{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:FBX3RFJ4FMDDASZ2LX52K2JJNR","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":"c225b67dbad23b7b5ae5540993804773215c3e7257d334753898d7480490116a","cross_cats_sorted":["math.AT","math.GT","math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2023-10-16T23:32:25Z","title_canon_sha256":"80b6f375d7b376c099dcbd0e5adf34c2aff22f81e64b890b78d890a926b9edcd"},"schema_version":"1.0","source":{"id":"2310.10883","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.10883","created_at":"2026-07-05T09:50:44Z"},{"alias_kind":"arxiv_version","alias_value":"2310.10883v2","created_at":"2026-07-05T09:50:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.10883","created_at":"2026-07-05T09:50:44Z"},{"alias_kind":"pith_short_12","alias_value":"FBX3RFJ4FMDD","created_at":"2026-07-05T09:50:44Z"},{"alias_kind":"pith_short_16","alias_value":"FBX3RFJ4FMDDASZ2","created_at":"2026-07-05T09:50:44Z"},{"alias_kind":"pith_short_8","alias_value":"FBX3RFJ4","created_at":"2026-07-05T09:50:44Z"}],"graph_snapshots":[{"event_id":"sha256:c6ad237fa55a4298fcc1387c08f997240c6b947381bf1ccdb57113f86ffd8537","target":"graph","created_at":"2026-07-05T09:50:44Z","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/2310.10883/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Shephard groups are common generalizations of Coxeter groups, Artin groups, and graph products of cyclic groups. Their definition is similar to that of a Coxeter group, but generators may have arbitrary order rather than strictly order 2. We extend a well known result that Coxeter groups are $\\mathrm{CAT}(0)$ to a class of Shephard groups that have \"enough\" finite parabolic subgroups. We also show that in this setting, if the associated Coxeter group is type (FC), then the Shephard group acts properly and cocompactly on a $\\mathrm{CAT}(0)$ cube complex. As part of our proof of the former resul","authors_text":"Katherine Goldman","cross_cats":["math.AT","math.GT","math.MG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2023-10-16T23:32:25Z","title":"CAT(0) and cubulated Shephard groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.10883","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":"sha256:2867c47a84b7bb05dcf88b6497ec6a081d455752d374313476f642a84557e99c","target":"record","created_at":"2026-07-05T09:50:44Z","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":"c225b67dbad23b7b5ae5540993804773215c3e7257d334753898d7480490116a","cross_cats_sorted":["math.AT","math.GT","math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2023-10-16T23:32:25Z","title_canon_sha256":"80b6f375d7b376c099dcbd0e5adf34c2aff22f81e64b890b78d890a926b9edcd"},"schema_version":"1.0","source":{"id":"2310.10883","kind":"arxiv","version":2}},"canonical_sha256":"286fb8953c2b06304b3a5dfba569296c73dbf0186efc15f0752b17e9ee42d7e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"286fb8953c2b06304b3a5dfba569296c73dbf0186efc15f0752b17e9ee42d7e5","first_computed_at":"2026-07-05T09:50:44.622043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:50:44.622043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZPFpYhJVRMItkAB08+sHzugHKGTC4Ok8XTrOiHOtlgy7CjeTqKkGKhCp3qGUzS/GrYJUAmfH+7tkXYN84TKZAw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:50:44.622679Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.10883","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2867c47a84b7bb05dcf88b6497ec6a081d455752d374313476f642a84557e99c","sha256:c6ad237fa55a4298fcc1387c08f997240c6b947381bf1ccdb57113f86ffd8537"],"state_sha256":"20db8b3f34fa14ae0bc979b15aefaf48f7d54d429ceec9a462f563704ddcdb4f"}