{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EKLHGH5BXTKOYYPJ2U72VXECOT","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":"ceee28dcdbb53b18f19b840ef08c101eeece27cb70357dceace30242414f925c","cross_cats_sorted":["math.IT","q-bio.MN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-09-27T16:36:20Z","title_canon_sha256":"e4094b9dd1564569760d44f7aa1b4616894d546ba8eae488cb6e442d4c36c8df"},"schema_version":"1.0","source":{"id":"1209.6277","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.6277","created_at":"2026-05-18T01:54:13Z"},{"alias_kind":"arxiv_version","alias_value":"1209.6277v4","created_at":"2026-05-18T01:54:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6277","created_at":"2026-05-18T01:54:13Z"},{"alias_kind":"pith_short_12","alias_value":"EKLHGH5BXTKO","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EKLHGH5BXTKOYYPJ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EKLHGH5B","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:f90a6feaa9bef0f1fe41fff8b682895f533e792cc46b4fb4db6d9c1a0342f370","target":"graph","created_at":"2026-05-18T01:54:13Z","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":"Nested canalizing Boolean (NCF) functions play an important role in biological motivated regulative networks and in signal processing, in particular describing stack filters. It has been conjectured that NCFs have a stabilizing effect on the network dynamics. It is well known that the average sensitivity plays a central role for the stability of (random) Boolean networks. Here we provide a tight upper bound on the average sensitivity for NCFs as a function of the number of relevant input variables. As conjectured in literature this bound is smaller than 4/3 This shows that a large number of fu","authors_text":"Johannes Georg Klotz, Reinhard Heckel, Steffen Schober","cross_cats":["math.IT","q-bio.MN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-09-27T16:36:20Z","title":"Bounds on the Average Sensitivity of Nested Canalizing Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6277","kind":"arxiv","version":4},"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:f8b9b538e24eb3a3742adecf2c41fa9055ac71374112b64a62af2bbeb7db3bd9","target":"record","created_at":"2026-05-18T01:54:13Z","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":"ceee28dcdbb53b18f19b840ef08c101eeece27cb70357dceace30242414f925c","cross_cats_sorted":["math.IT","q-bio.MN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-09-27T16:36:20Z","title_canon_sha256":"e4094b9dd1564569760d44f7aa1b4616894d546ba8eae488cb6e442d4c36c8df"},"schema_version":"1.0","source":{"id":"1209.6277","kind":"arxiv","version":4}},"canonical_sha256":"2296731fa1bcd4ec61e9d53faadc8274cdf2f9d2fb13e944c293a01965658f89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2296731fa1bcd4ec61e9d53faadc8274cdf2f9d2fb13e944c293a01965658f89","first_computed_at":"2026-05-18T01:54:13.236099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:54:13.236099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N66GkNi1/6iA8DRwk8O1UnMG7R8ucdAtJYZu9vE542d6H6CnU9w3VeMnIaqzGy43K7cXrZ7js1Q3ef0ZZ/YXDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:54:13.236651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.6277","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8b9b538e24eb3a3742adecf2c41fa9055ac71374112b64a62af2bbeb7db3bd9","sha256:f90a6feaa9bef0f1fe41fff8b682895f533e792cc46b4fb4db6d9c1a0342f370"],"state_sha256":"f312a1855cdcd08828d38a2179590027d39d45f5b0bbc2be2c341fdb1b9c2c92"}