{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YPONVKAALU37OFRRNYZRAEFUOM","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":"60f66843c1ffea113ad075b36cb9597c7079d83235f4b3f4d17777e908422682","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-08-26T10:01:49Z","title_canon_sha256":"bfa0fb65109da0e5b8002b4cccc3d9381f37df03a7033ed10beef8bb895f10dd"},"schema_version":"1.0","source":{"id":"1408.6063","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6063","created_at":"2026-05-18T01:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6063v3","created_at":"2026-05-18T01:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6063","created_at":"2026-05-18T01:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"YPONVKAALU37","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YPONVKAALU37OFRR","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YPONVKAA","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:76f761019e064a866edd59a06581d73fa8f1ee054d3f3e1c9d92e3a8af4e8e74","target":"graph","created_at":"2026-05-18T01:34:35Z","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":"A biclique of a graph $G$ is a maximal induced complete bipartite subgraph of $G$. The biclique graph of $G$ denoted by $KB(G)$, is the intersection graph of all the bicliques of $G$. The biclique graph can be thought as an operator between graphs. The iterated biclique graph of $G$ denoted by $KB^{k}(G)$, is the graph obtained by applying the biclique operator $k$ successive times to $G$. The associated problem is deciding whether an input graph converges, diverges or is periodic under the biclique operator when $k$ grows to infinity. All possible behaviors were characterized recently and an ","authors_text":"Andr\\'e Guedes, Leandro Montero, Marina Groshaus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-08-26T10:01:49Z","title":"Almost every graph is divergent under the biclique operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6063","kind":"arxiv","version":3},"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:eb6023113482f05998f86973485198870e0f8c7f5251f64614077e6bb5053586","target":"record","created_at":"2026-05-18T01:34:35Z","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":"60f66843c1ffea113ad075b36cb9597c7079d83235f4b3f4d17777e908422682","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-08-26T10:01:49Z","title_canon_sha256":"bfa0fb65109da0e5b8002b4cccc3d9381f37df03a7033ed10beef8bb895f10dd"},"schema_version":"1.0","source":{"id":"1408.6063","kind":"arxiv","version":3}},"canonical_sha256":"c3dcdaa8005d37f716316e331010b47302b429824f8f0750ce9412d5da20a21a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3dcdaa8005d37f716316e331010b47302b429824f8f0750ce9412d5da20a21a","first_computed_at":"2026-05-18T01:34:35.551076Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:35.551076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6End1a/vYUVCKtrf7s1Ua0R7kG0XV2pDo3wm7SgWJ62cuzVQU+3jHt1uhj5zhU95GiZw4jE+kwWQbuFgAP7BCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:35.551630Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6063","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb6023113482f05998f86973485198870e0f8c7f5251f64614077e6bb5053586","sha256:76f761019e064a866edd59a06581d73fa8f1ee054d3f3e1c9d92e3a8af4e8e74"],"state_sha256":"985cd1200d1f7f1fd7a2b4bf542757ebd8a34777ee64c5cff2d8417a2d6f7e62"}