{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SQEGLRMF7UCFBPOXO5JRZLUUXE","short_pith_number":"pith:SQEGLRMF","canonical_record":{"source":{"id":"1511.08682","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-27T14:17:38Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"ac665230a2c1bc46f28da3ab0f2ab528a895d88f550e50e10b030b5002f68edf","abstract_canon_sha256":"23ef5a8fe407a60d3043eebde2a92e2fa8421f323c7debbf6f5438fc26a2bfbb"},"schema_version":"1.0"},"canonical_sha256":"940865c585fd0450bdd777531cae94b927ac885598e4b143b9059010e7568661","source":{"kind":"arxiv","id":"1511.08682","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08682","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08682v3","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08682","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"SQEGLRMF7UCF","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SQEGLRMF7UCFBPOX","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SQEGLRMF","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SQEGLRMF7UCFBPOXO5JRZLUUXE","target":"record","payload":{"canonical_record":{"source":{"id":"1511.08682","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-27T14:17:38Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"ac665230a2c1bc46f28da3ab0f2ab528a895d88f550e50e10b030b5002f68edf","abstract_canon_sha256":"23ef5a8fe407a60d3043eebde2a92e2fa8421f323c7debbf6f5438fc26a2bfbb"},"schema_version":"1.0"},"canonical_sha256":"940865c585fd0450bdd777531cae94b927ac885598e4b143b9059010e7568661","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:41.227055Z","signature_b64":"2XCt8cPumhPf88wSHYkOvkJmcNaVvXMdHDGl1tG4NpeQr4ti+0t3lN5piDmJ5/UabpnMwoa8rYdm/DGJW8FfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"940865c585fd0450bdd777531cae94b927ac885598e4b143b9059010e7568661","last_reissued_at":"2026-05-18T01:11:41.226720Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:41.226720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.08682","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TxTzu908CymRfeYcz9YOxbvAxJucCQr/QZxufrxOXUGl38vmFWGvCWPJixjvAx05JzVGxSIVBePhHD3rUpQCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:55:17.999639Z"},"content_sha256":"95cd487fe13b05c775d2124d3515feb0e5cd7dce931a6638d4e9774658991295","schema_version":"1.0","event_id":"sha256:95cd487fe13b05c775d2124d3515feb0e5cd7dce931a6638d4e9774658991295"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SQEGLRMF7UCFBPOXO5JRZLUUXE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomials, Quantum Query Complexity, and Grothendieck's Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Andris Ambainis, J\\=anis Iraids, Juris Smotrovs, Martins Kokainis, Scott Aaronson","submitted_at":"2015-11-27T14:17:38Z","abstract_excerpt":"We show an equivalence between 1-query quantum algorithms and representations by degree-2 polynomials. Namely, a partial Boolean function $f$ is computable by a 1-query quantum algorithm with error bounded by $\\epsilon<1/2$ iff $f$ can be approximated by a degree-2 polynomial with error bounded by $\\epsilon'<1/2$. This result holds for two different notions of approximation by a polynomial: the standard definition of Nisan and Szegedy and the approximation by block-multilinear polynomials recently introduced by Aaronson and Ambainis (STOC'2015, arxiv:1411.5729).\n  We also show two results for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08682","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rj5LWVsD0+oKHCozqAZG4CF1jb+p6KKr85k2P1ZNI/XG6k5KAcON0roXXga7Dr0Ed1/PWIUOI7CIO4HNn7r8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:55:18Z"},"content_sha256":"60414677ddb96b40e5c2564a7969b65ce4b14cf9f1cea8aae6296a43b2c28ec7","schema_version":"1.0","event_id":"sha256:60414677ddb96b40e5c2564a7969b65ce4b14cf9f1cea8aae6296a43b2c28ec7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQEGLRMF7UCFBPOXO5JRZLUUXE/bundle.json","state_url":"https://pith.science/pith/SQEGLRMF7UCFBPOXO5JRZLUUXE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQEGLRMF7UCFBPOXO5JRZLUUXE/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":"2026-05-26T04:55:18Z","links":{"resolver":"https://pith.science/pith/SQEGLRMF7UCFBPOXO5JRZLUUXE","bundle":"https://pith.science/pith/SQEGLRMF7UCFBPOXO5JRZLUUXE/bundle.json","state":"https://pith.science/pith/SQEGLRMF7UCFBPOXO5JRZLUUXE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQEGLRMF7UCFBPOXO5JRZLUUXE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SQEGLRMF7UCFBPOXO5JRZLUUXE","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":"23ef5a8fe407a60d3043eebde2a92e2fa8421f323c7debbf6f5438fc26a2bfbb","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-27T14:17:38Z","title_canon_sha256":"ac665230a2c1bc46f28da3ab0f2ab528a895d88f550e50e10b030b5002f68edf"},"schema_version":"1.0","source":{"id":"1511.08682","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08682","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08682v3","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08682","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"SQEGLRMF7UCF","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SQEGLRMF7UCFBPOX","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SQEGLRMF","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:60414677ddb96b40e5c2564a7969b65ce4b14cf9f1cea8aae6296a43b2c28ec7","target":"graph","created_at":"2026-05-18T01:11:41Z","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":"We show an equivalence between 1-query quantum algorithms and representations by degree-2 polynomials. Namely, a partial Boolean function $f$ is computable by a 1-query quantum algorithm with error bounded by $\\epsilon<1/2$ iff $f$ can be approximated by a degree-2 polynomial with error bounded by $\\epsilon'<1/2$. This result holds for two different notions of approximation by a polynomial: the standard definition of Nisan and Szegedy and the approximation by block-multilinear polynomials recently introduced by Aaronson and Ambainis (STOC'2015, arxiv:1411.5729).\n  We also show two results for ","authors_text":"Andris Ambainis, J\\=anis Iraids, Juris Smotrovs, Martins Kokainis, Scott Aaronson","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-27T14:17:38Z","title":"Polynomials, Quantum Query Complexity, and Grothendieck's Inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08682","kind":"arxiv","version":3},"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":"sha256:95cd487fe13b05c775d2124d3515feb0e5cd7dce931a6638d4e9774658991295","target":"record","created_at":"2026-05-18T01:11:41Z","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":"23ef5a8fe407a60d3043eebde2a92e2fa8421f323c7debbf6f5438fc26a2bfbb","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-27T14:17:38Z","title_canon_sha256":"ac665230a2c1bc46f28da3ab0f2ab528a895d88f550e50e10b030b5002f68edf"},"schema_version":"1.0","source":{"id":"1511.08682","kind":"arxiv","version":3}},"canonical_sha256":"940865c585fd0450bdd777531cae94b927ac885598e4b143b9059010e7568661","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"940865c585fd0450bdd777531cae94b927ac885598e4b143b9059010e7568661","first_computed_at":"2026-05-18T01:11:41.226720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:41.226720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2XCt8cPumhPf88wSHYkOvkJmcNaVvXMdHDGl1tG4NpeQr4ti+0t3lN5piDmJ5/UabpnMwoa8rYdm/DGJW8FfAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:41.227055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.08682","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95cd487fe13b05c775d2124d3515feb0e5cd7dce931a6638d4e9774658991295","sha256:60414677ddb96b40e5c2564a7969b65ce4b14cf9f1cea8aae6296a43b2c28ec7"],"state_sha256":"cfdc1f460584ca29e4af72b11ca5631c8e08ddc6d94589640fa0fba4babbe5c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"06auLPeNQwXvRHpPa1LJPCIbK58UUWKSFZwqs4IO30ckFMdsUJ8XP+S6SitvL8VOGqdmKDgBqCowfw8k56eeDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:55:18.002969Z","bundle_sha256":"7794cdc6564c155e216107616ed57cbe54a2e715beccfe35d92a490483b4d1ea"}}