{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:KG5E6VDUBVSU4OHMXBCJLMRHOE","short_pith_number":"pith:KG5E6VDU","canonical_record":{"source":{"id":"2010.12629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-10-23T19:21:28Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"92048319113286053cc7135c24656808b39e532b89d8bfa19e4e54c4a586c620","abstract_canon_sha256":"b1e8ea03e37d47e5d1fdc80abafb1fa02d462e7e4cdd43045fd5ffda95311b58"},"schema_version":"1.0"},"canonical_sha256":"51ba4f54740d654e38ecb84495b227711e7928319291ceeb399b0524ff5c9cea","source":{"kind":"arxiv","id":"2010.12629","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.12629","created_at":"2026-07-05T01:45:46Z"},{"alias_kind":"arxiv_version","alias_value":"2010.12629v1","created_at":"2026-07-05T01:45:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.12629","created_at":"2026-07-05T01:45:46Z"},{"alias_kind":"pith_short_12","alias_value":"KG5E6VDUBVSU","created_at":"2026-07-05T01:45:46Z"},{"alias_kind":"pith_short_16","alias_value":"KG5E6VDUBVSU4OHM","created_at":"2026-07-05T01:45:46Z"},{"alias_kind":"pith_short_8","alias_value":"KG5E6VDU","created_at":"2026-07-05T01:45:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:KG5E6VDUBVSU4OHMXBCJLMRHOE","target":"record","payload":{"canonical_record":{"source":{"id":"2010.12629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-10-23T19:21:28Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"92048319113286053cc7135c24656808b39e532b89d8bfa19e4e54c4a586c620","abstract_canon_sha256":"b1e8ea03e37d47e5d1fdc80abafb1fa02d462e7e4cdd43045fd5ffda95311b58"},"schema_version":"1.0"},"canonical_sha256":"51ba4f54740d654e38ecb84495b227711e7928319291ceeb399b0524ff5c9cea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:45:46.605729Z","signature_b64":"AB+tmm/dVHkh6p7zzy7YU1mM6Il92ZRGkoNvkIu9qHkyPWLNV2IitvBU2odC3HAcHw6PUE7wpJ+KeKNu+PJtBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51ba4f54740d654e38ecb84495b227711e7928319291ceeb399b0524ff5c9cea","last_reissued_at":"2026-07-05T01:45:46.605380Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:45:46.605380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.12629","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":"2026-07-05T01:45:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bujXQWYC+mEr59ZaMjfMUp0Wp8avM83At6QV+T6wS/lGqtz9+o2EtXYVZdaSbEVgICFbUeuVp2nmMvyTq3YGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T21:32:18.444177Z"},"content_sha256":"a5c148d1d29ec569bf8bc1bf8d2f75eac666acf0f7f70ea92192776b485cf909","schema_version":"1.0","event_id":"sha256:a5c148d1d29ec569bf8bc1bf8d2f75eac666acf0f7f70ea92192776b485cf909"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:KG5E6VDUBVSU4OHMXBCJLMRHOE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Degree vs. Approximate Degree and Quantum Implications of Huang's Sensitivity Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Avishay Tal, Robin Kothari, Scott Aaronson, Shalev Ben-David, Shravas Rao","submitted_at":"2020-10-23T19:21:28Z","abstract_excerpt":"Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function $f$,\n  $\\bullet \\quad \\mathrm{deg}(f) = O(\\widetilde{\\mathrm{deg}}(f)^2)$: The degree of $f$ is at most quadratic in the approximate degree of $f$. This is optimal as witnessed by the OR function.\n  $\\bullet \\quad \\mathrm{D}(f) = O(\\mathrm{Q}(f)^4)$: The deterministic query complexity of $f$ is at most quartic in the quantum query complexity of $f$. This matches the known separation (up to log factors) due to Ambainis, Balodis, Belovs, Lee, Santha, and Smotrovs (2017).\n  We apply these results to reso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.12629","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.12629/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:45:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rojVD3J2fxCwyliwE6D5vBWEHi11pPs8+//DMmKtAMCg9mi/n6ejaIQ34Cum1Hu358wGFEwPlGzRqlhcTY1rBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T21:32:18.444789Z"},"content_sha256":"5fa9f597d970fea753a1bcafbe571a49574f129797f7b03a34e19fba5b71b07f","schema_version":"1.0","event_id":"sha256:5fa9f597d970fea753a1bcafbe571a49574f129797f7b03a34e19fba5b71b07f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KG5E6VDUBVSU4OHMXBCJLMRHOE/bundle.json","state_url":"https://pith.science/pith/KG5E6VDUBVSU4OHMXBCJLMRHOE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KG5E6VDUBVSU4OHMXBCJLMRHOE/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":"2026-08-21T21:32:18Z","links":{"resolver":"https://pith.science/pith/KG5E6VDUBVSU4OHMXBCJLMRHOE","bundle":"https://pith.science/pith/KG5E6VDUBVSU4OHMXBCJLMRHOE/bundle.json","state":"https://pith.science/pith/KG5E6VDUBVSU4OHMXBCJLMRHOE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KG5E6VDUBVSU4OHMXBCJLMRHOE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:KG5E6VDUBVSU4OHMXBCJLMRHOE","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":"b1e8ea03e37d47e5d1fdc80abafb1fa02d462e7e4cdd43045fd5ffda95311b58","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-10-23T19:21:28Z","title_canon_sha256":"92048319113286053cc7135c24656808b39e532b89d8bfa19e4e54c4a586c620"},"schema_version":"1.0","source":{"id":"2010.12629","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.12629","created_at":"2026-07-05T01:45:46Z"},{"alias_kind":"arxiv_version","alias_value":"2010.12629v1","created_at":"2026-07-05T01:45:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.12629","created_at":"2026-07-05T01:45:46Z"},{"alias_kind":"pith_short_12","alias_value":"KG5E6VDUBVSU","created_at":"2026-07-05T01:45:46Z"},{"alias_kind":"pith_short_16","alias_value":"KG5E6VDUBVSU4OHM","created_at":"2026-07-05T01:45:46Z"},{"alias_kind":"pith_short_8","alias_value":"KG5E6VDU","created_at":"2026-07-05T01:45:46Z"}],"graph_snapshots":[{"event_id":"sha256:5fa9f597d970fea753a1bcafbe571a49574f129797f7b03a34e19fba5b71b07f","target":"graph","created_at":"2026-07-05T01:45:46Z","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/2010.12629/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function $f$,\n  $\\bullet \\quad \\mathrm{deg}(f) = O(\\widetilde{\\mathrm{deg}}(f)^2)$: The degree of $f$ is at most quadratic in the approximate degree of $f$. This is optimal as witnessed by the OR function.\n  $\\bullet \\quad \\mathrm{D}(f) = O(\\mathrm{Q}(f)^4)$: The deterministic query complexity of $f$ is at most quartic in the quantum query complexity of $f$. This matches the known separation (up to log factors) due to Ambainis, Balodis, Belovs, Lee, Santha, and Smotrovs (2017).\n  We apply these results to reso","authors_text":"Avishay Tal, Robin Kothari, Scott Aaronson, Shalev Ben-David, Shravas Rao","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-10-23T19:21:28Z","title":"Degree vs. Approximate Degree and Quantum Implications of Huang's Sensitivity Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.12629","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:a5c148d1d29ec569bf8bc1bf8d2f75eac666acf0f7f70ea92192776b485cf909","target":"record","created_at":"2026-07-05T01:45:46Z","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":"b1e8ea03e37d47e5d1fdc80abafb1fa02d462e7e4cdd43045fd5ffda95311b58","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-10-23T19:21:28Z","title_canon_sha256":"92048319113286053cc7135c24656808b39e532b89d8bfa19e4e54c4a586c620"},"schema_version":"1.0","source":{"id":"2010.12629","kind":"arxiv","version":1}},"canonical_sha256":"51ba4f54740d654e38ecb84495b227711e7928319291ceeb399b0524ff5c9cea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51ba4f54740d654e38ecb84495b227711e7928319291ceeb399b0524ff5c9cea","first_computed_at":"2026-07-05T01:45:46.605380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:45:46.605380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AB+tmm/dVHkh6p7zzy7YU1mM6Il92ZRGkoNvkIu9qHkyPWLNV2IitvBU2odC3HAcHw6PUE7wpJ+KeKNu+PJtBA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:45:46.605729Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.12629","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5c148d1d29ec569bf8bc1bf8d2f75eac666acf0f7f70ea92192776b485cf909","sha256:5fa9f597d970fea753a1bcafbe571a49574f129797f7b03a34e19fba5b71b07f"],"state_sha256":"019d0bbca115c88f9ff120e7decc48b379caa22fb145f399906d03e7e771d15f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8F5IzpyUx1+KhFSl3NkAazAnNrppJgDHbmy+4IlgawP1zZpjyO7zLxhYKYr2Yc+afl6hZX9/bHeDDe527kMfAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T21:32:18.450346Z","bundle_sha256":"73f5faaf2bf0eeca9924683f4410a92db4a42e1b4d70f545903d8877d070d317"}}