{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BAHQDLCS4H3ZDDO2L3HPODRSLU","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":"02ef51e5faac666bda1e212536b1e5247643518027fa96bb2b8d93ae4ccfca3c","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-07-14T16:53:23Z","title_canon_sha256":"13ba5b0feac9ff26520116434869faa4c7833d6330b446429699759520705da4"},"schema_version":"1.0","source":{"id":"1407.3723","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.3723","created_at":"2026-05-18T02:47:41Z"},{"alias_kind":"arxiv_version","alias_value":"1407.3723v1","created_at":"2026-05-18T02:47:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3723","created_at":"2026-05-18T02:47:41Z"},{"alias_kind":"pith_short_12","alias_value":"BAHQDLCS4H3Z","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BAHQDLCS4H3ZDDO2","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BAHQDLCS","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:0ee5acc2b78c1cebd661aab1b183ab83f4a2b7f9e10f5ac9dda0dbcaaad6481f","target":"graph","created_at":"2026-05-18T02:47:41Z","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 first show that the braid group over a graph topologically containing no $\\Theta$-shape subgraph has a presentation related only by commutators. Then using discrete Morse theory and triple Massey products, we prove that a graph topologically contains none of four prescribed graphs if and only if its 4-braid groups is a right-angled Artin group.","authors_text":"Hyo Won Park, Joon Hyun La, Ki Hyoung Ko","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-07-14T16:53:23Z","title":"Graph 4-braid groups and Massey products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3723","kind":"arxiv","version":1},"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":"sha256:1a3a2ff55fe9c787a56057f68704d5ed67fa91c6897ede5c53b7ed0232d9ddb1","target":"record","created_at":"2026-05-18T02:47:41Z","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":"02ef51e5faac666bda1e212536b1e5247643518027fa96bb2b8d93ae4ccfca3c","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-07-14T16:53:23Z","title_canon_sha256":"13ba5b0feac9ff26520116434869faa4c7833d6330b446429699759520705da4"},"schema_version":"1.0","source":{"id":"1407.3723","kind":"arxiv","version":1}},"canonical_sha256":"080f01ac52e1f7918dda5ecef70e325d14ab47f5de15b6d4d1335d651a352259","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"080f01ac52e1f7918dda5ecef70e325d14ab47f5de15b6d4d1335d651a352259","first_computed_at":"2026-05-18T02:47:41.834858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:41.834858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PO9T+dus4+3Afs59UqvP8M79QlD5QWGpQVOUPMbgTaoUL4jnoFXu8SwNihVVvGQSIcwpFLv22JH6jPUYTnrxBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:41.835585Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.3723","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a3a2ff55fe9c787a56057f68704d5ed67fa91c6897ede5c53b7ed0232d9ddb1","sha256:0ee5acc2b78c1cebd661aab1b183ab83f4a2b7f9e10f5ac9dda0dbcaaad6481f"],"state_sha256":"3aed6f9c522bcc7606e934c436b5947b49b52ca64621707bda800f3d927fe33c"}