{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TRIFAZEYVNV33SX6BQ4JFGG2CK","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":"d26d66d84fbc1a7e675828a90b757b3cf10dbea98b38658c5ea8966bb77babf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2012-08-24T22:17:23Z","title_canon_sha256":"d75205fe298b26609d94bb7f0e64ec7f2eafcf79334d7e1ee77127c0c6e64c12"},"schema_version":"1.0","source":{"id":"1208.5075","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5075","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5075v4","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5075","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"TRIFAZEYVNV3","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TRIFAZEYVNV33SX6","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TRIFAZEY","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:f2ccf38ecbee377a0196052cd7b7318fb0b7ebd92e322c81f0d8a85f964c9864","target":"graph","created_at":"2026-05-18T02:58:32Z","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":"Consider a synchronous point-to-point network of n nodes connected by directed links, wherein each node has a binary input. This paper proves a tight necessary and sufficient condition on the underlying communication topology for achieving Byzantine consensus among these nodes in the presence of up to f Byzantine faults. We derive a necessary condition, and then we provide a constructive proof of sufficiency by presenting a Byzantine consensus algorithm for directed graphs that satisfy the necessary condition.\n  Prior work has developed analogous necessary and sufficient conditions for undirec","authors_text":"Lewis Tseng, Nitin Vaidya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2012-08-24T22:17:23Z","title":"Exact Byzantine Consensus in Directed Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5075","kind":"arxiv","version":4},"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":"sha256:166c9cd8602da725aca88b315b998d0979d406fe32a038fb48dcb6ba8d406b52","target":"record","created_at":"2026-05-18T02:58:32Z","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":"d26d66d84fbc1a7e675828a90b757b3cf10dbea98b38658c5ea8966bb77babf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2012-08-24T22:17:23Z","title_canon_sha256":"d75205fe298b26609d94bb7f0e64ec7f2eafcf79334d7e1ee77127c0c6e64c12"},"schema_version":"1.0","source":{"id":"1208.5075","kind":"arxiv","version":4}},"canonical_sha256":"9c50506498ab6bbdcafe0c389298da12bac21166d798ad3386af7aa357be985b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c50506498ab6bbdcafe0c389298da12bac21166d798ad3386af7aa357be985b","first_computed_at":"2026-05-18T02:58:32.800154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:32.800154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZgQreeNhlC65ZTt8K8tW2Wk97V/G9ehrMJZ2msUX1rN93fP+6PoSD2eJDB8JTFEbE9vqYu7VKOl12Mi6F1fJDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:32.800784Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.5075","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:166c9cd8602da725aca88b315b998d0979d406fe32a038fb48dcb6ba8d406b52","sha256:f2ccf38ecbee377a0196052cd7b7318fb0b7ebd92e322c81f0d8a85f964c9864"],"state_sha256":"c09439f942c492322c4ea1d1239f5c770baf6e74596aa15b2aa09c8182a2b644"}