{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WABL67PV4ZUVS3RH7QBFQIT3X2","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":"6485da9fa9c47fffbf452de4983fa0a4c164eca9b991b89abeeefaf087da1a7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-10-02T13:43:01Z","title_canon_sha256":"66775db07e4eacd4cc1539b88d7653403380f9ae443bcbf71f9a6f85d9bfcc5d"},"schema_version":"1.0","source":{"id":"2410.21278","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.21278","created_at":"2026-07-05T09:27:25Z"},{"alias_kind":"arxiv_version","alias_value":"2410.21278v1","created_at":"2026-07-05T09:27:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.21278","created_at":"2026-07-05T09:27:25Z"},{"alias_kind":"pith_short_12","alias_value":"WABL67PV4ZUV","created_at":"2026-07-05T09:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WABL67PV4ZUVS3RH","created_at":"2026-07-05T09:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WABL67PV","created_at":"2026-07-05T09:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:616f2978e0bf550b4049acb17b46fd0f922a490263e9544c61aa316624e854f6","target":"graph","created_at":"2026-07-05T09:27:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.21278/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recent advances in bipartite consensus on matrix-weighted networks, where agents are divided into two disjoint sets with those in the same set agreeing on a certain value and those in different sets converging to opposite values, have highlighted its potential applications across various fields. Traditional approaches often depend on the existence of a positive-negative spanning tree in matrix-weighted networks to achieve bipartite consensus, which greatly restricts the use of these approaches in engineering applications. This study relaxes that assumption by allowing weak connectivity within ","authors_text":"Chongzhi Wang, Dewei Li, Haibin Shao, Ying Tan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-10-02T13:43:01Z","title":"Sufficient Condition on Bipartite Consensus of Weakly Connected Matrix-weighted Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.21278","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:e1f00c2b3593eadb5d84b4a4cacce4d11a8a6a5dfe431f3c22d2f640b54f9aaa","target":"record","created_at":"2026-07-05T09:27:25Z","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":"6485da9fa9c47fffbf452de4983fa0a4c164eca9b991b89abeeefaf087da1a7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-10-02T13:43:01Z","title_canon_sha256":"66775db07e4eacd4cc1539b88d7653403380f9ae443bcbf71f9a6f85d9bfcc5d"},"schema_version":"1.0","source":{"id":"2410.21278","kind":"arxiv","version":1}},"canonical_sha256":"b002bf7df5e669596e27fc0258227bbea7df82824ebae71c404e8d0613f7cd4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b002bf7df5e669596e27fc0258227bbea7df82824ebae71c404e8d0613f7cd4d","first_computed_at":"2026-07-05T09:27:25.934782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:27:25.934782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k/yTdWvefCDyHvMuwXQgvGoBnCjnnMHNyYwkbz30i1S3HwqSPnWPhALU5abmbrY9m5rLCblY1Uf7e82IN1rLAw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:27:25.935214Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.21278","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1f00c2b3593eadb5d84b4a4cacce4d11a8a6a5dfe431f3c22d2f640b54f9aaa","sha256:616f2978e0bf550b4049acb17b46fd0f922a490263e9544c61aa316624e854f6"],"state_sha256":"93670e1fbf951e6c80581874872e574d3b97f865009aa5fa7f0a92e8e4915190"}