cYcOUdBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:02.673928Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03572","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71ccef8d5d011424973da1e5d1fb793ef03247d074049901f73c3fe91924b3e0","sha256:07b9be78ad85b9c5b47c9cfccd58afc418503b3e714889bb8413443b265f1bee"],"state_sha256":"48da1029898c76109601431e1fc8e69c5e2da4ea6f391a1f19164895eeb21e6d"}