{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:FSKYOAN6YAYULUIVYZPF322EMD","short_pith_number":"pith:FSKYOAN6","canonical_record":{"source":{"id":"2109.11481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-09-23T16:35:27Z","cross_cats_sorted":[],"title_canon_sha256":"1c96a306302e72473b2b58c57b03f95dbc4fd3ec7e2eec980a02854e08d94814","abstract_canon_sha256":"f1d04398414ec11022fbb11ec2ff466c2e362f197f6ca26f142d920ad2cc0ab5"},"schema_version":"1.0"},"canonical_sha256":"2c958701bec03145d115c65e5deb4460c2fc5f96a6fee5c3ab75741f74900b85","source":{"kind":"arxiv","id":"2109.11481","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.11481","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"arxiv_version","alias_value":"2109.11481v1","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.11481","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"pith_short_12","alias_value":"FSKYOAN6YAYU","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"pith_short_16","alias_value":"FSKYOAN6YAYULUIV","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"pith_short_8","alias_value":"FSKYOAN6","created_at":"2026-07-05T03:16:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:FSKYOAN6YAYULUIVYZPF322EMD","target":"record","payload":{"canonical_record":{"source":{"id":"2109.11481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-09-23T16:35:27Z","cross_cats_sorted":[],"title_canon_sha256":"1c96a306302e72473b2b58c57b03f95dbc4fd3ec7e2eec980a02854e08d94814","abstract_canon_sha256":"f1d04398414ec11022fbb11ec2ff466c2e362f197f6ca26f142d920ad2cc0ab5"},"schema_version":"1.0"},"canonical_sha256":"2c958701bec03145d115c65e5deb4460c2fc5f96a6fee5c3ab75741f74900b85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:16:58.462711Z","signature_b64":"TRKWAmNFAwaEajgztQI8rjQmR5OtCbAG7HM9Gs2kzR+YQ36gQYWETI+0MEfhTf0C16Sa2FtolmAcVDPC1K2XAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c958701bec03145d115c65e5deb4460c2fc5f96a6fee5c3ab75741f74900b85","last_reissued_at":"2026-07-05T03:16:58.462247Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:16:58.462247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.11481","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":"2026-07-05T03:16:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o47rbs1UodB+XD3hOyYe/1mEyVbqG+Z6Fqe1DPGccktYEE+j4CDqKfQeNZGTBWpF1Q6MoYIuvFLWuoPzEbD9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:54:36.482504Z"},"content_sha256":"36533a79224b34fb42e416c3f08581144ea5d1d1ab02e389a7ec9cb9a3f358f3","schema_version":"1.0","event_id":"sha256:36533a79224b34fb42e416c3f08581144ea5d1d1ab02e389a7ec9cb9a3f358f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:FSKYOAN6YAYULUIVYZPF322EMD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Degenerate Preconditioned Proximal Point algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Dirk A. Lorenz, Emanuele Naldi, Enis Chenchene, Kristian Bredies","submitted_at":"2021-09-23T16:35:27Z","abstract_excerpt":"In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild assumptions that can be easily employed in the context of splitting methods for monotone inclusion and convex minimization problems. Moreover, we show that the degeneracy of the preconditioner allows for a reduction of the variables involved in the iteration updates. We show the strength of the proposed framework in the context of splitting algorithms, providing new simplified proofs of convergence and highlighting "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.11481","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.11481/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:16:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xoc0sJpK6vGIMeURuDANhxKsZjGTjgEgFI78y1DOTbX/AVGufNxb1M3GpdAO4qwpAHnX6oIkNQ2DaE61x2/1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:54:36.483440Z"},"content_sha256":"a3cd9bb967b2a307b00ae1292c10acb9c13fd135252faf74d31b56a3b982648b","schema_version":"1.0","event_id":"sha256:a3cd9bb967b2a307b00ae1292c10acb9c13fd135252faf74d31b56a3b982648b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FSKYOAN6YAYULUIVYZPF322EMD/bundle.json","state_url":"https://pith.science/pith/FSKYOAN6YAYULUIVYZPF322EMD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FSKYOAN6YAYULUIVYZPF322EMD/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":"2026-08-04T04:54:36Z","links":{"resolver":"https://pith.science/pith/FSKYOAN6YAYULUIVYZPF322EMD","bundle":"https://pith.science/pith/FSKYOAN6YAYULUIVYZPF322EMD/bundle.json","state":"https://pith.science/pith/FSKYOAN6YAYULUIVYZPF322EMD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FSKYOAN6YAYULUIVYZPF322EMD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:FSKYOAN6YAYULUIVYZPF322EMD","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":"f1d04398414ec11022fbb11ec2ff466c2e362f197f6ca26f142d920ad2cc0ab5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-09-23T16:35:27Z","title_canon_sha256":"1c96a306302e72473b2b58c57b03f95dbc4fd3ec7e2eec980a02854e08d94814"},"schema_version":"1.0","source":{"id":"2109.11481","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.11481","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"arxiv_version","alias_value":"2109.11481v1","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.11481","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"pith_short_12","alias_value":"FSKYOAN6YAYU","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"pith_short_16","alias_value":"FSKYOAN6YAYULUIV","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"pith_short_8","alias_value":"FSKYOAN6","created_at":"2026-07-05T03:16:58Z"}],"graph_snapshots":[{"event_id":"sha256:a3cd9bb967b2a307b00ae1292c10acb9c13fd135252faf74d31b56a3b982648b","target":"graph","created_at":"2026-07-05T03:16:58Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.11481/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild assumptions that can be easily employed in the context of splitting methods for monotone inclusion and convex minimization problems. Moreover, we show that the degeneracy of the preconditioner allows for a reduction of the variables involved in the iteration updates. We show the strength of the proposed framework in the context of splitting algorithms, providing new simplified proofs of convergence and highlighting ","authors_text":"Dirk A. Lorenz, Emanuele Naldi, Enis Chenchene, Kristian Bredies","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-09-23T16:35:27Z","title":"Degenerate Preconditioned Proximal Point algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.11481","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":"sha256:36533a79224b34fb42e416c3f08581144ea5d1d1ab02e389a7ec9cb9a3f358f3","target":"record","created_at":"2026-07-05T03:16:58Z","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":"f1d04398414ec11022fbb11ec2ff466c2e362f197f6ca26f142d920ad2cc0ab5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-09-23T16:35:27Z","title_canon_sha256":"1c96a306302e72473b2b58c57b03f95dbc4fd3ec7e2eec980a02854e08d94814"},"schema_version":"1.0","source":{"id":"2109.11481","kind":"arxiv","version":1}},"canonical_sha256":"2c958701bec03145d115c65e5deb4460c2fc5f96a6fee5c3ab75741f74900b85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c958701bec03145d115c65e5deb4460c2fc5f96a6fee5c3ab75741f74900b85","first_computed_at":"2026-07-05T03:16:58.462247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:16:58.462247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TRKWAmNFAwaEajgztQI8rjQmR5OtCbAG7HM9Gs2kzR+YQ36gQYWETI+0MEfhTf0C16Sa2FtolmAcVDPC1K2XAg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:16:58.462711Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.11481","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36533a79224b34fb42e416c3f08581144ea5d1d1ab02e389a7ec9cb9a3f358f3","sha256:a3cd9bb967b2a307b00ae1292c10acb9c13fd135252faf74d31b56a3b982648b"],"state_sha256":"b43985c9c0ab5c95c45c146dfaebca675e627425748710c9b04bdbcddd066ac9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D0mHX/6wapOroMOhTGZeO3Uurs4fuP8oNzzsTf97WDFKr4fJKqEDnqbZXcPdnU7W8r175v4hckb5rmN3MRZdCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T04:54:36.492623Z","bundle_sha256":"287d6683684cf388fbbadfb50d1029c5e870055a0f8171364c83d531e8cb995b"}}