{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MKPOIBQU3QCZMBMYYRLLKTIBDY","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":"b883198ac7bb97133668f8146fa948bcf20a84ad78898af115e94e551a4d3616","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-23T13:10:02Z","title_canon_sha256":"f8c2304edb6d505ef4c46591d9c80c1377fcb267d2b27245059306fa3f44c7cd"},"schema_version":"1.0","source":{"id":"1207.5381","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5381","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5381v3","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5381","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"pith_short_12","alias_value":"MKPOIBQU3QCZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MKPOIBQU3QCZMBMY","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MKPOIBQU","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:5250261ddba83e993a705dc16787ccd86df5539b120dd56be189b4c3519936c0","target":"graph","created_at":"2026-05-18T03:09:34Z","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":"This paper is concerned with lower bounds for the connectivity of graphs (one-dimensional skeleta) of triangulations of compact manifolds. We introduce a structural invariant b_M for simplicial d-manifolds M taking values in the range 0 <= b_M <= d-1. The main result is that b_M influences connectivity in the following way: The graph of a d-dimensional simplicial compact manifold M is (2d - b_M)-connected.\n  The parameter b_M has the property that b_M = 0 if the complex M is flag. Hence, our result interpolates between Barnette's theorem (1982) that all d-manifold graphs are (d+1)-connected an","authors_text":"Anders Bj\\\"orner, Kathrin Vorwerk","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-23T13:10:02Z","title":"On the connectivity of manifold graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5381","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:fae91081c2728f974ce7e21a5aba9aebc265cc41068c373d02bd840858229a33","target":"record","created_at":"2026-05-18T03:09:34Z","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":"b883198ac7bb97133668f8146fa948bcf20a84ad78898af115e94e551a4d3616","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-23T13:10:02Z","title_canon_sha256":"f8c2304edb6d505ef4c46591d9c80c1377fcb267d2b27245059306fa3f44c7cd"},"schema_version":"1.0","source":{"id":"1207.5381","kind":"arxiv","version":3}},"canonical_sha256":"629ee40614dc05960598c456b54d011e39425b668fe98c9dfe88965350d58ede","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"629ee40614dc05960598c456b54d011e39425b668fe98c9dfe88965350d58ede","first_computed_at":"2026-05-18T03:09:34.117307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:34.117307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"emb3hGDd8E5Qi2VXPjESRSGReZFLSAR0CgVNPPxX5zPxQGaNiAx0+NkbPYv4abSYnhtXJA6CH7Fsm5p3IUyrBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:34.118056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5381","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fae91081c2728f974ce7e21a5aba9aebc265cc41068c373d02bd840858229a33","sha256:5250261ddba83e993a705dc16787ccd86df5539b120dd56be189b4c3519936c0"],"state_sha256":"68aa440b01d63281e41f94bc0d12ef8791d69a890dd7a6669313ddeab128b424"}