{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RWBHX2L5GRUKN63PNXPVWOJTMN","short_pith_number":"pith:RWBHX2L5","canonical_record":{"source":{"id":"1108.3198","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-08-16T10:12:31Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"7c3b7b2380607d01a6dca0938b8cb370f474567c8629f6831d06a5b44e3d7a0a","abstract_canon_sha256":"16026e5ff139416ae51bd99495f7b966f30dd52ff5b4b05829fdf9dd3ab60cbc"},"schema_version":"1.0"},"canonical_sha256":"8d827be97d3468a6fb6f6ddf5b3933637ae177a4fab0b4b9980255cea3813845","source":{"kind":"arxiv","id":"1108.3198","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3198","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3198v2","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3198","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"pith_short_12","alias_value":"RWBHX2L5GRUK","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RWBHX2L5GRUKN63P","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RWBHX2L5","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RWBHX2L5GRUKN63PNXPVWOJTMN","target":"record","payload":{"canonical_record":{"source":{"id":"1108.3198","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-08-16T10:12:31Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"7c3b7b2380607d01a6dca0938b8cb370f474567c8629f6831d06a5b44e3d7a0a","abstract_canon_sha256":"16026e5ff139416ae51bd99495f7b966f30dd52ff5b4b05829fdf9dd3ab60cbc"},"schema_version":"1.0"},"canonical_sha256":"8d827be97d3468a6fb6f6ddf5b3933637ae177a4fab0b4b9980255cea3813845","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:54.721598Z","signature_b64":"bSA71yUsRhtMHgldLxed0yRYHK3fKko3dRq9PJr2lG6Trp1VKmHrt/VK3N2r68Han06bhzF+Ey3r9SwymcuoCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d827be97d3468a6fb6f6ddf5b3933637ae177a4fab0b4b9980255cea3813845","last_reissued_at":"2026-05-18T04:14:54.720909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:54.720909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.3198","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":"2026-05-18T04:14:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uh4LIzm1cPkzQSdLtATALKo8u6juiiJesDNQ/2CrMCCuDmyPjSF3TMxfnIGLat1AZS7//czWhaW0qINyVXSnBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:01:18.784029Z"},"content_sha256":"fb21f4af4c52a060527f62172c227010cfeb6613ed298d3b9ca92be68fd62c2a","schema_version":"1.0","event_id":"sha256:fb21f4af4c52a060527f62172c227010cfeb6613ed298d3b9ca92be68fd62c2a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RWBHX2L5GRUKN63PNXPVWOJTMN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the average sensitivity of laced Boolean functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Jiyou Li","submitted_at":"2011-08-16T10:12:31Z","abstract_excerpt":"In this paper we obtain the average sensitivity of the laced Boolean functions. This confirms a conjecture of Shparlinski. We also compute the weights of the laced Boolean functions and show that they are almost balanced."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3198","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":"2026-05-18T04:14:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lDCtCHbCJZ0600dS3uLs0RojsokPUCqmFibxub19tnavSWKFC5G/w6Xh2pQf3+fwoczqRy9xFahAfL7rAl7GCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:01:18.784383Z"},"content_sha256":"f7a90efd1ab1c3f1d46ff229bb6141bb374e3bda077a835af9d472ed5a08a790","schema_version":"1.0","event_id":"sha256:f7a90efd1ab1c3f1d46ff229bb6141bb374e3bda077a835af9d472ed5a08a790"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RWBHX2L5GRUKN63PNXPVWOJTMN/bundle.json","state_url":"https://pith.science/pith/RWBHX2L5GRUKN63PNXPVWOJTMN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RWBHX2L5GRUKN63PNXPVWOJTMN/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":"2026-06-01T14:01:18Z","links":{"resolver":"https://pith.science/pith/RWBHX2L5GRUKN63PNXPVWOJTMN","bundle":"https://pith.science/pith/RWBHX2L5GRUKN63PNXPVWOJTMN/bundle.json","state":"https://pith.science/pith/RWBHX2L5GRUKN63PNXPVWOJTMN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RWBHX2L5GRUKN63PNXPVWOJTMN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RWBHX2L5GRUKN63PNXPVWOJTMN","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":"16026e5ff139416ae51bd99495f7b966f30dd52ff5b4b05829fdf9dd3ab60cbc","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-08-16T10:12:31Z","title_canon_sha256":"7c3b7b2380607d01a6dca0938b8cb370f474567c8629f6831d06a5b44e3d7a0a"},"schema_version":"1.0","source":{"id":"1108.3198","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3198","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3198v2","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3198","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"pith_short_12","alias_value":"RWBHX2L5GRUK","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RWBHX2L5GRUKN63P","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RWBHX2L5","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:f7a90efd1ab1c3f1d46ff229bb6141bb374e3bda077a835af9d472ed5a08a790","target":"graph","created_at":"2026-05-18T04:14:54Z","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 obtain the average sensitivity of the laced Boolean functions. This confirms a conjecture of Shparlinski. We also compute the weights of the laced Boolean functions and show that they are almost balanced.","authors_text":"Jiyou Li","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-08-16T10:12:31Z","title":"On the average sensitivity of laced Boolean functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3198","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:fb21f4af4c52a060527f62172c227010cfeb6613ed298d3b9ca92be68fd62c2a","target":"record","created_at":"2026-05-18T04:14:54Z","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":"16026e5ff139416ae51bd99495f7b966f30dd52ff5b4b05829fdf9dd3ab60cbc","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-08-16T10:12:31Z","title_canon_sha256":"7c3b7b2380607d01a6dca0938b8cb370f474567c8629f6831d06a5b44e3d7a0a"},"schema_version":"1.0","source":{"id":"1108.3198","kind":"arxiv","version":2}},"canonical_sha256":"8d827be97d3468a6fb6f6ddf5b3933637ae177a4fab0b4b9980255cea3813845","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d827be97d3468a6fb6f6ddf5b3933637ae177a4fab0b4b9980255cea3813845","first_computed_at":"2026-05-18T04:14:54.720909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:54.720909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bSA71yUsRhtMHgldLxed0yRYHK3fKko3dRq9PJr2lG6Trp1VKmHrt/VK3N2r68Han06bhzF+Ey3r9SwymcuoCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:54.721598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3198","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb21f4af4c52a060527f62172c227010cfeb6613ed298d3b9ca92be68fd62c2a","sha256:f7a90efd1ab1c3f1d46ff229bb6141bb374e3bda077a835af9d472ed5a08a790"],"state_sha256":"4d05d6435453f82e4eb75de7302f3792566df660a64635c669839d67937765c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H2Q/eZ/Rhodiydlsga8sUjcf/2dmV3H3nmDqBjw77KSJqxrOfGxQKxBJDmQkL8fFHmeg3eXlPDKvl0CQMgBSAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T14:01:18.786339Z","bundle_sha256":"7c909071d77b19ac6bd4a4149fbf4a82a27da66201e1880461681841d63e9a4f"}}