{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FNRRHW3G2Z7HUYSA7CARHMP7GQ","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":"8ed03df42e73eb2c949a634bd4a54da5cc004aaea8fac740a4b961ae57985179","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-13T15:04:53Z","title_canon_sha256":"34902c3e63110e53a6b9b9a5a485788a20da92533ac1185a3ef6492070a8119d"},"schema_version":"1.0","source":{"id":"1702.03801","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03801","created_at":"2026-05-18T00:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03801v2","created_at":"2026-05-18T00:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03801","created_at":"2026-05-18T00:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"FNRRHW3G2Z7H","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FNRRHW3G2Z7HUYSA","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FNRRHW3G","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:8df231d3bf5b0f5e020e01ab115ad53c8a214f151678d79bddbf29f960f05c32","target":"graph","created_at":"2026-05-18T00:34:35Z","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":"Let $(X,\\mathcal{R})$ be a commutative association scheme and let $\\Gamma=(X,R\\cup R^\\top)$ be a connected undirected graph where $R\\in \\mathcal{R}$. Godsil (resp., Brouwer) conjectured that the edge connectivity (resp., vertex connectivity) of $\\Gamma$ is equal to its valency. In this paper, we prove that the deletion of the neighborhood of any vertex leaves behind at most one non-singleton component. Two vertices $a,b\\in X$ are called \"twins\" in $\\Gamma$ if they have identical neighborhoods: $\\Gamma(a)=\\Gamma(b)$. We characterize twins in polynomial association schemes and show that, in the ","authors_text":"Brian G. Kodalen, William J. Martin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-13T15:04:53Z","title":"On the connectivity of graphs in association schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03801","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:cfb0186a19aed95fc6aeac5b0fc27e8c1ddd1c5281d5c3dc8223e5d17b84ca9f","target":"record","created_at":"2026-05-18T00:34:35Z","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":"8ed03df42e73eb2c949a634bd4a54da5cc004aaea8fac740a4b961ae57985179","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-13T15:04:53Z","title_canon_sha256":"34902c3e63110e53a6b9b9a5a485788a20da92533ac1185a3ef6492070a8119d"},"schema_version":"1.0","source":{"id":"1702.03801","kind":"arxiv","version":2}},"canonical_sha256":"2b6313db66d67e7a6240f88113b1ff34341f7a61300847016df37d00e11fe17a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b6313db66d67e7a6240f88113b1ff34341f7a61300847016df37d00e11fe17a","first_computed_at":"2026-05-18T00:34:35.118930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:35.118930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TLpNGGOHv49FqLBk7B4BLtLrVqtELUEoct2T5+Dl3sLn/otKq3THfr19Xdz6VNCk1ZPiRft/48UWnBDttfpmBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:35.119416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03801","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfb0186a19aed95fc6aeac5b0fc27e8c1ddd1c5281d5c3dc8223e5d17b84ca9f","sha256:8df231d3bf5b0f5e020e01ab115ad53c8a214f151678d79bddbf29f960f05c32"],"state_sha256":"0f09ea96226fc3a6fbd1023f865b66ff8ca36f29bd3bdcd3417fa860c3ea9091"}