{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:KZCOAODCLRNGPYSCCLAMACGD7T","short_pith_number":"pith:KZCOAODC","schema_version":"1.0","canonical_sha256":"5644e038625c5a67e24212c0c008c3fcff215d71a2794aa42432c717a8b56c3a","source":{"kind":"arxiv","id":"1009.2307","version":3},"attestation_state":"computed","paper":{"title":"Quasi-randomness of graph balanced cut properties","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Choongbum Lee, Hao Huang","submitted_at":"2010-09-13T06:56:59Z","abstract_excerpt":"Quasi-random graphs can be informally described as graphs whose edge distribution closely resembles that of a truly random graph of the same edge density. Recently, Shapira and Yuster proved the following result on quasi-randomness of graphs. Let $k \\ge 2$ be a fixed integer, $\\alpha_1,...,\\alpha_k$ be positive reals satisfying $\\sum_{i} \\alpha_i = 1$ and $(\\alpha_1,..., \\alpha_k) \\neq (1/k,...,1/k)$, and $G$ be a graph on $n$ vertices. If for every partition of the vertices of $G$ into sets $V_1,..., V_k$ of size $\\alpha_1 n,..., \\alpha_k n$, the number of complete graphs on $k$ vertices whic"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1009.2307","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2010-09-13T06:56:59Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"cbaece0432de0a0d4eebbe5a4f7033ef29ecf86e810e26e977fc5b56ccab8911","abstract_canon_sha256":"f65a2cb4a0f4b628e76beb5046459619319f814023cd46b8047e7970b052d430"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:29.633498Z","signature_b64":"JTnmcoEgTkAnLmNoy3w/uQTZBsiZNhqQMSdRmoTAn6a2cfh4hNNZkd0ebAh/4Fhn+0TodARLAK1BAvhpK6VCCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5644e038625c5a67e24212c0c008c3fcff215d71a2794aa42432c717a8b56c3a","last_reissued_at":"2026-05-18T04:22:29.632876Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:29.632876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasi-randomness of graph balanced cut properties","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Choongbum Lee, Hao Huang","submitted_at":"2010-09-13T06:56:59Z","abstract_excerpt":"Quasi-random graphs can be informally described as graphs whose edge distribution closely resembles that of a truly random graph of the same edge density. Recently, Shapira and Yuster proved the following result on quasi-randomness of graphs. Let $k \\ge 2$ be a fixed integer, $\\alpha_1,...,\\alpha_k$ be positive reals satisfying $\\sum_{i} \\alpha_i = 1$ and $(\\alpha_1,..., \\alpha_k) \\neq (1/k,...,1/k)$, and $G$ be a graph on $n$ vertices. If for every partition of the vertices of $G$ into sets $V_1,..., V_k$ of size $\\alpha_1 n,..., \\alpha_k n$, the number of complete graphs on $k$ vertices whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2307","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.2307","created_at":"2026-05-18T04:22:29.632971+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.2307v3","created_at":"2026-05-18T04:22:29.632971+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2307","created_at":"2026-05-18T04:22:29.632971+00:00"},{"alias_kind":"pith_short_12","alias_value":"KZCOAODCLRNG","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"KZCOAODCLRNGPYSC","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"KZCOAODC","created_at":"2026-05-18T12:26:09.077623+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KZCOAODCLRNGPYSCCLAMACGD7T","json":"https://pith.science/pith/KZCOAODCLRNGPYSCCLAMACGD7T.json","graph_json":"https://pith.science/api/pith-number/KZCOAODCLRNGPYSCCLAMACGD7T/graph.json","events_json":"https://pith.science/api/pith-number/KZCOAODCLRNGPYSCCLAMACGD7T/events.json","paper":"https://pith.science/paper/KZCOAODC"},"agent_actions":{"view_html":"https://pith.science/pith/KZCOAODCLRNGPYSCCLAMACGD7T","download_json":"https://pith.science/pith/KZCOAODCLRNGPYSCCLAMACGD7T.json","view_paper":"https://pith.science/paper/KZCOAODC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.2307&json=true","fetch_graph":"https://pith.science/api/pith-number/KZCOAODCLRNGPYSCCLAMACGD7T/graph.json","fetch_events":"https://pith.science/api/pith-number/KZCOAODCLRNGPYSCCLAMACGD7T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KZCOAODCLRNGPYSCCLAMACGD7T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KZCOAODCLRNGPYSCCLAMACGD7T/action/storage_attestation","attest_author":"https://pith.science/pith/KZCOAODCLRNGPYSCCLAMACGD7T/action/author_attestation","sign_citation":"https://pith.science/pith/KZCOAODCLRNGPYSCCLAMACGD7T/action/citation_signature","submit_replication":"https://pith.science/pith/KZCOAODCLRNGPYSCCLAMACGD7T/action/replication_record"}},"created_at":"2026-05-18T04:22:29.632971+00:00","updated_at":"2026-05-18T04:22:29.632971+00:00"}