{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:J2MY44UDZTZTZIECCETRMXJOL6","short_pith_number":"pith:J2MY44UD","canonical_record":{"source":{"id":"1503.03703","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-12T13:11:45Z","cross_cats_sorted":[],"title_canon_sha256":"1a9821a4bd67deddcc03f82532cc0ab46f7a94d5d5e212a675f09adacdadd5f3","abstract_canon_sha256":"090140082f04170e73a7b076596b2397a1cc343c51cc2651e391d2000ec8d089"},"schema_version":"1.0"},"canonical_sha256":"4e998e7283ccf33ca0821127165d2e5f89199d1522b8d591c9e87056c27b22b7","source":{"kind":"arxiv","id":"1503.03703","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03703","created_at":"2026-05-18T00:26:52Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03703v8","created_at":"2026-05-18T00:26:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03703","created_at":"2026-05-18T00:26:52Z"},{"alias_kind":"pith_short_12","alias_value":"J2MY44UDZTZT","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"J2MY44UDZTZTZIEC","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"J2MY44UD","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:J2MY44UDZTZTZIECCETRMXJOL6","target":"record","payload":{"canonical_record":{"source":{"id":"1503.03703","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-12T13:11:45Z","cross_cats_sorted":[],"title_canon_sha256":"1a9821a4bd67deddcc03f82532cc0ab46f7a94d5d5e212a675f09adacdadd5f3","abstract_canon_sha256":"090140082f04170e73a7b076596b2397a1cc343c51cc2651e391d2000ec8d089"},"schema_version":"1.0"},"canonical_sha256":"4e998e7283ccf33ca0821127165d2e5f89199d1522b8d591c9e87056c27b22b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:52.189026Z","signature_b64":"wCYF/LNkFQK15s0BsbIgcJslxOU/VSHGl8JIenRDi1scpd04y4mGzlnJMh4Sxrweb9+xDxZgHBKN2SDNkJdZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e998e7283ccf33ca0821127165d2e5f89199d1522b8d591c9e87056c27b22b7","last_reissued_at":"2026-05-18T00:26:52.188520Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:52.188520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.03703","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:26:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iQdfdM91iWXRxsuZNbCjcssH4PDaOxz9Op4z+hucN+Ntqah0J815R1PsndyxBVq3mO0i/Qd/k6c8eG1tF0njAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:48:23.409598Z"},"content_sha256":"3e427d4a7774359c7d5b71f98d9712383d9419653d6e70da83e1a4091f217ab9","schema_version":"1.0","event_id":"sha256:3e427d4a7774359c7d5b71f98d9712383d9419653d6e70da83e1a4091f217ab9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:J2MY44UDZTZTZIECCETRMXJOL6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Activity Identification and Local Linear Convergence of Forward--Backward-type methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gabriel Peyr\\'e, Jalal Fadili, Jingwei Liang","submitted_at":"2015-03-12T13:11:45Z","abstract_excerpt":"In this paper, we consider a class of Forward--Backward (FB) splitting methods that includes several variants (e.g. inertial schemes, FISTA) for minimizing the sum of two proper convex and lower semi-continuous functions, one of which has a Lipschitz continuous gradient, and the other is partly smooth relatively to a smooth active manifold $\\mathcal{M}$. We propose a unified framework, under which we show that, this class of FB-type algorithms (i) correctly identifies the active manifolds in a finite number of iterations (finite activity identification), and (ii) then enters a local linear con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03703","kind":"arxiv","version":8},"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":"2026-05-18T00:26:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N60atMC2bmD3YjWphCGO4xL97j5koxkR92TMesTpiQWDr48mtHpKyesaENfVjCr+KazBxDDG3snLnf8nLb+nDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:48:23.409954Z"},"content_sha256":"4afe9b4ed936cac8e0da61831ad51cbc2cff75fd0609913b79f962f2dce08273","schema_version":"1.0","event_id":"sha256:4afe9b4ed936cac8e0da61831ad51cbc2cff75fd0609913b79f962f2dce08273"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J2MY44UDZTZTZIECCETRMXJOL6/bundle.json","state_url":"https://pith.science/pith/J2MY44UDZTZTZIECCETRMXJOL6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J2MY44UDZTZTZIECCETRMXJOL6/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":"2026-05-26T02:48:23Z","links":{"resolver":"https://pith.science/pith/J2MY44UDZTZTZIECCETRMXJOL6","bundle":"https://pith.science/pith/J2MY44UDZTZTZIECCETRMXJOL6/bundle.json","state":"https://pith.science/pith/J2MY44UDZTZTZIECCETRMXJOL6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J2MY44UDZTZTZIECCETRMXJOL6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:J2MY44UDZTZTZIECCETRMXJOL6","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":"090140082f04170e73a7b076596b2397a1cc343c51cc2651e391d2000ec8d089","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-12T13:11:45Z","title_canon_sha256":"1a9821a4bd67deddcc03f82532cc0ab46f7a94d5d5e212a675f09adacdadd5f3"},"schema_version":"1.0","source":{"id":"1503.03703","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03703","created_at":"2026-05-18T00:26:52Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03703v8","created_at":"2026-05-18T00:26:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03703","created_at":"2026-05-18T00:26:52Z"},{"alias_kind":"pith_short_12","alias_value":"J2MY44UDZTZT","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"J2MY44UDZTZTZIEC","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"J2MY44UD","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:4afe9b4ed936cac8e0da61831ad51cbc2cff75fd0609913b79f962f2dce08273","target":"graph","created_at":"2026-05-18T00:26:52Z","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":"In this paper, we consider a class of Forward--Backward (FB) splitting methods that includes several variants (e.g. inertial schemes, FISTA) for minimizing the sum of two proper convex and lower semi-continuous functions, one of which has a Lipschitz continuous gradient, and the other is partly smooth relatively to a smooth active manifold $\\mathcal{M}$. We propose a unified framework, under which we show that, this class of FB-type algorithms (i) correctly identifies the active manifolds in a finite number of iterations (finite activity identification), and (ii) then enters a local linear con","authors_text":"Gabriel Peyr\\'e, Jalal Fadili, Jingwei Liang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-12T13:11:45Z","title":"Activity Identification and Local Linear Convergence of Forward--Backward-type methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03703","kind":"arxiv","version":8},"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":"sha256:3e427d4a7774359c7d5b71f98d9712383d9419653d6e70da83e1a4091f217ab9","target":"record","created_at":"2026-05-18T00:26:52Z","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":"090140082f04170e73a7b076596b2397a1cc343c51cc2651e391d2000ec8d089","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-12T13:11:45Z","title_canon_sha256":"1a9821a4bd67deddcc03f82532cc0ab46f7a94d5d5e212a675f09adacdadd5f3"},"schema_version":"1.0","source":{"id":"1503.03703","kind":"arxiv","version":8}},"canonical_sha256":"4e998e7283ccf33ca0821127165d2e5f89199d1522b8d591c9e87056c27b22b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e998e7283ccf33ca0821127165d2e5f89199d1522b8d591c9e87056c27b22b7","first_computed_at":"2026-05-18T00:26:52.188520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:52.188520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wCYF/LNkFQK15s0BsbIgcJslxOU/VSHGl8JIenRDi1scpd04y4mGzlnJMh4Sxrweb9+xDxZgHBKN2SDNkJdZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:52.189026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03703","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e427d4a7774359c7d5b71f98d9712383d9419653d6e70da83e1a4091f217ab9","sha256:4afe9b4ed936cac8e0da61831ad51cbc2cff75fd0609913b79f962f2dce08273"],"state_sha256":"4c5dfb0636e09708f7a13a18672ffb16b3998fac8f447210d9810722d98e9054"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HMhmaXNr12NWCL9HNFD1AtDU5TViYVTavtaL5kMDKQnXWzZaM537V27uzkaq9fmMbhvxAYTt6wI2OgVbU00WAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T02:48:23.413346Z","bundle_sha256":"9f10a4a107468929cf1be72981658467141ca59b468139b426ffa16761b53d07"}}