{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:U5HSCKLOLYQ5QWHS3L7ULWQUPB","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":"d00d55b12e11cea56a9e3cbaf17cd4368a8780b061bbd31e013defbf2e847351","cross_cats_sorted":["math.AT","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-20T17:50:38Z","title_canon_sha256":"7abcf5f0f4a24369fe7562df8dda9dbb91717c8a6b045ba18b59f22f74e0967e"},"schema_version":"1.0","source":{"id":"1009.3900","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3900","created_at":"2026-05-18T04:40:43Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3900v1","created_at":"2026-05-18T04:40:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3900","created_at":"2026-05-18T04:40:43Z"},{"alias_kind":"pith_short_12","alias_value":"U5HSCKLOLYQ5","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"U5HSCKLOLYQ5QWHS","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"U5HSCKLO","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:632ce1151f54f5bf9a760f7144b716ca5c75cb388a329c01d00fffff0f22311a","target":"graph","created_at":"2026-05-18T04:40:43Z","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":"For each finite simple graph $G$, Aharoni, Berger and Ziv consider a recursively defined number $\\psi (G) \\in \\mathbb{Z}\\cup \\{+ \\infty \\}$ which gives a lower bound for the topological connectivity of the independence complex $I_G$. They conjecture that this bound is optimal for every graph. We use a result of recursion theory to give a short disproof of this claim.","authors_text":"Jonathan Ariel Barmak","cross_cats":["math.AT","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-20T17:50:38Z","title":"The word problem and the Aharoni-Berger-Ziv conjecture on the connectivity of independence complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3900","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":"sha256:8f1c1bc17b576db143a9678e52a754de57678e01e7346c4360de2da3f0648c8c","target":"record","created_at":"2026-05-18T04:40:43Z","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":"d00d55b12e11cea56a9e3cbaf17cd4368a8780b061bbd31e013defbf2e847351","cross_cats_sorted":["math.AT","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-20T17:50:38Z","title_canon_sha256":"7abcf5f0f4a24369fe7562df8dda9dbb91717c8a6b045ba18b59f22f74e0967e"},"schema_version":"1.0","source":{"id":"1009.3900","kind":"arxiv","version":1}},"canonical_sha256":"a74f21296e5e21d858f2daff45da14785848e4a7073be4d96ca58937de8c77b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a74f21296e5e21d858f2daff45da14785848e4a7073be4d96ca58937de8c77b1","first_computed_at":"2026-05-18T04:40:43.522789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:43.522789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uDj3mTBbR5W6GsAehQhC9ljabYVbS7IHQpqU1zf+EgE2BphBSeNYdMtBlcIZ8TxamIVQtth7pcfSUQCqFvFEDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:43.523498Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3900","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f1c1bc17b576db143a9678e52a754de57678e01e7346c4360de2da3f0648c8c","sha256:632ce1151f54f5bf9a760f7144b716ca5c75cb388a329c01d00fffff0f22311a"],"state_sha256":"6c475ef163ac3df8ade8f4bbb92837f022fc5345afa9795ef7f5e562d460827d"}