{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:OB7PAM7RMQXWJ4LZXRLRUYO7Q4","short_pith_number":"pith:OB7PAM7R","canonical_record":{"source":{"id":"2608.00851","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.CC","submitted_at":"2026-08-01T20:15:23Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3bd15005b3394c093d15140fb81804808b2710abe85417633b5b01d19244a6ec","abstract_canon_sha256":"151200f2387957f0dba5ae445c05900559673007aec1d3fa49aa1bdb6e9bb450"},"schema_version":"1.0"},"canonical_sha256":"707ef033f1642f64f179bc571a61df8725211715cb3d448c48cc9685680628d1","source":{"kind":"arxiv","id":"2608.00851","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00851","created_at":"2026-08-04T01:55:15Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00851v1","created_at":"2026-08-04T01:55:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00851","created_at":"2026-08-04T01:55:15Z"},{"alias_kind":"pith_short_12","alias_value":"OB7PAM7RMQXW","created_at":"2026-08-04T01:55:15Z"},{"alias_kind":"pith_short_16","alias_value":"OB7PAM7RMQXWJ4LZ","created_at":"2026-08-04T01:55:15Z"},{"alias_kind":"pith_short_8","alias_value":"OB7PAM7R","created_at":"2026-08-04T01:55:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:OB7PAM7RMQXWJ4LZXRLRUYO7Q4","target":"record","payload":{"canonical_record":{"source":{"id":"2608.00851","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.CC","submitted_at":"2026-08-01T20:15:23Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3bd15005b3394c093d15140fb81804808b2710abe85417633b5b01d19244a6ec","abstract_canon_sha256":"151200f2387957f0dba5ae445c05900559673007aec1d3fa49aa1bdb6e9bb450"},"schema_version":"1.0"},"canonical_sha256":"707ef033f1642f64f179bc571a61df8725211715cb3d448c48cc9685680628d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T01:55:15.726216Z","signature_b64":"SGHH+Udl9Z3xmCNI7IHOwsoWXnuSMLfaJ3Ni3DG6SFPk7NrFNXSYpNLfcZxJoePJyZiYFLF0Hjfay6bb7+0CBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"707ef033f1642f64f179bc571a61df8725211715cb3d448c48cc9685680628d1","last_reissued_at":"2026-08-04T01:55:15.724702Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T01:55:15.724702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.00851","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":"2026-08-04T01:55:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"obsBO6Owc28oWdHgQjAY/5hG/cNWkgSzwpURn2Yxk8F6XgLUH5ECFyWuGpBalhqKaYT5nHUBYZ1uhFaWdcNIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T01:21:45.827819Z"},"content_sha256":"6014a85a4797bd3f7651a7d6be712870f7c938673771d82646da7b4d76c87b81","schema_version":"1.0","event_id":"sha256:6014a85a4797bd3f7651a7d6be712870f7c938673771d82646da7b4d76c87b81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:OB7PAM7RMQXWJ4LZXRLRUYO7Q4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Block Sensitivity can exceed Spectral Sensitivity Squared","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"Alexander Meiburg","submitted_at":"2026-08-01T20:15:23Z","abstract_excerpt":"The spectral sensitivity $\\lambda(f)$ of a Boolean function is the largest eigenvalue of the adjacency matrix of its sensitivity graph. It lower-bounds every standard measure of query complexity, and Aaronson, Ben-David, Kothari, Rao and Tal, who introduced it, asked whether block sensitivity is at most quadratic in it: is $bs(f)=O(\\lambda(f)^{2})$? We show that it is not. We construct a total Boolean function on $2017584$ variables with $bs(f)\\ge 14011$ and $\\lambda(f)\\le 89.0162$, so that $bs(f)\\ge\\lambda(f)^{2.127}$, and hence by composition a family with $\\lambda(f_n)\\to\\infty$ and $bs(f_n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00851","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/2608.00851/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":"2026-08-04T01:55:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tnkAJlIVQAqJnjcEgadwLMPwU+TB5lV8k1oWS5Y7+eZYCuM6J9IVrmxbmr4a0Gl5oxUxPiewangM2E+HBH5jDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T01:21:45.828696Z"},"content_sha256":"9774ebffc766b90a7e1d071d9327926751a395fae898ef155327753d12cbbe5a","schema_version":"1.0","event_id":"sha256:9774ebffc766b90a7e1d071d9327926751a395fae898ef155327753d12cbbe5a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OB7PAM7RMQXWJ4LZXRLRUYO7Q4/bundle.json","state_url":"https://pith.science/pith/OB7PAM7RMQXWJ4LZXRLRUYO7Q4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OB7PAM7RMQXWJ4LZXRLRUYO7Q4/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":"2026-08-17T01:21:45Z","links":{"resolver":"https://pith.science/pith/OB7PAM7RMQXWJ4LZXRLRUYO7Q4","bundle":"https://pith.science/pith/OB7PAM7RMQXWJ4LZXRLRUYO7Q4/bundle.json","state":"https://pith.science/pith/OB7PAM7RMQXWJ4LZXRLRUYO7Q4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OB7PAM7RMQXWJ4LZXRLRUYO7Q4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OB7PAM7RMQXWJ4LZXRLRUYO7Q4","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":"151200f2387957f0dba5ae445c05900559673007aec1d3fa49aa1bdb6e9bb450","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.CC","submitted_at":"2026-08-01T20:15:23Z","title_canon_sha256":"3bd15005b3394c093d15140fb81804808b2710abe85417633b5b01d19244a6ec"},"schema_version":"1.0","source":{"id":"2608.00851","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00851","created_at":"2026-08-04T01:55:15Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00851v1","created_at":"2026-08-04T01:55:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00851","created_at":"2026-08-04T01:55:15Z"},{"alias_kind":"pith_short_12","alias_value":"OB7PAM7RMQXW","created_at":"2026-08-04T01:55:15Z"},{"alias_kind":"pith_short_16","alias_value":"OB7PAM7RMQXWJ4LZ","created_at":"2026-08-04T01:55:15Z"},{"alias_kind":"pith_short_8","alias_value":"OB7PAM7R","created_at":"2026-08-04T01:55:15Z"}],"graph_snapshots":[{"event_id":"sha256:9774ebffc766b90a7e1d071d9327926751a395fae898ef155327753d12cbbe5a","target":"graph","created_at":"2026-08-04T01:55:15Z","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/2608.00851/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The spectral sensitivity $\\lambda(f)$ of a Boolean function is the largest eigenvalue of the adjacency matrix of its sensitivity graph. It lower-bounds every standard measure of query complexity, and Aaronson, Ben-David, Kothari, Rao and Tal, who introduced it, asked whether block sensitivity is at most quadratic in it: is $bs(f)=O(\\lambda(f)^{2})$? We show that it is not. We construct a total Boolean function on $2017584$ variables with $bs(f)\\ge 14011$ and $\\lambda(f)\\le 89.0162$, so that $bs(f)\\ge\\lambda(f)^{2.127}$, and hence by composition a family with $\\lambda(f_n)\\to\\infty$ and $bs(f_n","authors_text":"Alexander Meiburg","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.CC","submitted_at":"2026-08-01T20:15:23Z","title":"Block Sensitivity can exceed Spectral Sensitivity Squared"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00851","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":"sha256:6014a85a4797bd3f7651a7d6be712870f7c938673771d82646da7b4d76c87b81","target":"record","created_at":"2026-08-04T01:55:15Z","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":"151200f2387957f0dba5ae445c05900559673007aec1d3fa49aa1bdb6e9bb450","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.CC","submitted_at":"2026-08-01T20:15:23Z","title_canon_sha256":"3bd15005b3394c093d15140fb81804808b2710abe85417633b5b01d19244a6ec"},"schema_version":"1.0","source":{"id":"2608.00851","kind":"arxiv","version":1}},"canonical_sha256":"707ef033f1642f64f179bc571a61df8725211715cb3d448c48cc9685680628d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"707ef033f1642f64f179bc571a61df8725211715cb3d448c48cc9685680628d1","first_computed_at":"2026-08-04T01:55:15.724702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T01:55:15.724702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SGHH+Udl9Z3xmCNI7IHOwsoWXnuSMLfaJ3Ni3DG6SFPk7NrFNXSYpNLfcZxJoePJyZiYFLF0Hjfay6bb7+0CBw==","signature_status":"signed_v1","signed_at":"2026-08-04T01:55:15.726216Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.00851","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6014a85a4797bd3f7651a7d6be712870f7c938673771d82646da7b4d76c87b81","sha256:9774ebffc766b90a7e1d071d9327926751a395fae898ef155327753d12cbbe5a"],"state_sha256":"c33e28798d1e072f4fc0abac7c7329053a40992e2bdfe43e973fd97369c3259c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RG/dyCmblPTU+bVylA4HSJ2SGfpy7ijywhxIUTwX+jxy5iuSLgVZNE4N9k9VXgOy+jH4/5GZgsZ4e2gaiaMKCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T01:21:45.835866Z","bundle_sha256":"9809b069c634215bf7b9f1cb2ca33dd1be519846720f66d4a70a597b39d75b7e"}}