{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:J6ANS6RWJEWNJK63Q5RODQ6KSH","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":"95aabe18b79e15ce6091086111ca8107827e9253794fc92ffa5a16c407a6d447","cross_cats_sorted":["cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-10-02T03:52:05Z","title_canon_sha256":"06b3f8029f936b5eba4a5632457969f6f433684aa6b550f32c0b6576758461c7"},"schema_version":"1.0","source":{"id":"1810.01784","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.01784","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1810.01784v2","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01784","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"J6ANS6RWJEWN","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"J6ANS6RWJEWNJK63","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"J6ANS6RW","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:221b3d302b23e66bac47a558eac349ec96c5759dac15c98fc9887182d9500545","target":"graph","created_at":"2026-05-17T23:42:53Z","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":"Convergence guarantees of many resilient consensus algorithms are based on the graph theoretic properties of $r$- and $(r,s)$-robustness. These algorithms guarantee consensus of normally behaving agents in the presence of a bounded number of arbitrarily misbehaving agents if the values of the integers $r$ and $s$ are sufficiently high. However, determining the largest integer $r$ for which an arbitrary digraph is $r$-robust is highly nontrivial. This paper introduces a novel method for calculating this value using mixed integer linear programming. The method only requires knowledge of the grap","authors_text":"Dimitra Panagou, James Usevitch","cross_cats":["cs.MA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-10-02T03:52:05Z","title":"Determining r-Robustness of Digraphs Using Mixed Integer Linear Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01784","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":"sha256:37bab87aa1b3ebc919b2fa8af18db49c62b0bb7426ae6a536d60bd16590f5e31","target":"record","created_at":"2026-05-17T23:42:53Z","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":"95aabe18b79e15ce6091086111ca8107827e9253794fc92ffa5a16c407a6d447","cross_cats_sorted":["cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-10-02T03:52:05Z","title_canon_sha256":"06b3f8029f936b5eba4a5632457969f6f433684aa6b550f32c0b6576758461c7"},"schema_version":"1.0","source":{"id":"1810.01784","kind":"arxiv","version":2}},"canonical_sha256":"4f80d97a36492cd4abdb8762e1c3ca91c74b0eb6cdd8f777a5654c7e5952912b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f80d97a36492cd4abdb8762e1c3ca91c74b0eb6cdd8f777a5654c7e5952912b","first_computed_at":"2026-05-17T23:42:53.672036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:53.672036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ho00fvIHXRlHursQBnJg11l7lErE/su1Ti6COWWzkJ2U7gDlKBCzezBrhxFRhVyWqR8kV7Z+KlUPVXASj5+sAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:53.672653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.01784","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37bab87aa1b3ebc919b2fa8af18db49c62b0bb7426ae6a536d60bd16590f5e31","sha256:221b3d302b23e66bac47a558eac349ec96c5759dac15c98fc9887182d9500545"],"state_sha256":"7269e665d47c61d8450a9efa185a7d6d585bf2741f7f5c582fd736d7ad819ac3"}