{"as_of":"2026-08-09T09:30:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c6ad655ec6aefff2f8dda7be7a84089188960a79dc36488dd0a65acdb1180241","coverage":[{"denominator":39,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":39,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T19:00:01.117483Z","state":"measured"},{"denominator":41,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":41,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T16:40:13.841615Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-07-09T06:36:02.183597Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.07428","snapshot_observed_at":"2026-08-03T16:40:13.841615Z","title":"arXiv preprint arXiv:2507.07428 (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.12954","last_updated":"2026-07-07T03:23:49Z","snapshot_observed_at":"2026-08-06T18:44:14.091979Z","submitted_at":"2025-12-15T03:39:54Z","title":"Linear convergence of relocated fixed-point iterations","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T16:40:13.841615Z"},"links":{"cited_paper":"/paper/2507.07428","citing_paper":"/paper/2512.12954"},"observation_digest":"sha256:e3c49878556907d780dcc51c810595748a7484c5fa2d3d61a68cd8e45555afdb","observation_id":"51472b9d-8bc9-4f69-bc20-34d902494155","resolution":{"observed_at":"2026-08-03T16:40:13.841615Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"cited_work":{"arxiv_id":"2507.07428","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.07428","snapshot_observed_at":"2026-07-09T06:36:02.183597Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","venue":"math.OC","work_id":"17b2b256-f905-4170-b020-107d7068df16","year":2025},"citing_paper":{"arxiv_id":"2607.07585","last_updated":"2026-07-08T16:07:24Z","snapshot_observed_at":"2026-08-06T10:22:38.165296Z","submitted_at":"2026-07-08T16:07:24Z","title":"Convergence Analysis of the Restarted Moving-Anchored Extra-Gradient Method in the Absence of Local Lipschitz Continuity","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-09T06:27:25.912336Z"},"links":{"cited_paper":"/paper/2507.07428","citing_paper":"/paper/2607.07585"},"observation_digest":"sha256:c29d3f4c154288dc9ef0e1b9f91d2d622e0a6a051e5aafd95c2078a085443aa6","observation_id":"a3877441-be19-401a-a87b-07de9c5abb69","resolution":{"observed_at":"2026-07-09T06:36:02.186307Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.07428/citation-record","integrity":"/paper/2507.07428/integrity","json":"/paper/2507.07428/citation-record.json","paper":"/paper/2507.07428"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2504.10999","last_updated":"2025-04-15T09:15:58Z","snapshot_observed_at":"2026-08-07T16:05:36.011815Z","submitted_at":"2025-04-15T09:15:58Z","title":"Splitting the Forward-Backward Algorithm: A Full Characterization","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.10999","snapshot_observed_at":"2026-08-06T18:59:58.625389Z","title":"Splitting the Forward-Backward Algorithm: A Full Characterization","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:58.625389Z"},"links":{"cited_paper":"/paper/2504.10999","citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:0f4e26e73ed47266ec9056a4db4f7b3bee519cd83fea2ae672545078eb671af7","observation_id":"84bd9b61-4bfe-4121-a99b-2b11ed45fd7e","resolution":{"observed_at":"2026-08-06T18:59:58.625389Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2406.03309","last_updated":"2024-06-05T14:22:33Z","snapshot_observed_at":"2026-08-07T19:49:07.534558Z","submitted_at":"2024-06-05T14:22:33Z","title":"Forward-backward algorithms devised by graphs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.03309","snapshot_observed_at":"2026-08-06T18:59:58.726205Z","title":"Forward-backward algorithms de- vised by graphs","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:58.726205Z"},"links":{"cited_paper":"/paper/2406.03309","citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:993b4a3259a19288471ec237122fb93653a4b97080ad548ab4caf9fc4c1979ab","observation_id":"d86f3db5-63f0-440a-878b-123be30b2112","resolution":{"observed_at":"2026-08-06T18:59:58.726205Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.22004","last_updated":"2026-05-11T17:15:29Z","snapshot_observed_at":"2026-08-03T02:33:19.218975Z","submitted_at":"2025-03-27T21:42:43Z","title":"On Opial's Lemma","version":2},"cited_work":{"arxiv_id":"2503.22004","doi":null,"metadata_source":"pith","pith_arxiv_id":"2503.22004","snapshot_observed_at":"2026-08-06T19:00:01.221957Z","title":"On Opial's Lemma","venue":"math.OC","work_id":"472c659b-00f5-4c1b-964b-41b4ac1cd508","year":2025},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:58.799697Z"},"links":{"cited_paper":"/paper/2503.22004","citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:c12c6e09d38fc9cb7956408db7a7cc88e6b731cab2aa9ab10abe38e4ef196e86","observation_id":"a232b934-9177-4dd3-b7be-38dbc4c1813f","resolution":{"observed_at":"2026-08-06T19:00:01.271134Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.984318Z","title":"Understanding the Douglas–Rachford splitting method through the lenses of Moreau-type envelopes","venue":null,"work_id":"38ba6c69-7e5c-48ad-8b8a-292e171c5920","year":2025},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:58.889470Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:3829eddf77a239553f7d98c45127b1191037872dcf36212814b9f5902807487f","observation_id":"df9b7329-b6ea-479b-87c5-224263d63452","resolution":{"observed_at":"2026-08-06T19:00:01.989036Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.969581Z","title":"Bauschke and P","venue":null,"work_id":"01dd5ad7-2570-45ba-92c8-e24f68be7247","year":2017},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:58.981337Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:feb1100e4aa717e50d7a11a659136b2606468117aae14a892a2cc8046d34163b","observation_id":"fc385528-d771-4b44-a6c8-557c96d610f7","resolution":{"observed_at":"2026-08-06T19:00:01.974265Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.954006Z","title":"Bhatia.Perturbation Bounds for Matrix Eigenvalues","venue":null,"work_id":"37744096-a717-41ce-8cea-a51bb37545ac","year":2007},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.067505Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:964a8a513efd171acc91f3305d8da916bf493d7b858ca5091be124fe987005a1","observation_id":"b41cbf6b-50c2-4355-9f34-c3cf1dec64ec","resolution":{"observed_at":"2026-08-06T19:00:01.958333Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.938822Z","title":"Degenerate preconditioned proximal point algorithms","venue":null,"work_id":"b1bca551-3f0f-414f-8a40-f910672d0ca0","year":2022},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.156453Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:ae4c10978e1744e97e8fbe05fae1a5c5a2fab918fe9bde8ba0ff05de50993bd7","observation_id":"80d5783e-3cb7-4e45-8ee0-0d156b7dddf0","resolution":{"observed_at":"2026-08-06T19:00:01.944171Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.922980Z","title":"Graph and distributed extensions of the Douglas– Rachford method","venue":null,"work_id":"62f8ca97-09e1-43dd-bdf1-d480659ee630","year":2024},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.219008Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:42f65f8d24b05e2bdd7f6f263e589a81f77edcaf96371e60bf7c40aec75e260c","observation_id":"988bddb2-9657-49a0-968d-ba0d8ca0e2af","resolution":{"observed_at":"2026-08-06T19:00:01.927961Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.904859Z","title":"Semicontractive and semiaccretive nonlinear mappings in Banach spaces","venue":null,"work_id":"8b3f4bdb-e20e-45ee-8aee-84eb185a0697","year":1968},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.264440Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:b13a033e5b2f2ce2de2e69d9583d47ba4b5a958740a1d1b26bead8302921c1e7","observation_id":"bed97abd-dce8-4fba-8bb7-11d33fb76b87","resolution":{"observed_at":"2026-08-06T19:00:01.910563Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.889207Z","title":"Regular sequences of quasi-nonexpansive operators and their applications","venue":null,"work_id":"8fbdc1b8-751f-4714-9747-284525659b3f","year":2018},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.314491Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:58e8511b2596e5bb0b4c2e7fc2b7df2c11c39777b75b138db07ddee28bcaba5a","observation_id":"0202f989-0dcf-44e3-b3d0-7fc6ff1a2522","resolution":{"observed_at":"2026-08-06T19:00:01.893952Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.874403Z","title":"Quasi-Fej ´erian analysis of some optimization algorithms","venue":null,"work_id":"a4365517-cf51-417d-9e52-d7bd040635f2","year":2000},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.370854Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:906d97ca04658aacee563f8948b31f118aedddb11da4bf2f86b8bf3b986274a1","observation_id":"edc7c38c-8022-4863-a1f8-07718be06c4a","resolution":{"observed_at":"2026-08-06T19:00:01.879136Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.859797Z","title":"Adaptive Douglas–Rachford splitting algorithm for the sum of two operators","venue":null,"work_id":"4187aa5b-fe45-4697-8427-0ab60390f305","year":2019},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.415020Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:7bca3bdfc4586822a6b6577c5f72e53fec8c27faa580c8b518c47b3d743e2084","observation_id":"5d70e157-ccb9-4daf-8e5e-c058cf49cd8e","resolution":{"observed_at":"2026-08-06T19:00:01.864631Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.845236Z","title":"A general approach to distributed operator split- ting","venue":null,"work_id":"42fc4a32-0e47-4460-96c5-8a4ef259e7fa","year":2026},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.465797Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:eb8b8795b0c492b1dcfd25577848fc60d4bb0d17c726ec91b382e75a62917de8","observation_id":"a6ecd695-a85f-443e-9a23-54acc7bc88e3","resolution":{"observed_at":"2026-08-06T19:00:01.849456Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.830871Z","title":"A three-operator splitting scheme and its optimization applications","venue":null,"work_id":"b9185ce7-41c3-4b01-b9fc-6458c8eb26ad","year":2017},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.519672Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:6dd7b3bf28224490ce5d541193a1867d073ca22e1915d646f25300ebac1d94e4","observation_id":"bd8bcf4b-ef5c-4b39-85ca-45a0b6479e14","resolution":{"observed_at":"2026-08-06T19:00:01.835254Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.816321Z","title":"On the numerical solution of heat conduction problems in two and three space variables","venue":null,"work_id":"bcf323ce-31f6-4336-944e-8196341723fc","year":1956},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.577951Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:40e4765c89df1bd4ee4075fa1651187c35b0685899ab54eeba3b9457cc133cd0","observation_id":"a589a1ed-ab10-4094-abaa-c8b04d2f4d2a","resolution":{"observed_at":"2026-08-06T19:00:01.821012Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.800771Z","title":"From perspective maps to epigraphical projections","venue":null,"work_id":"414b3771-5813-4cf0-8cd1-b50391baba5c","year":2023},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.635031Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:2528681481445c1f8007090c71a2d21dc092f483461ba8349d04779cef033f97","observation_id":"b288788f-f4da-4c89-8184-95b2c14e8c1a","resolution":{"observed_at":"2026-08-06T19:00:01.805625Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.785650Z","title":"On the convergence of the proximal point algorithm for convex minimization","venue":null,"work_id":"947070d4-196e-423b-b845-14f70095c5c0","year":1991},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.674326Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:f7de67d2afb444bf050a3d52ceff25b0eaa5da46cb3c54a53019811ca8b6618d","observation_id":"d2a23cfb-d59d-4ed4-b9f6-e90c816785d0","resolution":{"observed_at":"2026-08-06T19:00:01.790288Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.770836Z","title":"Horn and C","venue":null,"work_id":"5be97950-9f3e-4541-8802-58968a78425e","year":2012},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.708033Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:68fd3c543b3544f033ff302e31cda5501ed953932e211b12c7a9ae1bb599a374","observation_id":"8d6409ad-e0b7-4cf7-8bad-0aa5d26691e9","resolution":{"observed_at":"2026-08-06T19:00:01.775296Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.755958Z","title":"Douglas–Rachford splitting for nonconvex optimization with appli- cation to nonconvex feasibility problems","venue":null,"work_id":"e4ca7e51-ff3a-4940-9c1d-6065007688a0","year":2016},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.761315Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:d0e068df68451d76e1cb812a9d3076b5624afd6ffc54e52198387c95b37d3371","observation_id":"2cf9cbb6-1953-4e4c-a03c-f752511a3feb","resolution":{"observed_at":"2026-08-06T19:00:01.760899Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.740667Z","title":"Survey: sixty years of Douglas–Rachford","venue":null,"work_id":"64f1c385-fff4-434d-94e5-4f34e0a8bfad","year":2021},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.817679Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:3518c617336e6c30b619f653091e26ff640e53eacf8b5259a6e2f59f4fb24aea","observation_id":"095accf2-de09-4963-935c-a4c3478432aa","resolution":{"observed_at":"2026-08-06T19:00:01.745556Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.724928Z","title":"Splitting algorithms for the sum of two nonlinear operators","venue":null,"work_id":"192f9c88-5943-4fb5-8dff-5b07002357e6","year":1979},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.867981Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:924ad44147a146a15b80accf08311075f85e8e4a5f98fd2bd4be6573a7c7e6ef","observation_id":"8def6753-6986-4d56-b9ea-e3a35825e28e","resolution":{"observed_at":"2026-08-06T19:00:01.729908Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.709636Z","title":"The degenerate variable metric proximal point algorithm and adaptive stepsizes for primal–dual Douglas–Rachford","venue":null,"work_id":"436ef53b-8afd-45c7-823c-5be36d657ff4","year":2025},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.930463Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:8e25c8cc43e8bc89c0a3fc07747c1fbb2e27d2b1e9c06ee490e2329de1ed1724","observation_id":"1dd919ac-b2e7-44b3-bf6f-c3a5847d9c97","resolution":{"observed_at":"2026-08-06T19:00:01.714322Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.693762Z","title":"Non-stationary Douglas–Rachford and alternating direc- tion method of multipliers: adaptive step-sizes and convergence","venue":null,"work_id":"1e99bd51-3b81-4366-b994-bc035a7079dd","year":2019},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T18:59:59.980714Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:e576cd1d5e31b6b1431381b52e75842d74176d423128ea6e07a38be87c55b2b6","observation_id":"b7d2781a-cc59-4c40-98f1-4dbc2049597b","resolution":{"observed_at":"2026-08-06T19:00:01.699372Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.678558Z","title":"A forward-backward splitting method for monotone inclusions without cocoercivity","venue":null,"work_id":"9b7f4b1c-3f92-4475-a9f9-900d04334fe8","year":2020},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:00.038787Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:56322a39d28a73b4960170a8a74663b1278bea81da77f66a7f79dab9794d10c0","observation_id":"5a95b962-1f37-439b-8cdc-76b7bb077fce","resolution":{"observed_at":"2026-08-06T19:00:01.682995Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.662555Z","title":"Resolvent splitting for sums of monotone operators with mini- mal lifting","venue":null,"work_id":"5aa269db-8eea-4f7b-bc8f-681390832bba","year":2023},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:00.101766Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:9eec66fc9bcfeb18f55ab5dc864da0ae8c0618e7657d712fdee00179d35c40a1","observation_id":"3a2307d2-2d08-483b-b5b4-d96b89032227","resolution":{"observed_at":"2026-08-06T19:00:01.666766Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.649675Z","title":"Monotone (nonlinear) operators in Hilbert space","venue":null,"work_id":"554eac4a-f3b9-461c-b0eb-af2aa7e286b6","year":1962},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:00.159335Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:5230a35f0f04e09215ebdf4e9eced67ce27cc5e5749b6665caaa632d61045fe0","observation_id":"a3239564-4d0f-445a-9c91-576a41423cd0","resolution":{"observed_at":"2026-08-06T19:00:01.653577Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.635899Z","title":"A quantitative Robbins-Siegmund theorem","venue":null,"work_id":"20d56302-d3ba-4560-8a15-6c4d1aa190d6","year":2026},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:00.216303Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:b56e2afdc2e61b2c47a3b4c36fd7f529295fa5ea9ad811c7246c6500942072b2","observation_id":"e203b628-60db-4524-9f87-c4ecc8c5d8c1","resolution":{"observed_at":"2026-08-06T19:00:01.640040Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.622041Z","title":"Weak convergence of the sequence of successive approximations for nonexpansive mappings","venue":null,"work_id":"7ddacd31-97ba-4c4e-8ffd-6b48632913bb","year":1967},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:00.284647Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:943ecfb3d4e4120b90ead8156467ab64b36f5e95c246481cff3c18857ac23324","observation_id":"82efb79f-e7c3-494c-a347-916369dcc3ce","resolution":{"observed_at":"2026-08-06T19:00:01.626764Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.608848Z","title":"Adaptive three operator splitting","venue":null,"work_id":"cdbf5a0e-4edf-4ec8-82cd-fb02040e7e6a","year":2018},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:00.334878Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:c545e0a8beac06f11bc6e294f0410bce81fba1cff307e2cd42aa9aedb88da1d0","observation_id":"81de8ce6-5089-4e0c-97b0-188781efc0e1","resolution":{"observed_at":"2026-08-06T19:00:01.613209Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.595900Z","title":"Peypouquet.Convex Optimization in Normed Spaces: Theory, Methods and Examples","venue":null,"work_id":"8969db40-2f55-41cc-a2c2-23f591fd6e05","year":2015},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:00.402233Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:0fd6575809030c945fc82c9ec4351ce5df47198cc46ab3b14a9a13979c70f784","observation_id":"5c0b5127-3bea-4d03-9cdf-084af066b777","resolution":{"observed_at":"2026-08-06T19:00:01.599932Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.582750Z","title":"Linear convergence of the Douglas–Rachford method for two closed sets","venue":null,"work_id":"e650b7fe-86f0-4b7e-be21-d7b2a4d2e6e4","year":2016},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:00.486930Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:29af51edc9531810ca196d2ed8796b13116d080ad73d96cd5400889bbf7a455c","observation_id":"39618926-01b7-4b34-a01e-9921058be1fd","resolution":{"observed_at":"2026-08-06T19:00:01.586979Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.569660Z","title":"Polyak.Introduction to Optimization","venue":null,"work_id":"ffe34968-773a-45e5-86da-03bb9e988f48","year":1987},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:00.751078Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:e8d21e64433a4d3d6de775b3412a0556c8cff0db2c28b5c99a3662fcf7b72acd","observation_id":"26c335dc-d522-4dd5-925b-5eb24bc4eb60","resolution":{"observed_at":"2026-08-06T19:00:01.573830Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.555503Z","title":"A convergence theorem for non negative almost super- martingales and some applications","venue":null,"work_id":"150ae848-d772-45fa-bf04-41a3a6470b28","year":1971},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:00.916420Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:af2bf2159a348ba38ffa23a3b555d95756d4956ffdb33bb5d6a860630873306d","observation_id":"6cc2869d-ec4b-4dfa-bf2b-2301c6524ce3","resolution":{"observed_at":"2026-08-06T19:00:01.559759Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.540121Z","title":"On the virtual convexity of the domain and range of a nonlinear maximal monotone operator","venue":null,"work_id":"1791781d-6d85-41ad-90c3-456b81500c90","year":1970},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:00.947363Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:dbd03baf5001392bb87833c4342b468bfcac4152c3552c40584ec8a96ecdadbb","observation_id":"57e10495-291c-40b8-b4a2-f1c66bdeb551","resolution":{"observed_at":"2026-08-06T19:00:01.545230Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.524403Z","title":"Uniqueness of DRS as the 2 operator resolvent-splitting and impossibility of 3 operator resolvent-splitting","venue":null,"work_id":"8250d8bf-11f0-48ea-bde1-0b30bc597493","year":2020},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:00.952008Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:6e3bee198f2c3168bda313450f51bcb65e8ea08da20f78faa035876b5749250a","observation_id":"dfbada4f-0ff0-44c7-888a-ff594c0c1cab","resolution":{"observed_at":"2026-08-06T19:00:01.529213Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.509221Z","title":"On weak convergence of the Douglas–Rachford method","venue":null,"work_id":"ded08a5b-9470-45e2-8220-f98176e1be1d","year":2011},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:00.956263Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:45b245c37a7b102e30c02014a68539cef7b641556c5501656fe645bca1a5a2b2","observation_id":"a44ca3ed-6c08-407d-b950-869d7c2b636f","resolution":{"observed_at":"2026-08-06T19:00:01.513907Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.494926Z","title":"Frugal and decentralised resolvent splittings defined by nonexpansive opera- tors","venue":null,"work_id":"e83e0022-5687-4fcd-ab8f-ea3dbf4ffcd7","year":2024},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:00.997423Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:2b565f9a999b50df1dc48bb203ca2a04dc27cdf725f65ad6c30b6e616e38c748","observation_id":"e314b731-0a7a-402b-8afe-764e7e85f882","resolution":{"observed_at":"2026-08-06T19:00:01.499150Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.476471Z","title":"Douglas–Rachford splitting and ADMM for nonconvex opti- mization: Tight convergence results","venue":null,"work_id":"91978633-b8db-4a75-9005-bdec74025afb","year":2020},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:01.052238Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:5fffc553be8fe25569ab3cefe0095da6152e0e44744b3396cacfa785f104f71f","observation_id":"d6994d59-41d8-4a04-8190-e9e1ac241848","resolution":{"observed_at":"2026-08-06T19:00:01.480780Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:00:01.383198Z","title":"Projections on convex sets in Hilbert space and spectral theory: Part I. projections on convex sets: Part II. spectral theory","venue":null,"work_id":"0897c233-9adf-46e4-9b7f-6417d063ead7","year":1971},"citing_paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting","version":3},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T19:00:01.117483Z"},"links":{"citing_paper":"/paper/2507.07428"},"observation_digest":"sha256:38beeb65eeb686b05962b32c2a3311fabff798606f3d0d87edb84604dd8bd62a","observation_id":"34366c26-308a-466b-884e-5c4b96ee9cc5","resolution":{"observed_at":"2026-08-06T19:00:01.422695Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.07428","last_updated":"2026-06-10T03:37:25Z","latest_version":3,"primary_category":"math.OC","snapshot_observed_at":"2026-08-08T11:43:29.516970Z","submitted_at":"2025-07-10T04:44:05Z","title":"Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting"},"reference_resolution":{"displayed":39,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":1,"verified_fuzzy":36},"total_outbound_references":39},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 2 inbound Pith citation observations for arXiv:2507.07428."}