{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:YM3BUPI2IQGODNPUYEOHFLFCLC","short_pith_number":"pith:YM3BUPI2","schema_version":"1.0","canonical_sha256":"c3361a3d1a440ce1b5f4c11c72aca258b399309810e4d1d05d2e8bd4b929497a","source":{"kind":"arxiv","id":"quant-ph/0608016","version":3},"attestation_state":"computed","paper":{"title":"On the quantum chromatic number of a graph","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"quant-ph","authors_text":"Andreas Winter, Ashley Montanaro, Michael W. Newman, Peter J. Cameron, Simone Severini","submitted_at":"2006-08-01T17:14:16Z","abstract_excerpt":"We investigate the notion of quantum chromatic number of a graph, which is the minimal number of colours necessary in a protocol in which two separated provers can convince an interrogator with certainty that they have a colouring of the graph.\n  After discussing this notion from first principles, we go on to establish relations with the clique number and orthogonal representations of the graph. We also prove several general facts about this graph parameter and find large separations between the clique number and the quantum chromatic number by looking at random graphs.\n  Finally, we show that"},"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":"quant-ph/0608016","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2006-08-01T17:14:16Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"d1ccdbe6974b47482a9495f869632a77eace2c7e3871236fce7d63df9e70a555","abstract_canon_sha256":"8e1beeb5aa7f9d8e85f41f7cef7fbfacf27fe80be477ecf3d191aa6be7bcfdb2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:45.806447Z","signature_b64":"GBgxq1DuRtfXjBk1tdL/EgLH52YjB271lluXxdn9qEHUgJPmV5XXB5KhKZhoN/qMg6xl0FlJQDUU3CcxSOdtAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3361a3d1a440ce1b5f4c11c72aca258b399309810e4d1d05d2e8bd4b929497a","last_reissued_at":"2026-05-18T04:08:45.805748Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:45.805748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the quantum chromatic number of a graph","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"quant-ph","authors_text":"Andreas Winter, Ashley Montanaro, Michael W. Newman, Peter J. Cameron, Simone Severini","submitted_at":"2006-08-01T17:14:16Z","abstract_excerpt":"We investigate the notion of quantum chromatic number of a graph, which is the minimal number of colours necessary in a protocol in which two separated provers can convince an interrogator with certainty that they have a colouring of the graph.\n  After discussing this notion from first principles, we go on to establish relations with the clique number and orthogonal representations of the graph. We also prove several general facts about this graph parameter and find large separations between the clique number and the quantum chromatic number by looking at random graphs.\n  Finally, we show that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0608016","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":"quant-ph/0608016","created_at":"2026-05-18T04:08:45.805864+00:00"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0608016v3","created_at":"2026-05-18T04:08:45.805864+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0608016","created_at":"2026-05-18T04:08:45.805864+00:00"},{"alias_kind":"pith_short_12","alias_value":"YM3BUPI2IQGO","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"YM3BUPI2IQGODNPU","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"YM3BUPI2","created_at":"2026-05-18T12:25:54.717736+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/YM3BUPI2IQGODNPUYEOHFLFCLC","json":"https://pith.science/pith/YM3BUPI2IQGODNPUYEOHFLFCLC.json","graph_json":"https://pith.science/api/pith-number/YM3BUPI2IQGODNPUYEOHFLFCLC/graph.json","events_json":"https://pith.science/api/pith-number/YM3BUPI2IQGODNPUYEOHFLFCLC/events.json","paper":"https://pith.science/paper/YM3BUPI2"},"agent_actions":{"view_html":"https://pith.science/pith/YM3BUPI2IQGODNPUYEOHFLFCLC","download_json":"https://pith.science/pith/YM3BUPI2IQGODNPUYEOHFLFCLC.json","view_paper":"https://pith.science/paper/YM3BUPI2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=quant-ph/0608016&json=true","fetch_graph":"https://pith.science/api/pith-number/YM3BUPI2IQGODNPUYEOHFLFCLC/graph.json","fetch_events":"https://pith.science/api/pith-number/YM3BUPI2IQGODNPUYEOHFLFCLC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YM3BUPI2IQGODNPUYEOHFLFCLC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YM3BUPI2IQGODNPUYEOHFLFCLC/action/storage_attestation","attest_author":"https://pith.science/pith/YM3BUPI2IQGODNPUYEOHFLFCLC/action/author_attestation","sign_citation":"https://pith.science/pith/YM3BUPI2IQGODNPUYEOHFLFCLC/action/citation_signature","submit_replication":"https://pith.science/pith/YM3BUPI2IQGODNPUYEOHFLFCLC/action/replication_record"}},"created_at":"2026-05-18T04:08:45.805864+00:00","updated_at":"2026-05-18T04:08:45.805864+00:00"}