{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AEMQLDNZTQMN3HR4PUBSCVVTNW","short_pith_number":"pith:AEMQLDNZ","canonical_record":{"source":{"id":"1203.2543","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.DS","submitted_at":"2012-03-12T16:45:21Z","cross_cats_sorted":[],"title_canon_sha256":"9286f604110bd87f62b46450b435e437d15edc86db7a8a8c041326ce43716121","abstract_canon_sha256":"43b05ca47fc6cbaa2bf9a11829e148f0e631da7a98574c39e4e7a6afa9913406"},"schema_version":"1.0"},"canonical_sha256":"0119058db99c18dd9e3c7d032156b36d91557e1fea91cb7d68d666efaf4028b1","source":{"kind":"arxiv","id":"1203.2543","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2543","created_at":"2026-05-18T03:29:16Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2543v2","created_at":"2026-05-18T03:29:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2543","created_at":"2026-05-18T03:29:16Z"},{"alias_kind":"pith_short_12","alias_value":"AEMQLDNZTQMN","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AEMQLDNZTQMN3HR4","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AEMQLDNZ","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AEMQLDNZTQMN3HR4PUBSCVVTNW","target":"record","payload":{"canonical_record":{"source":{"id":"1203.2543","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.DS","submitted_at":"2012-03-12T16:45:21Z","cross_cats_sorted":[],"title_canon_sha256":"9286f604110bd87f62b46450b435e437d15edc86db7a8a8c041326ce43716121","abstract_canon_sha256":"43b05ca47fc6cbaa2bf9a11829e148f0e631da7a98574c39e4e7a6afa9913406"},"schema_version":"1.0"},"canonical_sha256":"0119058db99c18dd9e3c7d032156b36d91557e1fea91cb7d68d666efaf4028b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:16.385213Z","signature_b64":"1wsQOWsQ8w58UfGSczwtmns528bS+uli8T9GS7RJysoiTgg7QUUxcQFYd9PAelkR81g3fg3RbOxktzvgRYNnAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0119058db99c18dd9e3c7d032156b36d91557e1fea91cb7d68d666efaf4028b1","last_reissued_at":"2026-05-18T03:29:16.384559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:16.384559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.2543","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:29:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XOoj6hozS1TB0RP59Wn5yZnmYuRzbS0LwVcukvZFaYzShUrCsl6VBgvpRVGblsYG42v/sf+I4FWFNLhvKjoFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:15:41.965711Z"},"content_sha256":"9e8da54723b4414896e358a68e7d13c77a7a27ca87bdfe14ff1ed20491960939","schema_version":"1.0","event_id":"sha256:9e8da54723b4414896e358a68e7d13c77a7a27ca87bdfe14ff1ed20491960939"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AEMQLDNZTQMN3HR4PUBSCVVTNW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Biclique-colouring verification complexity and biclique-colouring power graphs","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Celina M. H. de Figueiredo, H\\'elio B. Mac\\^edo Filho, Raphael C. S. Machado, Simone Dantas","submitted_at":"2012-03-12T16:45:21Z","abstract_excerpt":"Biclique-colouring is a colouring of the vertices of a graph in such a way that no maximal complete bipartite subgraph with at least one edge is monochromatic. We show that it is coNP-complete to check whether a given function that associates a colour to each vertex is a biclique-colouring, a result that justifies the search for structured classes where the biclique-colouring problem could be efficiently solved. We consider biclique-colouring restricted to powers of paths and powers of cycles. We determine the biclique-chromatic number of powers of paths and powers of cycles. The biclique-chro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2543","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:29:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"etvhZ8/pudPsoox1u+YaEWZIMInKivrOsS0R6n3RPF2R9IZHQw/BGXzGBcu8nMIV0oeEf20y1iuqIl9YL150Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:15:41.966189Z"},"content_sha256":"2f94dc51e77a7ee627e9cabdaea9bb094125ac479fa8ff0b47c9ca7077109cb5","schema_version":"1.0","event_id":"sha256:2f94dc51e77a7ee627e9cabdaea9bb094125ac479fa8ff0b47c9ca7077109cb5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AEMQLDNZTQMN3HR4PUBSCVVTNW/bundle.json","state_url":"https://pith.science/pith/AEMQLDNZTQMN3HR4PUBSCVVTNW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AEMQLDNZTQMN3HR4PUBSCVVTNW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T06:15:41Z","links":{"resolver":"https://pith.science/pith/AEMQLDNZTQMN3HR4PUBSCVVTNW","bundle":"https://pith.science/pith/AEMQLDNZTQMN3HR4PUBSCVVTNW/bundle.json","state":"https://pith.science/pith/AEMQLDNZTQMN3HR4PUBSCVVTNW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AEMQLDNZTQMN3HR4PUBSCVVTNW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AEMQLDNZTQMN3HR4PUBSCVVTNW","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":"43b05ca47fc6cbaa2bf9a11829e148f0e631da7a98574c39e4e7a6afa9913406","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.DS","submitted_at":"2012-03-12T16:45:21Z","title_canon_sha256":"9286f604110bd87f62b46450b435e437d15edc86db7a8a8c041326ce43716121"},"schema_version":"1.0","source":{"id":"1203.2543","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2543","created_at":"2026-05-18T03:29:16Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2543v2","created_at":"2026-05-18T03:29:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2543","created_at":"2026-05-18T03:29:16Z"},{"alias_kind":"pith_short_12","alias_value":"AEMQLDNZTQMN","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AEMQLDNZTQMN3HR4","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AEMQLDNZ","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:2f94dc51e77a7ee627e9cabdaea9bb094125ac479fa8ff0b47c9ca7077109cb5","target":"graph","created_at":"2026-05-18T03:29:16Z","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":"Biclique-colouring is a colouring of the vertices of a graph in such a way that no maximal complete bipartite subgraph with at least one edge is monochromatic. We show that it is coNP-complete to check whether a given function that associates a colour to each vertex is a biclique-colouring, a result that justifies the search for structured classes where the biclique-colouring problem could be efficiently solved. We consider biclique-colouring restricted to powers of paths and powers of cycles. We determine the biclique-chromatic number of powers of paths and powers of cycles. The biclique-chro","authors_text":"Celina M. H. de Figueiredo, H\\'elio B. Mac\\^edo Filho, Raphael C. S. Machado, Simone Dantas","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.DS","submitted_at":"2012-03-12T16:45:21Z","title":"Biclique-colouring verification complexity and biclique-colouring power graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2543","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":"sha256:9e8da54723b4414896e358a68e7d13c77a7a27ca87bdfe14ff1ed20491960939","target":"record","created_at":"2026-05-18T03:29:16Z","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":"43b05ca47fc6cbaa2bf9a11829e148f0e631da7a98574c39e4e7a6afa9913406","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.DS","submitted_at":"2012-03-12T16:45:21Z","title_canon_sha256":"9286f604110bd87f62b46450b435e437d15edc86db7a8a8c041326ce43716121"},"schema_version":"1.0","source":{"id":"1203.2543","kind":"arxiv","version":2}},"canonical_sha256":"0119058db99c18dd9e3c7d032156b36d91557e1fea91cb7d68d666efaf4028b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0119058db99c18dd9e3c7d032156b36d91557e1fea91cb7d68d666efaf4028b1","first_computed_at":"2026-05-18T03:29:16.384559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:16.384559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1wsQOWsQ8w58UfGSczwtmns528bS+uli8T9GS7RJysoiTgg7QUUxcQFYd9PAelkR81g3fg3RbOxktzvgRYNnAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:16.385213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2543","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e8da54723b4414896e358a68e7d13c77a7a27ca87bdfe14ff1ed20491960939","sha256:2f94dc51e77a7ee627e9cabdaea9bb094125ac479fa8ff0b47c9ca7077109cb5"],"state_sha256":"11255b9dc6f838f3328c18e33a801a93f25143123ebdce132c3b2c1f14d50e56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Skfua6bcM/GSSGev93S0FqwnQ7/qoT2a99Yeworg2m4FeErSCqDf841MEaz6w/Lp/peWkUS5VktLLdE8X6nCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T06:15:41.968781Z","bundle_sha256":"025ae71afe0fcf47e744b7eadc29805b99abce210b24a1107b069cb7a970e8f9"}}