{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QON5L42KV57FLU2BDFQNRQS3ZG","short_pith_number":"pith:QON5L42K","canonical_record":{"source":{"id":"1809.10477","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-27T12:11:56Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"465447aeb03973eb00f811e08ed3ebc5f64b71e00a4ceec0e601fed8f11d7d05","abstract_canon_sha256":"35c4469a4592c17b43c4aec41bd6e13d955e14433f93c7fc0925b54b949e1cf3"},"schema_version":"1.0"},"canonical_sha256":"839bd5f34aaf7e55d3411960d8c25bc991a53a606fc87723c1766551c29129bc","source":{"kind":"arxiv","id":"1809.10477","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10477","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10477v1","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10477","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"QON5L42KV57F","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QON5L42KV57FLU2B","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QON5L42K","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QON5L42KV57FLU2BDFQNRQS3ZG","target":"record","payload":{"canonical_record":{"source":{"id":"1809.10477","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-27T12:11:56Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"465447aeb03973eb00f811e08ed3ebc5f64b71e00a4ceec0e601fed8f11d7d05","abstract_canon_sha256":"35c4469a4592c17b43c4aec41bd6e13d955e14433f93c7fc0925b54b949e1cf3"},"schema_version":"1.0"},"canonical_sha256":"839bd5f34aaf7e55d3411960d8c25bc991a53a606fc87723c1766551c29129bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:38.282056Z","signature_b64":"U6dFUxOjA84H6xRM74aYLXgQcyOMFjDM2WUptUrc5/AjOMyOgiDbICVxTDachVPq3AzEAOazVzPJY645eRDSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"839bd5f34aaf7e55d3411960d8c25bc991a53a606fc87723c1766551c29129bc","last_reissued_at":"2026-05-18T00:04:38.281539Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:38.281539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.10477","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":"2026-05-18T00:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"defnQ9JMHU7lpsmfef8zxu9G7+UMVCMT/SLBVLYOUKq1fBmIOiwbZtkO8/z+7++iPRnjFnpRy2T7P9xzdyDJBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:11:15.527025Z"},"content_sha256":"eae32d2ed7f747d0bf5d7db34ca0b28a1d90900dd9ea71c283c744db6b2dd331","schema_version":"1.0","event_id":"sha256:eae32d2ed7f747d0bf5d7db34ca0b28a1d90900dd9ea71c283c744db6b2dd331"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QON5L42KV57FLU2BDFQNRQS3ZG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast Stochastic Algorithms for Low-rank and Nonsmooth Matrix Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Atara Kaplan, Dan Garber","submitted_at":"2018-09-27T12:11:56Z","abstract_excerpt":"Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is simultaneously low-rank and sparse. However, such problems are highly challenging to solve in large-scale: the low-rank promoting term prohibits efficient implementations of proximal methods for composite optimization and even simple subgradient methods. On the other hand, methods which are tailored for low-rank optimization, such as conditional gradient-type m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10477","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":"2026-05-18T00:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"syeyjgJyKaZ91OXr8zEs5kQ/yYDyX9wRnqVGR3pkY44lqd3/9fdlgfwHhK2bunSi3cg+Lek7GVh0SLNGPQ5kBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:11:15.527393Z"},"content_sha256":"6129bc41436ffbc4dd976dbd0a31b2ea669dabc7b0853620373b44c18bd969a4","schema_version":"1.0","event_id":"sha256:6129bc41436ffbc4dd976dbd0a31b2ea669dabc7b0853620373b44c18bd969a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QON5L42KV57FLU2BDFQNRQS3ZG/bundle.json","state_url":"https://pith.science/pith/QON5L42KV57FLU2BDFQNRQS3ZG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QON5L42KV57FLU2BDFQNRQS3ZG/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":"2026-06-24T18:11:15Z","links":{"resolver":"https://pith.science/pith/QON5L42KV57FLU2BDFQNRQS3ZG","bundle":"https://pith.science/pith/QON5L42KV57FLU2BDFQNRQS3ZG/bundle.json","state":"https://pith.science/pith/QON5L42KV57FLU2BDFQNRQS3ZG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QON5L42KV57FLU2BDFQNRQS3ZG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QON5L42KV57FLU2BDFQNRQS3ZG","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":"35c4469a4592c17b43c4aec41bd6e13d955e14433f93c7fc0925b54b949e1cf3","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-27T12:11:56Z","title_canon_sha256":"465447aeb03973eb00f811e08ed3ebc5f64b71e00a4ceec0e601fed8f11d7d05"},"schema_version":"1.0","source":{"id":"1809.10477","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10477","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10477v1","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10477","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"QON5L42KV57F","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QON5L42KV57FLU2B","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QON5L42K","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:6129bc41436ffbc4dd976dbd0a31b2ea669dabc7b0853620373b44c18bd969a4","target":"graph","created_at":"2026-05-18T00:04:38Z","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":"Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is simultaneously low-rank and sparse. However, such problems are highly challenging to solve in large-scale: the low-rank promoting term prohibits efficient implementations of proximal methods for composite optimization and even simple subgradient methods. On the other hand, methods which are tailored for low-rank optimization, such as conditional gradient-type m","authors_text":"Atara Kaplan, Dan Garber","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-27T12:11:56Z","title":"Fast Stochastic Algorithms for Low-rank and Nonsmooth Matrix Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10477","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:eae32d2ed7f747d0bf5d7db34ca0b28a1d90900dd9ea71c283c744db6b2dd331","target":"record","created_at":"2026-05-18T00:04:38Z","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":"35c4469a4592c17b43c4aec41bd6e13d955e14433f93c7fc0925b54b949e1cf3","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-27T12:11:56Z","title_canon_sha256":"465447aeb03973eb00f811e08ed3ebc5f64b71e00a4ceec0e601fed8f11d7d05"},"schema_version":"1.0","source":{"id":"1809.10477","kind":"arxiv","version":1}},"canonical_sha256":"839bd5f34aaf7e55d3411960d8c25bc991a53a606fc87723c1766551c29129bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"839bd5f34aaf7e55d3411960d8c25bc991a53a606fc87723c1766551c29129bc","first_computed_at":"2026-05-18T00:04:38.281539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:38.281539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U6dFUxOjA84H6xRM74aYLXgQcyOMFjDM2WUptUrc5/AjOMyOgiDbICVxTDachVPq3AzEAOazVzPJY645eRDSBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:38.282056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10477","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eae32d2ed7f747d0bf5d7db34ca0b28a1d90900dd9ea71c283c744db6b2dd331","sha256:6129bc41436ffbc4dd976dbd0a31b2ea669dabc7b0853620373b44c18bd969a4"],"state_sha256":"3726ba09ceace0661be6ec704a2920f86f25b45c78e7316bd266a3759f309eda"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CzU3A6enwrfFMUJzC/tRZUQzWakXJKX3qum792sDNTsWCjckFLzE43O3CqO02FKUNEC/eR8GoFQ/g6GmoyPvCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:11:15.529379Z","bundle_sha256":"75af592e97337540e4f1d52012ac7ce84ec11b5e3f92766973e629b584601835"}}