{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RSUPVMXUFZGZ3LLFJYOE5E5LTW","short_pith_number":"pith:RSUPVMXU","canonical_record":{"source":{"id":"1311.6192","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-25T01:23:02Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"3dcad1c081441357bb21fcd9632d9be532707c217100318f368ee5ef67cdd190","abstract_canon_sha256":"f335b153fee1488b8ddab6d0e5c38aa2d0619b8feb937d144308919adfe0fa25"},"schema_version":"1.0"},"canonical_sha256":"8ca8fab2f42e4d9dad654e1c4e93ab9db4bb21a0258b78094dbaf6261189d688","source":{"kind":"arxiv","id":"1311.6192","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6192","created_at":"2026-05-18T03:03:46Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6192v2","created_at":"2026-05-18T03:03:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6192","created_at":"2026-05-18T03:03:46Z"},{"alias_kind":"pith_short_12","alias_value":"RSUPVMXUFZGZ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RSUPVMXUFZGZ3LLF","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RSUPVMXU","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RSUPVMXUFZGZ3LLFJYOE5E5LTW","target":"record","payload":{"canonical_record":{"source":{"id":"1311.6192","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-25T01:23:02Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"3dcad1c081441357bb21fcd9632d9be532707c217100318f368ee5ef67cdd190","abstract_canon_sha256":"f335b153fee1488b8ddab6d0e5c38aa2d0619b8feb937d144308919adfe0fa25"},"schema_version":"1.0"},"canonical_sha256":"8ca8fab2f42e4d9dad654e1c4e93ab9db4bb21a0258b78094dbaf6261189d688","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:46.752393Z","signature_b64":"jdHhpGHWZZfsk/JeOP7izjE0D7BsccXttXDdVS38998mAHh01PUnsiSqIzKenawsnqYmAQQia8FYC9ThvKBdBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ca8fab2f42e4d9dad654e1c4e93ab9db4bb21a0258b78094dbaf6261189d688","last_reissued_at":"2026-05-18T03:03:46.751645Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:46.751645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.6192","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":"2026-05-18T03:03:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wSCC0nGPiLr/TE5DQ8ARACPFp9hOV5q6dlxwFZd0T2odNMzQEJJTr4WPdHurmMoHiYKIDIpbpVJweeKooIfeAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:42:54.808303Z"},"content_sha256":"8b47785c97b22bf7612810d18b7f46e1b5e1cb894171e022ffa5a8c7c2d5af8c","schema_version":"1.0","event_id":"sha256:8b47785c97b22bf7612810d18b7f46e1b5e1cb894171e022ffa5a8c7c2d5af8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RSUPVMXUFZGZ3LLFJYOE5E5LTW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ordered Biclique Partitions and Communication Complexity Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.CC","authors_text":"Kazuyuki Amano, Manami Shigeta","submitted_at":"2013-11-25T01:23:02Z","abstract_excerpt":"An ordered biclique partition of the complete graph $K_n$ on $n$ vertices is a collection of bicliques (i.e., complete bipartite graphs) such that (i) every edge of $K_n$ is covered by at least one and at most two bicliques in the collection, and (ii) if an edge $e$ is covered by two bicliques then each endpoint of $e$ is in the first class in one of these bicliques and in the second class in other one. In this note, we give an explicit construction of such a collection of size $n^{1/2+o(1)}$, which improves the $O(n^{2/3})$ bound shown in the previous work [Disc. Appl. Math., 2014].\n  As the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6192","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":"2026-05-18T03:03:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ro5P+hGvcqjZSsB3Ikl4nTIBi268zA+LXy9IlXK64+yr6/Cz3LPu90PpkwnsgTV/mG4JA7NKHDM3nDbWO3j2DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:42:54.809054Z"},"content_sha256":"51cc875b134b23b14b22b8407bcae17f15a8acb20859cfc441af101399559488","schema_version":"1.0","event_id":"sha256:51cc875b134b23b14b22b8407bcae17f15a8acb20859cfc441af101399559488"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RSUPVMXUFZGZ3LLFJYOE5E5LTW/bundle.json","state_url":"https://pith.science/pith/RSUPVMXUFZGZ3LLFJYOE5E5LTW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RSUPVMXUFZGZ3LLFJYOE5E5LTW/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":"2026-05-30T14:42:54Z","links":{"resolver":"https://pith.science/pith/RSUPVMXUFZGZ3LLFJYOE5E5LTW","bundle":"https://pith.science/pith/RSUPVMXUFZGZ3LLFJYOE5E5LTW/bundle.json","state":"https://pith.science/pith/RSUPVMXUFZGZ3LLFJYOE5E5LTW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RSUPVMXUFZGZ3LLFJYOE5E5LTW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RSUPVMXUFZGZ3LLFJYOE5E5LTW","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":"f335b153fee1488b8ddab6d0e5c38aa2d0619b8feb937d144308919adfe0fa25","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-25T01:23:02Z","title_canon_sha256":"3dcad1c081441357bb21fcd9632d9be532707c217100318f368ee5ef67cdd190"},"schema_version":"1.0","source":{"id":"1311.6192","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6192","created_at":"2026-05-18T03:03:46Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6192v2","created_at":"2026-05-18T03:03:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6192","created_at":"2026-05-18T03:03:46Z"},{"alias_kind":"pith_short_12","alias_value":"RSUPVMXUFZGZ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RSUPVMXUFZGZ3LLF","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RSUPVMXU","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:51cc875b134b23b14b22b8407bcae17f15a8acb20859cfc441af101399559488","target":"graph","created_at":"2026-05-18T03:03:46Z","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":"An ordered biclique partition of the complete graph $K_n$ on $n$ vertices is a collection of bicliques (i.e., complete bipartite graphs) such that (i) every edge of $K_n$ is covered by at least one and at most two bicliques in the collection, and (ii) if an edge $e$ is covered by two bicliques then each endpoint of $e$ is in the first class in one of these bicliques and in the second class in other one. In this note, we give an explicit construction of such a collection of size $n^{1/2+o(1)}$, which improves the $O(n^{2/3})$ bound shown in the previous work [Disc. Appl. Math., 2014].\n  As the ","authors_text":"Kazuyuki Amano, Manami Shigeta","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-25T01:23:02Z","title":"Ordered Biclique Partitions and Communication Complexity Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6192","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":"sha256:8b47785c97b22bf7612810d18b7f46e1b5e1cb894171e022ffa5a8c7c2d5af8c","target":"record","created_at":"2026-05-18T03:03:46Z","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":"f335b153fee1488b8ddab6d0e5c38aa2d0619b8feb937d144308919adfe0fa25","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-25T01:23:02Z","title_canon_sha256":"3dcad1c081441357bb21fcd9632d9be532707c217100318f368ee5ef67cdd190"},"schema_version":"1.0","source":{"id":"1311.6192","kind":"arxiv","version":2}},"canonical_sha256":"8ca8fab2f42e4d9dad654e1c4e93ab9db4bb21a0258b78094dbaf6261189d688","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ca8fab2f42e4d9dad654e1c4e93ab9db4bb21a0258b78094dbaf6261189d688","first_computed_at":"2026-05-18T03:03:46.751645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:46.751645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jdHhpGHWZZfsk/JeOP7izjE0D7BsccXttXDdVS38998mAHh01PUnsiSqIzKenawsnqYmAQQia8FYC9ThvKBdBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:46.752393Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6192","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b47785c97b22bf7612810d18b7f46e1b5e1cb894171e022ffa5a8c7c2d5af8c","sha256:51cc875b134b23b14b22b8407bcae17f15a8acb20859cfc441af101399559488"],"state_sha256":"224c8dc2bbe8a773ff48c5a70ed537a788d5cb64ee931a8f8ae121a61cbbc633"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GJLim05HkheAOYmJcGGUIJoo3ANHtWDy2FL/UOlVwZYluyqrANkeHzLXw7toabWpvDZEu7HwcH/AIGTgfiMFCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T14:42:54.813097Z","bundle_sha256":"b35575806d3f89fe72a479f316c370cb4241983154afc9e40196f4788a3fe6ba"}}