{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GD5S3NV23S4ENYBEHKGSDSLMGM","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":"065bd1a67b7d76c1c1d8fe89be8057175ab74e206ff128b0a13017afce4e024e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-12T17:12:59Z","title_canon_sha256":"cd47d26db5001b8004020718ccd3b5efba3070782fa2dff3293ec8cd661f9765"},"schema_version":"1.0","source":{"id":"1110.2708","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2708","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2708v3","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2708","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"pith_short_12","alias_value":"GD5S3NV23S4E","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GD5S3NV23S4ENYBE","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GD5S3NV2","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:55501de90ddb0be33fe80ce4b1839415d1be655e40a1e401b9bdfd0a666ee40f","target":"graph","created_at":"2026-05-18T04:10:23Z","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":"We prove three results about the graph product $G=\\G(\\Gamma;G_v, v \\in V(\\Gamma))$ of groups $G_v$ over a graph $\\Gamma$. The first result generalises a result of Servatius, Droms and Servatius, proved by them for right-angled Artin groups; we prove a necessary and sufficient condition on a finite graph $\\Gamma$ for the kernel of the map from $G$ to the associated direct product to be free (one part of this result already follows from a result in S. Kim's Ph.D. thesis). The second result generalises a result of Hermiller and Sunic, again from right-angled Artin groups; we prove that for a grap","authors_text":"Derek F. Holt, Sarah Rees","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-12T17:12:59Z","title":"Generalising some results about right-angled Artin groups to graph products of groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2708","kind":"arxiv","version":3},"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":"sha256:810d4765640b9ae44d5f1f2573c78d54e9980a633434ed1f67f45b5cc599a1ee","target":"record","created_at":"2026-05-18T04:10:23Z","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":"065bd1a67b7d76c1c1d8fe89be8057175ab74e206ff128b0a13017afce4e024e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-12T17:12:59Z","title_canon_sha256":"cd47d26db5001b8004020718ccd3b5efba3070782fa2dff3293ec8cd661f9765"},"schema_version":"1.0","source":{"id":"1110.2708","kind":"arxiv","version":3}},"canonical_sha256":"30fb2db6badcb846e0243a8d21c96c331006427154d962961ebb927d95fa6bb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30fb2db6badcb846e0243a8d21c96c331006427154d962961ebb927d95fa6bb1","first_computed_at":"2026-05-18T04:10:23.166082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:23.166082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YlfYDWWb2nQGlDEdVB5yTUAKv6pz0W/2YDdHqCu6BgOMzLCuzJMoFCirhL2xpnBg64GVc0U9pby6PWJnky09AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:23.166834Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2708","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:810d4765640b9ae44d5f1f2573c78d54e9980a633434ed1f67f45b5cc599a1ee","sha256:55501de90ddb0be33fe80ce4b1839415d1be655e40a1e401b9bdfd0a666ee40f"],"state_sha256":"14b2c5c873d432b611cdb3cfffe7660fbbb26c68d2467bcb31a096df96848dbe"}