{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LNWSVBWNXNZXHGOM7PKQLOZSHD","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":"4504f43b70a85df5d23fa245bbfc118ee8ccfe472879abdec86361ffd4c61dc2","cross_cats_sorted":["cs.DM","cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-09-02T12:00:04Z","title_canon_sha256":"1906bc37f4925e2afe187e1a4e78aca4b6b33f65f0cc37058bec128121c91ab5"},"schema_version":"1.0","source":{"id":"1109.0418","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0418","created_at":"2026-05-18T04:14:15Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0418v1","created_at":"2026-05-18T04:14:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0418","created_at":"2026-05-18T04:14:15Z"},{"alias_kind":"pith_short_12","alias_value":"LNWSVBWNXNZX","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LNWSVBWNXNZXHGOM","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LNWSVBWN","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:a3d2d0ba2263e1bca5097bf2f0eb085e0a18f1e20cfd59a2ac46f524a469e76e","target":"graph","created_at":"2026-05-18T04:14:15Z","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":"In this paper we study the convergence of the max-consensus protocol. Tropical algebra is used to formulate the problem. Necessary and sufficient conditions for convergence of the max-consensus protocol over fixed as well as switching topology networks are given.","authors_text":"Ambedkar Dukkipati, Dabasish Ghose, Joel George Manathara","cross_cats":["cs.DM","cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-09-02T12:00:04Z","title":"Tropical Algebraic approach to Consensus over Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0418","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":"sha256:41a12a25d402120850a8330aeb688468be8873848ca980ccdaf9c2f2c92dedc7","target":"record","created_at":"2026-05-18T04:14:15Z","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":"4504f43b70a85df5d23fa245bbfc118ee8ccfe472879abdec86361ffd4c61dc2","cross_cats_sorted":["cs.DM","cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-09-02T12:00:04Z","title_canon_sha256":"1906bc37f4925e2afe187e1a4e78aca4b6b33f65f0cc37058bec128121c91ab5"},"schema_version":"1.0","source":{"id":"1109.0418","kind":"arxiv","version":1}},"canonical_sha256":"5b6d2a86cdbb737399ccfbd505bb3238dc51eba3f536288c74b8d444cf7906c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b6d2a86cdbb737399ccfbd505bb3238dc51eba3f536288c74b8d444cf7906c7","first_computed_at":"2026-05-18T04:14:15.734261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:15.734261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6FIY0OkAOcg9jfy3T/RyhBAJONtniAvZ211LhTfGs1sx6cHgQO1Iuo1dckJ/5s+nFQukbZKRIU2rRlpxFSA+Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:15.734794Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0418","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41a12a25d402120850a8330aeb688468be8873848ca980ccdaf9c2f2c92dedc7","sha256:a3d2d0ba2263e1bca5097bf2f0eb085e0a18f1e20cfd59a2ac46f524a469e76e"],"state_sha256":"8ae48535f20b5c155a0d64ae9741336cd812a50eacaf2ecede1fb589afacbfbf"}