{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:ZTFQ4XCH4GPCILUT6BSR6C4HBC","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":"ecaefe9754ee36974982fb5f2516018cc59a793fb0c2384afb9a5415d8b049fd","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2023-05-19T12:02:53Z","title_canon_sha256":"bd5a9b741a8dae1fba58ef41630b944c081a71f0c32a038a86a023627ce44b28"},"schema_version":"1.0","source":{"id":"2305.11622","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.11622","created_at":"2026-07-05T09:21:00Z"},{"alias_kind":"arxiv_version","alias_value":"2305.11622v2","created_at":"2026-07-05T09:21:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.11622","created_at":"2026-07-05T09:21:00Z"},{"alias_kind":"pith_short_12","alias_value":"ZTFQ4XCH4GPC","created_at":"2026-07-05T09:21:00Z"},{"alias_kind":"pith_short_16","alias_value":"ZTFQ4XCH4GPCILUT","created_at":"2026-07-05T09:21:00Z"},{"alias_kind":"pith_short_8","alias_value":"ZTFQ4XCH","created_at":"2026-07-05T09:21:00Z"}],"graph_snapshots":[{"event_id":"sha256:8f3e394ea72455537671c0705fcedccba79df1338d41c07e73dda280b2a34f1a","target":"graph","created_at":"2026-07-05T09:21:00Z","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/2305.11622/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Garside groups are combinatorial generalizations of braid groups which enjoy many nice algebraic, geometric, and algorithmic properties. In this article we propose a method for turning the direct product of a group $G$ by $\\mathbb{Z}$ into a Garside group, under simple assumptions on $G$. This method gives many new examples of Garside groups, including groups satisfying certain small cancellation condition (including surface groups) and groups with a systolic presentation.\n  Our method also works for a large class of Artin groups, leading to many new group theoretic, geometric and topological ","authors_text":"Jingyin Huang, Thomas Haettel","cross_cats":["math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2023-05-19T12:02:53Z","title":"New Garside structures and applications to Artin groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.11622","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":"sha256:2be4fa44bb6c31234a9da2b103b2cace70cb289e192dbd7d43395f6153c6c1db","target":"record","created_at":"2026-07-05T09:21:00Z","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":"ecaefe9754ee36974982fb5f2516018cc59a793fb0c2384afb9a5415d8b049fd","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2023-05-19T12:02:53Z","title_canon_sha256":"bd5a9b741a8dae1fba58ef41630b944c081a71f0c32a038a86a023627ce44b28"},"schema_version":"1.0","source":{"id":"2305.11622","kind":"arxiv","version":2}},"canonical_sha256":"cccb0e5c47e19e242e93f0651f0b8708ae308c8d8e73a0d303a8f5e3ef42cb8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cccb0e5c47e19e242e93f0651f0b8708ae308c8d8e73a0d303a8f5e3ef42cb8b","first_computed_at":"2026-07-05T09:21:00.551146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:21:00.551146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ic2SfmB7txz7TX8EBTBouluMQWVMhHtRZmQawLMeYI/CnDAjwPG4UsZMN1wgaQ5pKsp/279t6IY6RgPcht75AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:21:00.551695Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.11622","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2be4fa44bb6c31234a9da2b103b2cace70cb289e192dbd7d43395f6153c6c1db","sha256:8f3e394ea72455537671c0705fcedccba79df1338d41c07e73dda280b2a34f1a"],"state_sha256":"ef27952851848616f56ebf4c4a53ad1119a745418363923ca85a5860dcee43f2"}