{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6G2SJCYFT36HG45QBRIVSW5R7A","short_pith_number":"pith:6G2SJCYF","canonical_record":{"source":{"id":"1405.1374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-05-03T22:18:05Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"14f3631a542cd7ebe52c260d112b3608dea79a9ed56ea3e50d4c31d49efcad6b","abstract_canon_sha256":"d38c9e4def3c901a605dde3c48928fe5d6ac3aecac5a45fd6e8b546317a4cae4"},"schema_version":"1.0"},"canonical_sha256":"f1b5248b059efc7373b00c51595bb1f8196fd2d1e70b5217ca8ffeb9bd73765d","source":{"kind":"arxiv","id":"1405.1374","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.1374","created_at":"2026-05-18T02:52:32Z"},{"alias_kind":"arxiv_version","alias_value":"1405.1374v1","created_at":"2026-05-18T02:52:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1374","created_at":"2026-05-18T02:52:32Z"},{"alias_kind":"pith_short_12","alias_value":"6G2SJCYFT36H","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6G2SJCYFT36HG45Q","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6G2SJCYF","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6G2SJCYFT36HG45QBRIVSW5R7A","target":"record","payload":{"canonical_record":{"source":{"id":"1405.1374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-05-03T22:18:05Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"14f3631a542cd7ebe52c260d112b3608dea79a9ed56ea3e50d4c31d49efcad6b","abstract_canon_sha256":"d38c9e4def3c901a605dde3c48928fe5d6ac3aecac5a45fd6e8b546317a4cae4"},"schema_version":"1.0"},"canonical_sha256":"f1b5248b059efc7373b00c51595bb1f8196fd2d1e70b5217ca8ffeb9bd73765d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:32.948711Z","signature_b64":"SmzwWM8g1iQrhConbmEmEEFTx7V7tiYZJ5rt8Agci0GDl84qyVPsZ4NlNj2eM/LR5XdKrOArQQlOqmjKnRSVDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1b5248b059efc7373b00c51595bb1f8196fd2d1e70b5217ca8ffeb9bd73765d","last_reissued_at":"2026-05-18T02:52:32.948215Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:32.948215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.1374","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:52:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4zrEzq4u9WUUEvHwbGo9qQTmwPBbkX2bOQuHAR/kfKcNMDA0Z+77gn2vweHs11ZzsFzT8KjyJp2lPiXNqQdCDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:21:04.607481Z"},"content_sha256":"7afc352797f2104ff46946d0c2e3ddd4338cdb5d715fa82fa6ca9ff5ba5dc21f","schema_version":"1.0","event_id":"sha256:7afc352797f2104ff46946d0c2e3ddd4338cdb5d715fa82fa6ca9ff5ba5dc21f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6G2SJCYFT36HG45QBRIVSW5R7A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unique Games on the Hypercube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Alexandra Kolla, Guy Kindler, Luca Trevisan, Naman Agarwal","submitted_at":"2014-05-03T22:18:05Z","abstract_excerpt":"In this paper, we investigate the validity of the Unique Games Conjecture when the constraint graph is the boolean hypercube. We construct an almost optimal integrality gap instance on the Hypercube for the Goemans-Williamson semidefinite program (SDP) for Max-2-LIN$(\\mathbb{Z}_2)$. We conjecture that adding triangle inequalities to the SDP provides a polynomial time algorithm to solve Unique Games on the hypercube."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1374","kind":"arxiv","version":1},"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":"2026-05-18T02:52:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z3HPnQX3Ci1NlejWbpqq2z5I8rqLF+c+TBmS/nW0EhVNZL4Hoq8qACmWEYDiQ9FQzex0gAJeTNaRyYj8xp7ODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:21:04.608079Z"},"content_sha256":"15b2f7d8370fe6a828746f143d28925c29839390d2f6465021ec23685de28bf6","schema_version":"1.0","event_id":"sha256:15b2f7d8370fe6a828746f143d28925c29839390d2f6465021ec23685de28bf6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6G2SJCYFT36HG45QBRIVSW5R7A/bundle.json","state_url":"https://pith.science/pith/6G2SJCYFT36HG45QBRIVSW5R7A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6G2SJCYFT36HG45QBRIVSW5R7A/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":"2026-05-30T13:21:04Z","links":{"resolver":"https://pith.science/pith/6G2SJCYFT36HG45QBRIVSW5R7A","bundle":"https://pith.science/pith/6G2SJCYFT36HG45QBRIVSW5R7A/bundle.json","state":"https://pith.science/pith/6G2SJCYFT36HG45QBRIVSW5R7A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6G2SJCYFT36HG45QBRIVSW5R7A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6G2SJCYFT36HG45QBRIVSW5R7A","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":"d38c9e4def3c901a605dde3c48928fe5d6ac3aecac5a45fd6e8b546317a4cae4","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-05-03T22:18:05Z","title_canon_sha256":"14f3631a542cd7ebe52c260d112b3608dea79a9ed56ea3e50d4c31d49efcad6b"},"schema_version":"1.0","source":{"id":"1405.1374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.1374","created_at":"2026-05-18T02:52:32Z"},{"alias_kind":"arxiv_version","alias_value":"1405.1374v1","created_at":"2026-05-18T02:52:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1374","created_at":"2026-05-18T02:52:32Z"},{"alias_kind":"pith_short_12","alias_value":"6G2SJCYFT36H","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6G2SJCYFT36HG45Q","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6G2SJCYF","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:15b2f7d8370fe6a828746f143d28925c29839390d2f6465021ec23685de28bf6","target":"graph","created_at":"2026-05-18T02:52:32Z","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":"In this paper, we investigate the validity of the Unique Games Conjecture when the constraint graph is the boolean hypercube. We construct an almost optimal integrality gap instance on the Hypercube for the Goemans-Williamson semidefinite program (SDP) for Max-2-LIN$(\\mathbb{Z}_2)$. We conjecture that adding triangle inequalities to the SDP provides a polynomial time algorithm to solve Unique Games on the hypercube.","authors_text":"Alexandra Kolla, Guy Kindler, Luca Trevisan, Naman Agarwal","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-05-03T22:18:05Z","title":"Unique Games on the Hypercube"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1374","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":"sha256:7afc352797f2104ff46946d0c2e3ddd4338cdb5d715fa82fa6ca9ff5ba5dc21f","target":"record","created_at":"2026-05-18T02:52:32Z","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":"d38c9e4def3c901a605dde3c48928fe5d6ac3aecac5a45fd6e8b546317a4cae4","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-05-03T22:18:05Z","title_canon_sha256":"14f3631a542cd7ebe52c260d112b3608dea79a9ed56ea3e50d4c31d49efcad6b"},"schema_version":"1.0","source":{"id":"1405.1374","kind":"arxiv","version":1}},"canonical_sha256":"f1b5248b059efc7373b00c51595bb1f8196fd2d1e70b5217ca8ffeb9bd73765d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1b5248b059efc7373b00c51595bb1f8196fd2d1e70b5217ca8ffeb9bd73765d","first_computed_at":"2026-05-18T02:52:32.948215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:32.948215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SmzwWM8g1iQrhConbmEmEEFTx7V7tiYZJ5rt8Agci0GDl84qyVPsZ4NlNj2eM/LR5XdKrOArQQlOqmjKnRSVDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:32.948711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.1374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7afc352797f2104ff46946d0c2e3ddd4338cdb5d715fa82fa6ca9ff5ba5dc21f","sha256:15b2f7d8370fe6a828746f143d28925c29839390d2f6465021ec23685de28bf6"],"state_sha256":"d19b2ca75ff6ed8cc0e8483929420a47bf30da656a1ac6fd4c967d866f20a3e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2VsADeA8CM+gx+MP8FFt/yc5t6YBlWkt8dtWZlYILGUQujri+c2Gqhg/u+IdsDDkPSv58qv+TDxTBG1Z/ZNMBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:21:04.611183Z","bundle_sha256":"2ef41a0d4e4becfc1c020de609c79a17f607cb1e44256aec3be181a5bc76866b"}}