{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:NG4GZKSYKUTZI6RHNFQY3DMYUL","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":"b84f6bf8b714e78ab7ee02922e207fe0fb1199fb644389f99e895bebc6507283","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-12-27T02:05:37Z","title_canon_sha256":"166f8059b63d121f37f192500a2df2e23e469afe154227e4ccb5a65ee5aed7df"},"schema_version":"1.0","source":{"id":"2412.19405","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.19405","created_at":"2026-07-05T09:54:35Z"},{"alias_kind":"arxiv_version","alias_value":"2412.19405v1","created_at":"2026-07-05T09:54:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.19405","created_at":"2026-07-05T09:54:35Z"},{"alias_kind":"pith_short_12","alias_value":"NG4GZKSYKUTZ","created_at":"2026-07-05T09:54:35Z"},{"alias_kind":"pith_short_16","alias_value":"NG4GZKSYKUTZI6RH","created_at":"2026-07-05T09:54:35Z"},{"alias_kind":"pith_short_8","alias_value":"NG4GZKSY","created_at":"2026-07-05T09:54:35Z"}],"graph_snapshots":[{"event_id":"sha256:7efd08305e5759297f14db2f656f836ed737a85fcdbe3861cd1f9116828548f8","target":"graph","created_at":"2026-07-05T09:54:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.19405/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that, to each synchronous non-local game $\\mathcal{G}=(I,O,\\lambda)$ with $|I|=n$ and $|O|=m \\geq 3$, there is an associated graph $G_{\\lambda}$ for which approximate winning strategies for the game $\\mathcal{G}$ and the $3$-coloring game for $G_{\\lambda}$ are preserved. That is, using a similar graph to previous work of the author (Ann. Henri Poincar\\'{e}, 2024), any synchronous strategy for $\\text{Hom}(G_{\\lambda},K_3)$ that wins the game with probability $1-\\varepsilon$ with respect to the uniform probability distribution on the edges, yields a strategy in the same model that wins ","authors_text":"Samuel J. Harris","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-12-27T02:05:37Z","title":"Approximate quantum 3-colorings of graphs and the quantum Max 3-Cut problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19405","kind":"arxiv","version":1},"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":"sha256:4e0f3c1f2619a1ff1073c730a2b5e22c73263e418e6bf7bf38af703a9087d63b","target":"record","created_at":"2026-07-05T09:54:35Z","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":"b84f6bf8b714e78ab7ee02922e207fe0fb1199fb644389f99e895bebc6507283","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-12-27T02:05:37Z","title_canon_sha256":"166f8059b63d121f37f192500a2df2e23e469afe154227e4ccb5a65ee5aed7df"},"schema_version":"1.0","source":{"id":"2412.19405","kind":"arxiv","version":1}},"canonical_sha256":"69b86caa585527947a2769618d8d98a2dffc67e1a7b8b18a6b5f692c3a9c905c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69b86caa585527947a2769618d8d98a2dffc67e1a7b8b18a6b5f692c3a9c905c","first_computed_at":"2026-07-05T09:54:35.041124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:54:35.041124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zwZVjtxPksZZ06WEn+4Y+xwpnrXzrmwK/9yEjinwYzpctRp+RkIiQ+iqYY3xyJBCa8VByU1jbvhLCULfsOU8Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:54:35.041601Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.19405","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e0f3c1f2619a1ff1073c730a2b5e22c73263e418e6bf7bf38af703a9087d63b","sha256:7efd08305e5759297f14db2f656f836ed737a85fcdbe3861cd1f9116828548f8"],"state_sha256":"576377c09325b384797fceacbb5fc7c1107d1d68b9feec0f905b120213444173"}