{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:B53UVULMNPFTMAGSWCFVBCTCOX","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":"f60fe9a49213fc3da327d00c7291fcf017d82454e871d6cc9b1cd2bb1ea7552d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-22T15:47:41Z","title_canon_sha256":"46625315743fc85c85df798bdeb40a69648be527a9fb3e5e4325f1697c524af5"},"schema_version":"1.0","source":{"id":"1304.5990","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5990","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5990v2","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5990","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"pith_short_12","alias_value":"B53UVULMNPFT","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"B53UVULMNPFTMAGS","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"B53UVULM","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:a709532e14b8a94c73ada17ab4482fa68f37ba8adc30f8d71c0eb3fcb5e701cd","target":"graph","created_at":"2026-05-18T01:06:41Z","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 show that braid groups with at most 6 strands are CAT(0) using the close connection between these groups, the associated non-crossing partition complexes and the embeddability of their diagonal links into spherical buildings of type A. Furthermore, we prove that the orthoscheme complex of any bounded graded modular complemented lattice is CAT(0), giving a partial answer to a conjecture of Brady and McCammond.","authors_text":"Dawid Kielak, Petra Schwer, Thomas Haettel","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-22T15:47:41Z","title":"The 6-strand braid group is CAT(0)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5990","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":"sha256:833068364d9efecd3cad80796e06c7283bf41bcb771516b8833f65737fcb84c6","target":"record","created_at":"2026-05-18T01:06:41Z","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":"f60fe9a49213fc3da327d00c7291fcf017d82454e871d6cc9b1cd2bb1ea7552d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-22T15:47:41Z","title_canon_sha256":"46625315743fc85c85df798bdeb40a69648be527a9fb3e5e4325f1697c524af5"},"schema_version":"1.0","source":{"id":"1304.5990","kind":"arxiv","version":2}},"canonical_sha256":"0f774ad16c6bcb3600d2b08b508a6275c2b2c6ce30fd55f8b348e849e8af1ae9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f774ad16c6bcb3600d2b08b508a6275c2b2c6ce30fd55f8b348e849e8af1ae9","first_computed_at":"2026-05-18T01:06:41.304769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:41.304769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8G9pAWatWl3iLyP3YFSqOyGbTrFTuA8A3uNuefwDIh/h6z8ivv0X/PuY21x/Da0v9chojp1SjLJ5szdKh+vMCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:41.305251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5990","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:833068364d9efecd3cad80796e06c7283bf41bcb771516b8833f65737fcb84c6","sha256:a709532e14b8a94c73ada17ab4482fa68f37ba8adc30f8d71c0eb3fcb5e701cd"],"state_sha256":"2b5e9a5cb6a3251c4e6809bb6a5819d19c9f41a8943cb4bff76145a8c1d7a056"}