{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:EWABZZXU4G2UPAXPVU4GZV6E7C","short_pith_number":"pith:EWABZZXU","canonical_record":{"source":{"id":"1204.3730","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-17T08:52:35Z","cross_cats_sorted":[],"title_canon_sha256":"6076e3285818fc84d774a41f48dcd93dbd741334c2ae6900d744bb79875f7356","abstract_canon_sha256":"a4e7e8fb4bc347aa43f9325aeba6ebbcd0fadfdcb77c27a9c68b969efa1b864c"},"schema_version":"1.0"},"canonical_sha256":"25801ce6f4e1b54782efad386cd7c4f8bc2f28c0a86ed3854602fc91bb37225a","source":{"kind":"arxiv","id":"1204.3730","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3730","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3730v3","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3730","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"EWABZZXU4G2U","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EWABZZXU4G2UPAXP","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EWABZZXU","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:EWABZZXU4G2UPAXPVU4GZV6E7C","target":"record","payload":{"canonical_record":{"source":{"id":"1204.3730","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-17T08:52:35Z","cross_cats_sorted":[],"title_canon_sha256":"6076e3285818fc84d774a41f48dcd93dbd741334c2ae6900d744bb79875f7356","abstract_canon_sha256":"a4e7e8fb4bc347aa43f9325aeba6ebbcd0fadfdcb77c27a9c68b969efa1b864c"},"schema_version":"1.0"},"canonical_sha256":"25801ce6f4e1b54782efad386cd7c4f8bc2f28c0a86ed3854602fc91bb37225a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:46.199152Z","signature_b64":"U8R2ThNU4RMlk1GOxn7iPzZQsStN2dqcRSPUzA3pIDzHB8SWF7daF+GH7KjQmGEea/wSjerM1geRS1+C9k+sBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25801ce6f4e1b54782efad386cd7c4f8bc2f28c0a86ed3854602fc91bb37225a","last_reissued_at":"2026-05-18T03:38:46.198255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:46.198255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.3730","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0B4p+hg1UCl6fxVXCGaj0K1l1kf5AAGBNMJwY/pgf5Y71IuLVkWj9VqmzjPOt7idpf0HV7WEchmWeBpy1prIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:42:35.499680Z"},"content_sha256":"ac3a60c82164aa12977a6edb9513e02cc759b3d2b8ee2d85dbc02088b98096bd","schema_version":"1.0","event_id":"sha256:ac3a60c82164aa12977a6edb9513e02cc759b3d2b8ee2d85dbc02088b98096bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:EWABZZXU4G2UPAXPVU4GZV6E7C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Concentration Bounds for Stochastic Approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Noufel Frikha (LPMA), Stephane Menozzi","submitted_at":"2012-04-17T08:52:35Z","abstract_excerpt":"We obtain non asymptotic concentration bounds for two kinds of stochastic approximations. We first consider the deviations between the expectation of a given function of the Euler scheme of some diffusion process at a fixed deterministic time and its empirical mean obtained by the Monte-Carlo procedure. We then give some estimates concerning the deviation between the value at a given time-step of a stochastic approximation algorithm and its target. Under suitable assumptions both concentration bounds turn out to be Gaussian. The key tool consists in exploiting accurately the concentration prop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3730","kind":"arxiv","version":3},"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":"2026-05-18T03:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZLuhIPvdRRbjpS1KHLk9C9QVyOUrXhClZW1QOtKy8SAK1DinCMtgMbN2k585GyMpgVb0Jg41Iw1iw1Mtg3sCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:42:35.500024Z"},"content_sha256":"83f714214cf09f0a6427662c34276a30e31ad715b42b92ec1e0b050a1d4365a3","schema_version":"1.0","event_id":"sha256:83f714214cf09f0a6427662c34276a30e31ad715b42b92ec1e0b050a1d4365a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EWABZZXU4G2UPAXPVU4GZV6E7C/bundle.json","state_url":"https://pith.science/pith/EWABZZXU4G2UPAXPVU4GZV6E7C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EWABZZXU4G2UPAXPVU4GZV6E7C/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":"2026-06-03T00:42:35Z","links":{"resolver":"https://pith.science/pith/EWABZZXU4G2UPAXPVU4GZV6E7C","bundle":"https://pith.science/pith/EWABZZXU4G2UPAXPVU4GZV6E7C/bundle.json","state":"https://pith.science/pith/EWABZZXU4G2UPAXPVU4GZV6E7C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EWABZZXU4G2UPAXPVU4GZV6E7C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EWABZZXU4G2UPAXPVU4GZV6E7C","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":"a4e7e8fb4bc347aa43f9325aeba6ebbcd0fadfdcb77c27a9c68b969efa1b864c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-17T08:52:35Z","title_canon_sha256":"6076e3285818fc84d774a41f48dcd93dbd741334c2ae6900d744bb79875f7356"},"schema_version":"1.0","source":{"id":"1204.3730","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3730","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3730v3","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3730","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"EWABZZXU4G2U","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EWABZZXU4G2UPAXP","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EWABZZXU","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:83f714214cf09f0a6427662c34276a30e31ad715b42b92ec1e0b050a1d4365a3","target":"graph","created_at":"2026-05-18T03:38:46Z","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 obtain non asymptotic concentration bounds for two kinds of stochastic approximations. We first consider the deviations between the expectation of a given function of the Euler scheme of some diffusion process at a fixed deterministic time and its empirical mean obtained by the Monte-Carlo procedure. We then give some estimates concerning the deviation between the value at a given time-step of a stochastic approximation algorithm and its target. Under suitable assumptions both concentration bounds turn out to be Gaussian. The key tool consists in exploiting accurately the concentration prop","authors_text":"Noufel Frikha (LPMA), Stephane Menozzi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-17T08:52:35Z","title":"Concentration Bounds for Stochastic Approximations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3730","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:ac3a60c82164aa12977a6edb9513e02cc759b3d2b8ee2d85dbc02088b98096bd","target":"record","created_at":"2026-05-18T03:38:46Z","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":"a4e7e8fb4bc347aa43f9325aeba6ebbcd0fadfdcb77c27a9c68b969efa1b864c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-17T08:52:35Z","title_canon_sha256":"6076e3285818fc84d774a41f48dcd93dbd741334c2ae6900d744bb79875f7356"},"schema_version":"1.0","source":{"id":"1204.3730","kind":"arxiv","version":3}},"canonical_sha256":"25801ce6f4e1b54782efad386cd7c4f8bc2f28c0a86ed3854602fc91bb37225a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25801ce6f4e1b54782efad386cd7c4f8bc2f28c0a86ed3854602fc91bb37225a","first_computed_at":"2026-05-18T03:38:46.198255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:46.198255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U8R2ThNU4RMlk1GOxn7iPzZQsStN2dqcRSPUzA3pIDzHB8SWF7daF+GH7KjQmGEea/wSjerM1geRS1+C9k+sBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:46.199152Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3730","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac3a60c82164aa12977a6edb9513e02cc759b3d2b8ee2d85dbc02088b98096bd","sha256:83f714214cf09f0a6427662c34276a30e31ad715b42b92ec1e0b050a1d4365a3"],"state_sha256":"4c04dd398b11af620c4a5bf66c1398814f85d93f2ba3305001cc92b916e658da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lwZ7tSw/t5+AX4Nvi7+ITsZr1YWxSF9fFEB1/dXhX5EHWBhR6UqOaSRqIkmPNO/BsDCtsO9EMozrEjT0xTB+DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:42:35.501981Z","bundle_sha256":"532320f0be1d1d863d679cdd340a205e428d70f1e85231f1031296d95a036089"}}