{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:T6PBH5KSSILN3OFLZ3K75JUEWT","short_pith_number":"pith:T6PBH5KS","canonical_record":{"source":{"id":"1610.03278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-11T11:24:48Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"abb0e7cd4cae6ab8a019d3aedd1bc2be479a6aad386f2a50115e818476e1acdc","abstract_canon_sha256":"fbb195566fceae58a4b29d3ff42615cf42d9175fd0f9f172f81a8284e09aa255"},"schema_version":"1.0"},"canonical_sha256":"9f9e13f5529216ddb8abced5fea684b4de8eb8bfcaba325f48c7a72258a698cb","source":{"kind":"arxiv","id":"1610.03278","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03278","created_at":"2026-05-18T01:02:31Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03278v1","created_at":"2026-05-18T01:02:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03278","created_at":"2026-05-18T01:02:31Z"},{"alias_kind":"pith_short_12","alias_value":"T6PBH5KSSILN","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"T6PBH5KSSILN3OFL","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"T6PBH5KS","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:T6PBH5KSSILN3OFLZ3K75JUEWT","target":"record","payload":{"canonical_record":{"source":{"id":"1610.03278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-11T11:24:48Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"abb0e7cd4cae6ab8a019d3aedd1bc2be479a6aad386f2a50115e818476e1acdc","abstract_canon_sha256":"fbb195566fceae58a4b29d3ff42615cf42d9175fd0f9f172f81a8284e09aa255"},"schema_version":"1.0"},"canonical_sha256":"9f9e13f5529216ddb8abced5fea684b4de8eb8bfcaba325f48c7a72258a698cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:31.923497Z","signature_b64":"WipC9v34FMu3s7gsE/cZZ+1B76Zjd0aEWML7xFmiuVvNb/tAq6WsK6YiLhyq7+ztPhV9KXwSx6RU53u0V1zMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f9e13f5529216ddb8abced5fea684b4de8eb8bfcaba325f48c7a72258a698cb","last_reissued_at":"2026-05-18T01:02:31.923019Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:31.923019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.03278","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qTry7sMM28uEfxFWIIlvNo5dqYaB2F0L7GvLU/imNs2Qxwl+gKRG6FlFF7RLMqkR+LjaM4B1SF94lbGZwl+FAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:58:58.444206Z"},"content_sha256":"f499b4baad89aa77958a4f49b2c703793a2acd86ff4ae34abf4681a1639b45d2","schema_version":"1.0","event_id":"sha256:f499b4baad89aa77958a4f49b2c703793a2acd86ff4ae34abf4681a1639b45d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:T6PBH5KSSILN3OFLZ3K75JUEWT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On strict convergence of stochastic gradients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Michel Benaim","submitted_at":"2016-10-11T11:24:48Z","abstract_excerpt":"We discuss conditions ensuring the (strict) convergence of stochastic gradient algorithms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03278","kind":"arxiv","version":1},"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":"2026-05-18T01:02:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JqaFUi+8MFAalBJJG1OBPvBTs7/X/ofQLxnhkqUHoC4oP2WNc7Dp543fqRqSQHJ7ENzp/viD6EXP3Zr144hoAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:58:58.444901Z"},"content_sha256":"606dde2584761872b35101ceb3845e010c0a189762a8ee47d71992995252757d","schema_version":"1.0","event_id":"sha256:606dde2584761872b35101ceb3845e010c0a189762a8ee47d71992995252757d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T6PBH5KSSILN3OFLZ3K75JUEWT/bundle.json","state_url":"https://pith.science/pith/T6PBH5KSSILN3OFLZ3K75JUEWT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T6PBH5KSSILN3OFLZ3K75JUEWT/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":"2026-06-08T17:58:58Z","links":{"resolver":"https://pith.science/pith/T6PBH5KSSILN3OFLZ3K75JUEWT","bundle":"https://pith.science/pith/T6PBH5KSSILN3OFLZ3K75JUEWT/bundle.json","state":"https://pith.science/pith/T6PBH5KSSILN3OFLZ3K75JUEWT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T6PBH5KSSILN3OFLZ3K75JUEWT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:T6PBH5KSSILN3OFLZ3K75JUEWT","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":"fbb195566fceae58a4b29d3ff42615cf42d9175fd0f9f172f81a8284e09aa255","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-11T11:24:48Z","title_canon_sha256":"abb0e7cd4cae6ab8a019d3aedd1bc2be479a6aad386f2a50115e818476e1acdc"},"schema_version":"1.0","source":{"id":"1610.03278","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03278","created_at":"2026-05-18T01:02:31Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03278v1","created_at":"2026-05-18T01:02:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03278","created_at":"2026-05-18T01:02:31Z"},{"alias_kind":"pith_short_12","alias_value":"T6PBH5KSSILN","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"T6PBH5KSSILN3OFL","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"T6PBH5KS","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:606dde2584761872b35101ceb3845e010c0a189762a8ee47d71992995252757d","target":"graph","created_at":"2026-05-18T01:02:31Z","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 discuss conditions ensuring the (strict) convergence of stochastic gradient algorithms.","authors_text":"Michel Benaim","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-11T11:24:48Z","title":"On strict convergence of stochastic gradients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03278","kind":"arxiv","version":1},"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:f499b4baad89aa77958a4f49b2c703793a2acd86ff4ae34abf4681a1639b45d2","target":"record","created_at":"2026-05-18T01:02:31Z","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":"fbb195566fceae58a4b29d3ff42615cf42d9175fd0f9f172f81a8284e09aa255","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-11T11:24:48Z","title_canon_sha256":"abb0e7cd4cae6ab8a019d3aedd1bc2be479a6aad386f2a50115e818476e1acdc"},"schema_version":"1.0","source":{"id":"1610.03278","kind":"arxiv","version":1}},"canonical_sha256":"9f9e13f5529216ddb8abced5fea684b4de8eb8bfcaba325f48c7a72258a698cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f9e13f5529216ddb8abced5fea684b4de8eb8bfcaba325f48c7a72258a698cb","first_computed_at":"2026-05-18T01:02:31.923019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:31.923019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WipC9v34FMu3s7gsE/cZZ+1B76Zjd0aEWML7xFmiuVvNb/tAq6WsK6YiLhyq7+ztPhV9KXwSx6RU53u0V1zMDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:31.923497Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03278","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f499b4baad89aa77958a4f49b2c703793a2acd86ff4ae34abf4681a1639b45d2","sha256:606dde2584761872b35101ceb3845e010c0a189762a8ee47d71992995252757d"],"state_sha256":"835f5e8bdbc42037fc2beab61bb4790d0e48f2682a643b2be5b07725cc8fec7b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EWGHoUI9PIMkaJUmjn/5ad91wNANIzQrpvyEK91zG94FIqnyGBcIaBiaoTkDoaEai+QVshODeLuNftM4KPE3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:58:58.448727Z","bundle_sha256":"ae8cd05f98ca72cd806d5ec8fd5970ddb7704d67318ae0eee9ffbf8f2d6b9e74"}}