{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6VOUQMRM6SDY4Z7OS2K5P5B3IE","short_pith_number":"pith:6VOUQMRM","canonical_record":{"source":{"id":"1501.06711","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-27T09:35:57Z","cross_cats_sorted":[],"title_canon_sha256":"d93cbfa58289d55e2b03cd901dd96ea929753cee3a0d22b02402dfce8da01a3e","abstract_canon_sha256":"9961392d6eb3b569ca832e37d77bb3273a3373bff0c611bfc03fe030a29de337"},"schema_version":"1.0"},"canonical_sha256":"f55d48322cf4878e67ee9695d7f43b410deccd4cd53843acc895d837bcad3edc","source":{"kind":"arxiv","id":"1501.06711","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06711","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06711v4","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06711","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"6VOUQMRM6SDY","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6VOUQMRM6SDY4Z7O","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6VOUQMRM","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6VOUQMRM6SDY4Z7OS2K5P5B3IE","target":"record","payload":{"canonical_record":{"source":{"id":"1501.06711","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-27T09:35:57Z","cross_cats_sorted":[],"title_canon_sha256":"d93cbfa58289d55e2b03cd901dd96ea929753cee3a0d22b02402dfce8da01a3e","abstract_canon_sha256":"9961392d6eb3b569ca832e37d77bb3273a3373bff0c611bfc03fe030a29de337"},"schema_version":"1.0"},"canonical_sha256":"f55d48322cf4878e67ee9695d7f43b410deccd4cd53843acc895d837bcad3edc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:53.414965Z","signature_b64":"GOXWSYlXmwtwv1phKuufBgqpnHDgA4JMU1wS/xZ+aJK8A5dz17dCeKUOUO7O3R7bScJ9znLMK/9zgZ/eyToIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f55d48322cf4878e67ee9695d7f43b410deccd4cd53843acc895d837bcad3edc","last_reissued_at":"2026-05-18T01:03:53.414304Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:53.414304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.06711","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"apfQmxCu+ZgBXGSjE55xso7xDggnwid/rKrCvtD3ZuHZ5r1LsKKAZfswd2mI/DfTzqs6053RTKw//h5oF/AoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:16:50.046362Z"},"content_sha256":"fd4e241c87737a42745d6a7ab2c645ceb34f9ee9cee571e4ee7e93e2a1ca6b03","schema_version":"1.0","event_id":"sha256:fd4e241c87737a42745d6a7ab2c645ceb34f9ee9cee571e4ee7e93e2a1ca6b03"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6VOUQMRM6SDY4Z7OS2K5P5B3IE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decomposable Norm Minimization with Proximal-Gradient Homotopy Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Maryam Fazel, Reza Eghbali","submitted_at":"2015-01-27T09:35:57Z","abstract_excerpt":"We study the convergence rate of the proximal-gradient homotopy algorithm applied to norm-regularized linear least squares problems, for a general class of norms. The homotopy algorithm reduces the regularization parameter in a series of steps, and uses a proximal-gradient algorithm to solve the problem at each step. Proximal-gradient algorithm has a linear rate of convergence given that the objective function is strongly convex, and the gradient of the smooth component of the objective function is Lipschitz continuous. In many applications, the objective function in this type of problem is no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06711","kind":"arxiv","version":4},"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":"2026-05-18T01:03:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y9tJFqMjmJAgmD+8FvlT1MdYrTZxaAoXSc8AAP1YJrd1rJYIWTlBBO6Bpwr0CJVyIU1emUPAPTXFSbcD4kJeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:16:50.047000Z"},"content_sha256":"3faca17c01da74e38337b6d424436ee214ebdef1dc27bc3e78f319c34ca2c4f0","schema_version":"1.0","event_id":"sha256:3faca17c01da74e38337b6d424436ee214ebdef1dc27bc3e78f319c34ca2c4f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6VOUQMRM6SDY4Z7OS2K5P5B3IE/bundle.json","state_url":"https://pith.science/pith/6VOUQMRM6SDY4Z7OS2K5P5B3IE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6VOUQMRM6SDY4Z7OS2K5P5B3IE/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":"2026-05-31T17:16:50Z","links":{"resolver":"https://pith.science/pith/6VOUQMRM6SDY4Z7OS2K5P5B3IE","bundle":"https://pith.science/pith/6VOUQMRM6SDY4Z7OS2K5P5B3IE/bundle.json","state":"https://pith.science/pith/6VOUQMRM6SDY4Z7OS2K5P5B3IE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6VOUQMRM6SDY4Z7OS2K5P5B3IE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6VOUQMRM6SDY4Z7OS2K5P5B3IE","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":"9961392d6eb3b569ca832e37d77bb3273a3373bff0c611bfc03fe030a29de337","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-27T09:35:57Z","title_canon_sha256":"d93cbfa58289d55e2b03cd901dd96ea929753cee3a0d22b02402dfce8da01a3e"},"schema_version":"1.0","source":{"id":"1501.06711","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06711","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06711v4","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06711","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"6VOUQMRM6SDY","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6VOUQMRM6SDY4Z7O","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6VOUQMRM","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:3faca17c01da74e38337b6d424436ee214ebdef1dc27bc3e78f319c34ca2c4f0","target":"graph","created_at":"2026-05-18T01:03:53Z","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 study the convergence rate of the proximal-gradient homotopy algorithm applied to norm-regularized linear least squares problems, for a general class of norms. The homotopy algorithm reduces the regularization parameter in a series of steps, and uses a proximal-gradient algorithm to solve the problem at each step. Proximal-gradient algorithm has a linear rate of convergence given that the objective function is strongly convex, and the gradient of the smooth component of the objective function is Lipschitz continuous. In many applications, the objective function in this type of problem is no","authors_text":"Maryam Fazel, Reza Eghbali","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-27T09:35:57Z","title":"Decomposable Norm Minimization with Proximal-Gradient Homotopy Algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06711","kind":"arxiv","version":4},"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:fd4e241c87737a42745d6a7ab2c645ceb34f9ee9cee571e4ee7e93e2a1ca6b03","target":"record","created_at":"2026-05-18T01:03:53Z","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":"9961392d6eb3b569ca832e37d77bb3273a3373bff0c611bfc03fe030a29de337","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-27T09:35:57Z","title_canon_sha256":"d93cbfa58289d55e2b03cd901dd96ea929753cee3a0d22b02402dfce8da01a3e"},"schema_version":"1.0","source":{"id":"1501.06711","kind":"arxiv","version":4}},"canonical_sha256":"f55d48322cf4878e67ee9695d7f43b410deccd4cd53843acc895d837bcad3edc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f55d48322cf4878e67ee9695d7f43b410deccd4cd53843acc895d837bcad3edc","first_computed_at":"2026-05-18T01:03:53.414304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:53.414304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GOXWSYlXmwtwv1phKuufBgqpnHDgA4JMU1wS/xZ+aJK8A5dz17dCeKUOUO7O3R7bScJ9znLMK/9zgZ/eyToIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:53.414965Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06711","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd4e241c87737a42745d6a7ab2c645ceb34f9ee9cee571e4ee7e93e2a1ca6b03","sha256:3faca17c01da74e38337b6d424436ee214ebdef1dc27bc3e78f319c34ca2c4f0"],"state_sha256":"4c5804f488cc37e7ecfb1c79592920669b715d6221c74c8ddd66ae73f685f8c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OZ2YqMoj5fGwI6PAcySZ9cBZmY8TXRjIu27KV4gu8/vI+PQezyBOpG0yHuLiiBzQOFUd3vASybmjKbwvFXgiAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T17:16:50.050670Z","bundle_sha256":"924a82150e1852aa003f49a94fe244ad1db1be3fae8acc977eeab4640792ac53"}}