{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UWQJ375JAZBPPP35DZRYHAUATW","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":"5a08ec7d7a03f574f2e254b0678736f7c35d3d208bf2e52867c507970d520ef7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-05T13:28:14Z","title_canon_sha256":"930d0547d4c7c4546ffaac288916e0ad43b781b71666d911abd29c23cb0874f8"},"schema_version":"1.0","source":{"id":"1007.0677","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0677","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0677v3","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0677","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"pith_short_12","alias_value":"UWQJ375JAZBP","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UWQJ375JAZBPPP35","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UWQJ375J","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:a73c4557be663d433558021e54921d5308c591ad45f48a0f8bc11e898b1cfbc2","target":"graph","created_at":"2026-05-18T04:16:53Z","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":"Let X_1,..., X_n be independent Bernoulli random variables and $f$ a function on {0,1}^n. In the well-known paper (Talagrand1994) Talagrand gave an upper bound for the variance of f in terms of the individual influences of the X_i's. This bound turned out to be very useful, for instance in percolation theory and related fields. In many situations a similar bound was needed for random variables taking more than two values. Generalizations of this type have indeed been obtained in the literature (see e.g. (Cordero-Erausquin2011), but the proofs are quite different from that in (Talagrand1994). T","authors_text":"Demeter Kiss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-05T13:28:14Z","title":"A note on Talagrand's variance bound in terms of influences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0677","kind":"arxiv","version":3},"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:e1003f277a1d12868fa3c2dc9c21aa10dcf6657ffb7a4e7c4f735ad9641059d6","target":"record","created_at":"2026-05-18T04:16:53Z","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":"5a08ec7d7a03f574f2e254b0678736f7c35d3d208bf2e52867c507970d520ef7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-05T13:28:14Z","title_canon_sha256":"930d0547d4c7c4546ffaac288916e0ad43b781b71666d911abd29c23cb0874f8"},"schema_version":"1.0","source":{"id":"1007.0677","kind":"arxiv","version":3}},"canonical_sha256":"a5a09dffa90642f7bf7d1e638382809d8b3e8259c5c8036e9d367e9c852ef65d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5a09dffa90642f7bf7d1e638382809d8b3e8259c5c8036e9d367e9c852ef65d","first_computed_at":"2026-05-18T04:16:53.627689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:53.627689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kmd7wZgiTvvx+kQUKv8pdjC0V60zCqIPI92otNe9cOR6+z4K8VwdiprMog/UKWiyxKsZQoAX9BhYrkJEhYLrCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:53.628100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0677","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1003f277a1d12868fa3c2dc9c21aa10dcf6657ffb7a4e7c4f735ad9641059d6","sha256:a73c4557be663d433558021e54921d5308c591ad45f48a0f8bc11e898b1cfbc2"],"state_sha256":"7c707de5df70fc417721ab454a71b97ee62be7bb2ac8a59b002500610058b835"}