{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5D2BMQ443OUQM3CJZ6JYSV7NNY","short_pith_number":"pith:5D2BMQ44","canonical_record":{"source":{"id":"1109.5193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-23T20:27:58Z","cross_cats_sorted":[],"title_canon_sha256":"14c8f5774364d362e257a09ab7cd588792b060607c1b456654dd47fa6bbc4a71","abstract_canon_sha256":"3f127c0afc6943454a44b508edad88d423075702d90e5df8df6842739ebfbf63"},"schema_version":"1.0"},"canonical_sha256":"e8f416439cdba9066c49cf938957ed6e1f58e3da7cc7990edc29fc011f14465d","source":{"kind":"arxiv","id":"1109.5193","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5193","created_at":"2026-05-18T03:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5193v2","created_at":"2026-05-18T03:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5193","created_at":"2026-05-18T03:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"5D2BMQ443OUQ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5D2BMQ443OUQM3CJ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5D2BMQ44","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5D2BMQ443OUQM3CJZ6JYSV7NNY","target":"record","payload":{"canonical_record":{"source":{"id":"1109.5193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-23T20:27:58Z","cross_cats_sorted":[],"title_canon_sha256":"14c8f5774364d362e257a09ab7cd588792b060607c1b456654dd47fa6bbc4a71","abstract_canon_sha256":"3f127c0afc6943454a44b508edad88d423075702d90e5df8df6842739ebfbf63"},"schema_version":"1.0"},"canonical_sha256":"e8f416439cdba9066c49cf938957ed6e1f58e3da7cc7990edc29fc011f14465d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:04.378669Z","signature_b64":"e77OKusasMjVKN0d2MgvY0TbxC5+Ciz6VDk0wkb+jKvAQ2BG75Z0BsKVd3VAxMmuj+EGXWG0vFYUqm9Xfgv3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8f416439cdba9066c49cf938957ed6e1f58e3da7cc7990edc29fc011f14465d","last_reissued_at":"2026-05-18T03:54:04.378055Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:04.378055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.5193","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":"2026-05-18T03:54:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8rS6pUFeoOunmmw5kfDObUGIMzMuPjYZ9l0iFp6wj/BDvhePGsX+1F++mMo8XuKxrH8IoAxjmvkIrtSB/grwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:15:03.689707Z"},"content_sha256":"a7862bf6145bffd35df6adddfd376db925889de7eebc30ea302e23f2d58737f2","schema_version":"1.0","event_id":"sha256:a7862bf6145bffd35df6adddfd376db925889de7eebc30ea302e23f2d58737f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5D2BMQ443OUQM3CJZ6JYSV7NNY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bernstein-like Concentration and Moment Inequalities for Polynomials of Independent Random Variables: Multilinear Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Maxim Sviridenko, Warren Schudy","submitted_at":"2011-09-23T20:27:58Z","abstract_excerpt":"We show that the probability that a multilinear polynomial $f$ of independent random variables exceeds its mean by $\\lambda$ is at most $e^{-\\lambda^2 / (R^q Var(f))}$ for sufficiently small $\\lambda$, where $R$ is an absolute constant. This matches (up to constants in the exponent) what one would expect from the central limit theorem. Our methods handle a variety of types of random variables including Gaussian, Boolean, exponential, and Poisson. Previous work by Kim-Vu and Schudy-Sviridenko gave bounds of the same form that involved less natural parameters in place of the variance."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5193","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":"2026-05-18T03:54:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YdMAy/lxUHLQ8smy7iFS2pG6/hfAvRQHIGhxTcJ1oIjz4F2iPxfEdcGzP5ngr/NcZeKbpyTTprd7OgjUcxdmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:15:03.690053Z"},"content_sha256":"09c4ded9ad6b07d53fbfe4fa3f3fdce0167e01129811ad7959705a48c773dd1b","schema_version":"1.0","event_id":"sha256:09c4ded9ad6b07d53fbfe4fa3f3fdce0167e01129811ad7959705a48c773dd1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5D2BMQ443OUQM3CJZ6JYSV7NNY/bundle.json","state_url":"https://pith.science/pith/5D2BMQ443OUQM3CJZ6JYSV7NNY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5D2BMQ443OUQM3CJZ6JYSV7NNY/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":"2026-06-01T19:15:03Z","links":{"resolver":"https://pith.science/pith/5D2BMQ443OUQM3CJZ6JYSV7NNY","bundle":"https://pith.science/pith/5D2BMQ443OUQM3CJZ6JYSV7NNY/bundle.json","state":"https://pith.science/pith/5D2BMQ443OUQM3CJZ6JYSV7NNY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5D2BMQ443OUQM3CJZ6JYSV7NNY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5D2BMQ443OUQM3CJZ6JYSV7NNY","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":"3f127c0afc6943454a44b508edad88d423075702d90e5df8df6842739ebfbf63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-23T20:27:58Z","title_canon_sha256":"14c8f5774364d362e257a09ab7cd588792b060607c1b456654dd47fa6bbc4a71"},"schema_version":"1.0","source":{"id":"1109.5193","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5193","created_at":"2026-05-18T03:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5193v2","created_at":"2026-05-18T03:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5193","created_at":"2026-05-18T03:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"5D2BMQ443OUQ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5D2BMQ443OUQM3CJ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5D2BMQ44","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:09c4ded9ad6b07d53fbfe4fa3f3fdce0167e01129811ad7959705a48c773dd1b","target":"graph","created_at":"2026-05-18T03:54:04Z","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 show that the probability that a multilinear polynomial $f$ of independent random variables exceeds its mean by $\\lambda$ is at most $e^{-\\lambda^2 / (R^q Var(f))}$ for sufficiently small $\\lambda$, where $R$ is an absolute constant. This matches (up to constants in the exponent) what one would expect from the central limit theorem. Our methods handle a variety of types of random variables including Gaussian, Boolean, exponential, and Poisson. Previous work by Kim-Vu and Schudy-Sviridenko gave bounds of the same form that involved less natural parameters in place of the variance.","authors_text":"Maxim Sviridenko, Warren Schudy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-23T20:27:58Z","title":"Bernstein-like Concentration and Moment Inequalities for Polynomials of Independent Random Variables: Multilinear Case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5193","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:a7862bf6145bffd35df6adddfd376db925889de7eebc30ea302e23f2d58737f2","target":"record","created_at":"2026-05-18T03:54:04Z","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":"3f127c0afc6943454a44b508edad88d423075702d90e5df8df6842739ebfbf63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-23T20:27:58Z","title_canon_sha256":"14c8f5774364d362e257a09ab7cd588792b060607c1b456654dd47fa6bbc4a71"},"schema_version":"1.0","source":{"id":"1109.5193","kind":"arxiv","version":2}},"canonical_sha256":"e8f416439cdba9066c49cf938957ed6e1f58e3da7cc7990edc29fc011f14465d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8f416439cdba9066c49cf938957ed6e1f58e3da7cc7990edc29fc011f14465d","first_computed_at":"2026-05-18T03:54:04.378055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:04.378055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e77OKusasMjVKN0d2MgvY0TbxC5+Ciz6VDk0wkb+jKvAQ2BG75Z0BsKVd3VAxMmuj+EGXWG0vFYUqm9Xfgv3Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:04.378669Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5193","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7862bf6145bffd35df6adddfd376db925889de7eebc30ea302e23f2d58737f2","sha256:09c4ded9ad6b07d53fbfe4fa3f3fdce0167e01129811ad7959705a48c773dd1b"],"state_sha256":"268661b26bc1a2400a483a50b2f24b8082334ac2557f8e109314a1caadc622e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ww//WQ4YAeaPElNrStxRz6c+TJUm82yOB2lNIvL+oGfN0/Y79SvnR8Tx/i48AIN+3DRT6PdX6sIoer3JRHVnCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:15:03.691994Z","bundle_sha256":"3b51fd76655015aa61096bd18ae64f5e7239f5efb1b0038a04874b0936d17ddf"}}