{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:45AH5O5EGRKX2M5V6GTNMFM3PL","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":"63c698b874a1513322681bbae8a76515806a9916b4006e6e621d635227e6a6fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-03-12T09:24:57Z","title_canon_sha256":"a09bf5df53cff55eb67546c277a16176477d31e56f434d1c05389ba549e9139f"},"schema_version":"1.0","source":{"id":"2603.11719","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.11719","created_at":"2026-05-20T00:00:36Z"},{"alias_kind":"arxiv_version","alias_value":"2603.11719v2","created_at":"2026-05-20T00:00:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.11719","created_at":"2026-05-20T00:00:36Z"},{"alias_kind":"pith_short_12","alias_value":"45AH5O5EGRKX","created_at":"2026-05-20T00:00:36Z"},{"alias_kind":"pith_short_16","alias_value":"45AH5O5EGRKX2M5V","created_at":"2026-05-20T00:00:36Z"},{"alias_kind":"pith_short_8","alias_value":"45AH5O5E","created_at":"2026-05-20T00:00:36Z"}],"graph_snapshots":[{"event_id":"sha256:087bb01105b1152e555f707e21227046aa3c96dd34e9afa0b44c6b1bc3cf6c51","target":"graph","created_at":"2026-05-20T00:00:36Z","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/2603.11719/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Bipartite networks, which encode interactions between two distinct types of entities, arise widely in applications and exhibit inherent asymmetry across node sets. Despite a growing literature on bipartite community detection, estimating community numbers $(K_1, K_2)$, a critical issue for bipartite network analysis, remains theoretically underdeveloped without any model selection consistency established, to our knowledge. Indeed, the inherent asymmetry and the two-dimensional parameter space with possibly drastically different $K_1$ and $K_2$ pose unique challenges that differ from unipartite","authors_text":"Bokai Yang, Yuanxing Chen, Yuhong Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-03-12T09:24:57Z","title":"Cross-Validation in Bipartite Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.11719","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:a3076c96d7b6d2a2afab292889d03a9c30b0e2f1a6acbf38e0b89a57aea1ce8e","target":"record","created_at":"2026-05-20T00:00:36Z","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":"63c698b874a1513322681bbae8a76515806a9916b4006e6e621d635227e6a6fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-03-12T09:24:57Z","title_canon_sha256":"a09bf5df53cff55eb67546c277a16176477d31e56f434d1c05389ba549e9139f"},"schema_version":"1.0","source":{"id":"2603.11719","kind":"arxiv","version":2}},"canonical_sha256":"e7407ebba434557d33b5f1a6d6159b7ac4de8c774f430ad1b9fb394c73df98c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7407ebba434557d33b5f1a6d6159b7ac4de8c774f430ad1b9fb394c73df98c3","first_computed_at":"2026-05-20T00:00:36.499954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:36.499954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"prmpPULnV6u/tEEj+MrH/eq3YdpX5HRHt3Y6RUfbezqgsWZhMarFWcER8v4OkolU3CcgwNuSx5Q9Utx7AVrXAQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:36.500542Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.11719","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3076c96d7b6d2a2afab292889d03a9c30b0e2f1a6acbf38e0b89a57aea1ce8e","sha256:087bb01105b1152e555f707e21227046aa3c96dd34e9afa0b44c6b1bc3cf6c51"],"state_sha256":"20ad084029280dfbbda51a0171ed2d53a4b80b249646952ae98e3cf0d9d1dc4b"}