{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:JKDN334JCK5TXUNIVAOG6A5WKX","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":"d6202a9f910229df05a277331a34a8fb9c9f851af60658b2fc07964b176a4ebe","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2006-07-21T13:41:39Z","title_canon_sha256":"cc290d20c071ae2af099d4c7270154de939a7a92e7fb44dd7f664963a97bf27d"},"schema_version":"1.0","source":{"id":"math/0607528","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0607528","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0607528v2","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607528","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"JKDN334JCK5T","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"JKDN334JCK5TXUNI","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"JKDN334J","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:3772aa1f1737585075a5ec241f0a84460e4316364be781984705ac9e7cc7e896","target":"graph","created_at":"2026-05-18T02:57:45Z","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":"Pride groups, or ``groups given by presentations in which each defining relator involves at most two types of generators'', include Coxeter groups, Artin groups, triangles of groups, and Vinberg's groups defined by periodic paired relations. We show that every non-spherical Pride group that is not a triangle of groups satisfies the Tits alternative.","authors_text":"Gerald Williams, Natalia Kopteva","cross_cats":[],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2006-07-21T13:41:39Z","title":"The Tits alternative for non-spherical Pride groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607528","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":"sha256:126dabe40eadfb82ab173f6a6ac41fcdcd9ef05df011089c0a705e938ff5dbdc","target":"record","created_at":"2026-05-18T02:57:45Z","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":"d6202a9f910229df05a277331a34a8fb9c9f851af60658b2fc07964b176a4ebe","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2006-07-21T13:41:39Z","title_canon_sha256":"cc290d20c071ae2af099d4c7270154de939a7a92e7fb44dd7f664963a97bf27d"},"schema_version":"1.0","source":{"id":"math/0607528","kind":"arxiv","version":2}},"canonical_sha256":"4a86ddef8912bb3bd1a8a81c6f03b655d849d7a4770d1031fb14b6c47bf90a72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a86ddef8912bb3bd1a8a81c6f03b655d849d7a4770d1031fb14b6c47bf90a72","first_computed_at":"2026-05-18T02:57:45.559232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:45.559232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PRiBzFFYQdI32MqlVOMQQ9eLHacxyCbrwURl85bX7d+NWq9bj3ecsSaF2x2zOU5MIqxdkvYgcPAy/sFffFQ2Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:45.559805Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0607528","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:126dabe40eadfb82ab173f6a6ac41fcdcd9ef05df011089c0a705e938ff5dbdc","sha256:3772aa1f1737585075a5ec241f0a84460e4316364be781984705ac9e7cc7e896"],"state_sha256":"234f5d65ce3e6a98bccff4ee37cf451c2eb84b139dbd1d752a925fa81c3371f8"}