{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:RVLGJWWUZKDMEA5MDOTBQNIKV3","short_pith_number":"pith:RVLGJWWU","canonical_record":{"source":{"id":"1807.00255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-01T01:49:22Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"0a857e14652c7041776c51f683083aeb2e3a6f61f42636a6a767926328ed3e5c","abstract_canon_sha256":"99267b4dcd1cef52c98ae7353fd97bbd4931dc638905109ee39d7881071ed2dc"},"schema_version":"1.0"},"canonical_sha256":"8d5664dad4ca86c203ac1ba618350aaeeb2ef42f2fd98e99541581280cd5faa1","source":{"kind":"arxiv","id":"1807.00255","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00255","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00255v1","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00255","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"RVLGJWWUZKDM","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RVLGJWWUZKDMEA5M","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RVLGJWWU","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:RVLGJWWUZKDMEA5MDOTBQNIKV3","target":"record","payload":{"canonical_record":{"source":{"id":"1807.00255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-01T01:49:22Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"0a857e14652c7041776c51f683083aeb2e3a6f61f42636a6a767926328ed3e5c","abstract_canon_sha256":"99267b4dcd1cef52c98ae7353fd97bbd4931dc638905109ee39d7881071ed2dc"},"schema_version":"1.0"},"canonical_sha256":"8d5664dad4ca86c203ac1ba618350aaeeb2ef42f2fd98e99541581280cd5faa1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:55.531463Z","signature_b64":"jqUUqF/rcswIJQTpmNwtYBH2TsJmIRpFrcKH+ZJqg0lkg/NjuqaU2a2ICKNpWxktzLzfaR8c97JqQhVwG9b0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d5664dad4ca86c203ac1ba618350aaeeb2ef42f2fd98e99541581280cd5faa1","last_reissued_at":"2026-05-18T00:11:55.530949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:55.530949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.00255","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":"2026-05-18T00:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T6vkUUMJiws9eO4zEX2YDNe4zXyRpGDBU/OggZECw9dWbiX1JDsYQXc6q8GtfuuMk0UWWmBRntEtUwbZgJoDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T21:36:59.873582Z"},"content_sha256":"e9372c4cb8d73af8dea5d75df86b2ce4b13caf1f199163943600ca3204fd961f","schema_version":"1.0","event_id":"sha256:e9372c4cb8d73af8dea5d75df86b2ce4b13caf1f199163943600ca3204fd961f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:RVLGJWWUZKDMEA5MDOTBQNIKV3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic model-based minimization under high-order growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Damek Davis, Dmitriy Drusvyatskiy, Kellie J. MacPhee","submitted_at":"2018-07-01T01:49:22Z","abstract_excerpt":"Given a nonsmooth, nonconvex minimization problem, we consider algorithms that iteratively sample and minimize stochastic convex models of the objective function. Assuming that the one-sided approximation quality and the variation of the models is controlled by a Bregman divergence, we show that the scheme drives a natural stationarity measure to zero at the rate $O(k^{-1/4})$. Under additional convexity and relative strong convexity assumptions, the function values converge to the minimum at the rate of $O(k^{-1/2})$ and $\\widetilde{O}(k^{-1})$, respectively. We discuss consequences for stoch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00255","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":"2026-05-18T00:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NID6Q0TB2DMtVXB4FxZRmgAPJDspB/WRJFkX2w/qruONn4QNMNEqDV40YgRp8FQkhB1UgXVdBzxeAQ9Fsdn6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T21:36:59.873922Z"},"content_sha256":"7c953b4f69be609dee01247d2a4d7b60399b5d8263d350f4e982351fba988006","schema_version":"1.0","event_id":"sha256:7c953b4f69be609dee01247d2a4d7b60399b5d8263d350f4e982351fba988006"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3/bundle.json","state_url":"https://pith.science/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3/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":"2026-06-27T21:36:59Z","links":{"resolver":"https://pith.science/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3","bundle":"https://pith.science/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3/bundle.json","state":"https://pith.science/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RVLGJWWUZKDMEA5MDOTBQNIKV3","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":"99267b4dcd1cef52c98ae7353fd97bbd4931dc638905109ee39d7881071ed2dc","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-01T01:49:22Z","title_canon_sha256":"0a857e14652c7041776c51f683083aeb2e3a6f61f42636a6a767926328ed3e5c"},"schema_version":"1.0","source":{"id":"1807.00255","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00255","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00255v1","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00255","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"RVLGJWWUZKDM","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RVLGJWWUZKDMEA5M","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RVLGJWWU","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:7c953b4f69be609dee01247d2a4d7b60399b5d8263d350f4e982351fba988006","target":"graph","created_at":"2026-05-18T00:11:55Z","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":"Given a nonsmooth, nonconvex minimization problem, we consider algorithms that iteratively sample and minimize stochastic convex models of the objective function. Assuming that the one-sided approximation quality and the variation of the models is controlled by a Bregman divergence, we show that the scheme drives a natural stationarity measure to zero at the rate $O(k^{-1/4})$. Under additional convexity and relative strong convexity assumptions, the function values converge to the minimum at the rate of $O(k^{-1/2})$ and $\\widetilde{O}(k^{-1})$, respectively. We discuss consequences for stoch","authors_text":"Damek Davis, Dmitriy Drusvyatskiy, Kellie J. MacPhee","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-01T01:49:22Z","title":"Stochastic model-based minimization under high-order growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00255","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:e9372c4cb8d73af8dea5d75df86b2ce4b13caf1f199163943600ca3204fd961f","target":"record","created_at":"2026-05-18T00:11:55Z","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":"99267b4dcd1cef52c98ae7353fd97bbd4931dc638905109ee39d7881071ed2dc","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-01T01:49:22Z","title_canon_sha256":"0a857e14652c7041776c51f683083aeb2e3a6f61f42636a6a767926328ed3e5c"},"schema_version":"1.0","source":{"id":"1807.00255","kind":"arxiv","version":1}},"canonical_sha256":"8d5664dad4ca86c203ac1ba618350aaeeb2ef42f2fd98e99541581280cd5faa1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d5664dad4ca86c203ac1ba618350aaeeb2ef42f2fd98e99541581280cd5faa1","first_computed_at":"2026-05-18T00:11:55.530949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:55.530949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jqUUqF/rcswIJQTpmNwtYBH2TsJmIRpFrcKH+ZJqg0lkg/NjuqaU2a2ICKNpWxktzLzfaR8c97JqQhVwG9b0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:55.531463Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.00255","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9372c4cb8d73af8dea5d75df86b2ce4b13caf1f199163943600ca3204fd961f","sha256:7c953b4f69be609dee01247d2a4d7b60399b5d8263d350f4e982351fba988006"],"state_sha256":"4cc49664c8df6109fb3c84b48785770757e5769db22415905bb819dee23d0f9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"23qmMtvRf+LsgoT5T5VCjJb7Km6kibeGjzAEIjem3mPkIb7NMdo+2vLHopHJ2rTBrPGVZ/xvuMVCzirHbdroBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T21:36:59.875783Z","bundle_sha256":"e2aec902204ddbf9fae9f7b6ca031cfb56ee50108f29715329623c642a207bc6"}}