{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4IEBCE3OX4FMXOPST7QVL6MJRP","short_pith_number":"pith:4IEBCE3O","canonical_record":{"source":{"id":"1605.07084","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-05-23T16:38:40Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"8ac950293a432ef2ab27b5490d2b6bb302c16d8944a8c5c12afbdc063c116a66","abstract_canon_sha256":"cc6578eed3dd3bc9a20957b20e0636263ac6e8022a3c613e89a3ad248f694b4a"},"schema_version":"1.0"},"canonical_sha256":"e20811136ebf0acbb9f29fe155f9898bd43312be48a69b4d7c57a5d74851181c","source":{"kind":"arxiv","id":"1605.07084","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07084","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07084v2","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07084","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"pith_short_12","alias_value":"4IEBCE3OX4FM","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4IEBCE3OX4FMXOPS","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4IEBCE3O","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4IEBCE3OX4FMXOPST7QVL6MJRP","target":"record","payload":{"canonical_record":{"source":{"id":"1605.07084","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-05-23T16:38:40Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"8ac950293a432ef2ab27b5490d2b6bb302c16d8944a8c5c12afbdc063c116a66","abstract_canon_sha256":"cc6578eed3dd3bc9a20957b20e0636263ac6e8022a3c613e89a3ad248f694b4a"},"schema_version":"1.0"},"canonical_sha256":"e20811136ebf0acbb9f29fe155f9898bd43312be48a69b4d7c57a5d74851181c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:28.800949Z","signature_b64":"rfgQtQJGC0d9bGnokIQUw4kC+92Gnyx70QFtrzfCpBplafs1xNCbW0K4Q8BqCOInZeIlntaDqNB5FFmImdIfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e20811136ebf0acbb9f29fe155f9898bd43312be48a69b4d7c57a5d74851181c","last_reissued_at":"2026-05-18T00:30:28.800341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:28.800341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.07084","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:30:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5wdJ7uOCHNBtBH/1+m7BWiEmXgkJc6rCA27JFPNHj3otKtZ1/4a40qq1h4E5cAEnSRdH8u3HeAMdEAK4UGEcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:36:45.375966Z"},"content_sha256":"1c8e2af58c6ea41e469a535d1eacf8707f8206eb2dc9f7ec45adf100fbef5aed","schema_version":"1.0","event_id":"sha256:1c8e2af58c6ea41e469a535d1eacf8707f8206eb2dc9f7ec45adf100fbef5aed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4IEBCE3OX4FMXOPST7QVL6MJRP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low-Sensitivity Functions from Unambiguous Certificates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.CC","authors_text":"Avishay Tal, Pooya Hatami, Shalev Ben-David","submitted_at":"2016-05-23T16:38:40Z","abstract_excerpt":"We provide new query complexity separations against sensitivity for total Boolean functions: a power $3$ separation between deterministic (and even randomized or quantum) query complexity and sensitivity, and a power $2.22$ separation between certificate complexity and sensitivity. We get these separations by using a new connection between sensitivity and a seemingly unrelated measure called one-sided unambiguous certificate complexity ($UC_{min}$). We also show that $UC_{min}$ is lower-bounded by fractional block sensitivity, which means we cannot use these techniques to get a super-quadratic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07084","kind":"arxiv","version":2},"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":"2026-05-18T00:30:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5pjWTMH08Fo3UJg0AuXHTB3/sRUt4+d3C9Qy4H3n73QJBkgeZV0h2H5qQtMUtKiMvnns/lhh4AYCq5qFSFF6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:36:45.376348Z"},"content_sha256":"e3841b2575719ba62496316b86f947b95074f3e345a9f7c58a5157cbd7ed2f88","schema_version":"1.0","event_id":"sha256:e3841b2575719ba62496316b86f947b95074f3e345a9f7c58a5157cbd7ed2f88"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4IEBCE3OX4FMXOPST7QVL6MJRP/bundle.json","state_url":"https://pith.science/pith/4IEBCE3OX4FMXOPST7QVL6MJRP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4IEBCE3OX4FMXOPST7QVL6MJRP/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":"2026-05-26T12:36:45Z","links":{"resolver":"https://pith.science/pith/4IEBCE3OX4FMXOPST7QVL6MJRP","bundle":"https://pith.science/pith/4IEBCE3OX4FMXOPST7QVL6MJRP/bundle.json","state":"https://pith.science/pith/4IEBCE3OX4FMXOPST7QVL6MJRP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4IEBCE3OX4FMXOPST7QVL6MJRP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4IEBCE3OX4FMXOPST7QVL6MJRP","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":"cc6578eed3dd3bc9a20957b20e0636263ac6e8022a3c613e89a3ad248f694b4a","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-05-23T16:38:40Z","title_canon_sha256":"8ac950293a432ef2ab27b5490d2b6bb302c16d8944a8c5c12afbdc063c116a66"},"schema_version":"1.0","source":{"id":"1605.07084","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07084","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07084v2","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07084","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"pith_short_12","alias_value":"4IEBCE3OX4FM","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4IEBCE3OX4FMXOPS","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4IEBCE3O","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:e3841b2575719ba62496316b86f947b95074f3e345a9f7c58a5157cbd7ed2f88","target":"graph","created_at":"2026-05-18T00:30:28Z","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 provide new query complexity separations against sensitivity for total Boolean functions: a power $3$ separation between deterministic (and even randomized or quantum) query complexity and sensitivity, and a power $2.22$ separation between certificate complexity and sensitivity. We get these separations by using a new connection between sensitivity and a seemingly unrelated measure called one-sided unambiguous certificate complexity ($UC_{min}$). We also show that $UC_{min}$ is lower-bounded by fractional block sensitivity, which means we cannot use these techniques to get a super-quadratic","authors_text":"Avishay Tal, Pooya Hatami, Shalev Ben-David","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-05-23T16:38:40Z","title":"Low-Sensitivity Functions from Unambiguous Certificates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07084","kind":"arxiv","version":2},"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":"sha256:1c8e2af58c6ea41e469a535d1eacf8707f8206eb2dc9f7ec45adf100fbef5aed","target":"record","created_at":"2026-05-18T00:30:28Z","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":"cc6578eed3dd3bc9a20957b20e0636263ac6e8022a3c613e89a3ad248f694b4a","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-05-23T16:38:40Z","title_canon_sha256":"8ac950293a432ef2ab27b5490d2b6bb302c16d8944a8c5c12afbdc063c116a66"},"schema_version":"1.0","source":{"id":"1605.07084","kind":"arxiv","version":2}},"canonical_sha256":"e20811136ebf0acbb9f29fe155f9898bd43312be48a69b4d7c57a5d74851181c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e20811136ebf0acbb9f29fe155f9898bd43312be48a69b4d7c57a5d74851181c","first_computed_at":"2026-05-18T00:30:28.800341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:28.800341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rfgQtQJGC0d9bGnokIQUw4kC+92Gnyx70QFtrzfCpBplafs1xNCbW0K4Q8BqCOInZeIlntaDqNB5FFmImdIfDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:28.800949Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.07084","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c8e2af58c6ea41e469a535d1eacf8707f8206eb2dc9f7ec45adf100fbef5aed","sha256:e3841b2575719ba62496316b86f947b95074f3e345a9f7c58a5157cbd7ed2f88"],"state_sha256":"8fcdf5258ad335fc844c3e42dc6e431beba6a68bc3e440f898f323b0387c21e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J2MVa0uSOshhSbjqg5s0cV5VTo7NTE6Y3uIPm9FBY2G8kO4OqtQDJS7zURFZdvtIp+OQL+dmUXnLXC803wcbCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:36:45.379467Z","bundle_sha256":"2d3d8f9fa175721e4ccb6c4e2f87578070141db6c2041ebf3dbe945b6a54184f"}}