{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ES64IGONSBKRIBHJSEJOQCRAOU","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":"887b96bdf23da96bd96f81cf917944f50cbec8897f279374eabcfbcb634d1b15","cross_cats_sorted":["cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-11-27T15:27:44Z","title_canon_sha256":"7c9abe1989910517b9531ce4b2a2657b760fb38ebdd159cb20d73e358e3a35e1"},"schema_version":"1.0","source":{"id":"1211.6324","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6324","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6324v3","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6324","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"ES64IGONSBKR","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"ES64IGONSBKRIBHJ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"ES64IGON","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:a80017a3337096155c3cdb95ecf61198629ec786d455cff0da8fd2019416f2fc","target":"graph","created_at":"2026-05-18T03:14:40Z","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 consider the problem of achieving average consensus in the minimum number of linear iterations on a fixed, undirected graph. We are motivated by the task of deriving lower bounds for consensus protocols and by the so-called \"definitive consensus conjecture\" which states that for an undirected connected graph G with diameter D there exist D matrices whose nonzero-pattern complies with the edges in G and whose product equals the all-ones matrix. Our first result is a counterexample to the definitive consensus conjecture, which is the first improvement of the diameter lower bound for linear co","authors_text":"Alexander Olshevsky, Guillaume Vankeerberghen, Julien M. Hendrickx, Rapha\\\"el M. Jungers","cross_cats":["cs.MA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-11-27T15:27:44Z","title":"Graph diameter, eigenvalues, and minimum-time consensus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6324","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:c3b635a6e7691210dbc4f52310b4d95442137892b59b578a0c4eccafd583ba4f","target":"record","created_at":"2026-05-18T03:14:40Z","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":"887b96bdf23da96bd96f81cf917944f50cbec8897f279374eabcfbcb634d1b15","cross_cats_sorted":["cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-11-27T15:27:44Z","title_canon_sha256":"7c9abe1989910517b9531ce4b2a2657b760fb38ebdd159cb20d73e358e3a35e1"},"schema_version":"1.0","source":{"id":"1211.6324","kind":"arxiv","version":3}},"canonical_sha256":"24bdc419cd90551404e99112e80a207535c871c9ee1a7d7252ba8598e620fb27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24bdc419cd90551404e99112e80a207535c871c9ee1a7d7252ba8598e620fb27","first_computed_at":"2026-05-18T03:14:40.987196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:40.987196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Siej+6Y4mk32qcIgKpiZ3Qpmbrnx5A2afcEq0uS6XmY5pVf3Xs1y3JSaimcYN41FfZsTu0lhkdb2xHY3IDBNAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:40.987907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.6324","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3b635a6e7691210dbc4f52310b4d95442137892b59b578a0c4eccafd583ba4f","sha256:a80017a3337096155c3cdb95ecf61198629ec786d455cff0da8fd2019416f2fc"],"state_sha256":"dfd353756b0a9681f23183bc8b6391b864709face6780699e5b3affb12f886fc"}