{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2RGH7RJDZMA7QBZXCNG5ZVCDTD","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":"aebdca54beb29fa021df72a9413d79c34e057900efd052a229bed3a576dc5b74","cross_cats_sorted":["cs.LG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-02-16T05:43:31Z","title_canon_sha256":"cb2fce1f91bd1665782be7d64bb230707a8b49c9323d16ce0414e508c9a4027a"},"schema_version":"1.0","source":{"id":"1602.04915","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04915","created_at":"2026-05-18T01:19:38Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04915v2","created_at":"2026-05-18T01:19:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04915","created_at":"2026-05-18T01:19:38Z"},{"alias_kind":"pith_short_12","alias_value":"2RGH7RJDZMA7","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2RGH7RJDZMA7QBZX","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2RGH7RJD","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:129ae7652e9171a0b26479fda3a5c3dfe3b0171ce35a95bceccd87f76ee6b66e","target":"graph","created_at":"2026-05-18T01:19:38Z","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 gradient descent converges to a local minimizer, almost surely with random initialization. This is proved by applying the Stable Manifold Theorem from dynamical systems theory.","authors_text":"Benjamin Recht, Jason D. Lee, Max Simchowitz, Michael I. Jordan","cross_cats":["cs.LG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-02-16T05:43:31Z","title":"Gradient Descent Converges to Minimizers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04915","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":"sha256:0db55f0e734a0cb067989729fe642884e86e84658b1fbe1afad47077009fef27","target":"record","created_at":"2026-05-18T01:19:38Z","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":"aebdca54beb29fa021df72a9413d79c34e057900efd052a229bed3a576dc5b74","cross_cats_sorted":["cs.LG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-02-16T05:43:31Z","title_canon_sha256":"cb2fce1f91bd1665782be7d64bb230707a8b49c9323d16ce0414e508c9a4027a"},"schema_version":"1.0","source":{"id":"1602.04915","kind":"arxiv","version":2}},"canonical_sha256":"d44c7fc523cb01f80737134ddcd44398ee5e899e35c0681b57773165c48b4c10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d44c7fc523cb01f80737134ddcd44398ee5e899e35c0681b57773165c48b4c10","first_computed_at":"2026-05-18T01:19:38.145161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:38.145161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6MYwu5lLa5XeQQqHkG+5SqnXSjZuF2714ayJSkGw70bUhwsHjuhe8lHkZDZ+NKRrcDtJdaYapmsR4hYXWgMODA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:38.145814Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04915","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0db55f0e734a0cb067989729fe642884e86e84658b1fbe1afad47077009fef27","sha256:129ae7652e9171a0b26479fda3a5c3dfe3b0171ce35a95bceccd87f76ee6b66e"],"state_sha256":"84c47b0d876368e4ab5b814b126ac760e3ffa6231fa60f4a99695fa2ebea38e6"}