{"as_of":"2026-08-08T07:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:70a75cf4cdb24fba3cde8d6ef11df73d82bbdcbfcd082ac7353d2bc0bc89bd89","coverage":[{"denominator":8,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":8,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T10:44:31.060172Z","state":"measured"},{"denominator":8,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":8,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2506.04866/citation-record","integrity":"/paper/2506.04866/integrity","json":"/paper/2506.04866/citation-record.json","paper":"/paper/2506.04866"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:44:33.470544Z","title":"Оптимизационный метод решения обратной задачи термоакустики // Сибирские электронные математические известия, 2011, Т","venue":null,"work_id":"9d75fcdd-4cb6-4f9b-9c3a-03d945fb1221","year":2011},"citing_paper":{"arxiv_id":"2506.04866","last_updated":"2025-06-05T10:37:43Z","snapshot_observed_at":"2026-08-07T10:29:10.268821Z","submitted_at":"2025-06-05T10:37:43Z","title":"On the construction of a gradient method of quadratic optimization, optimal from the point of view of minimizing the distance to the exact solution","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-07T10:44:29.972668Z"},"links":{"citing_paper":"/paper/2506.04866"},"observation_digest":"sha256:8fc562a5cad4d556905d894aa0943299064445e32983ff3dc11de04f27c21b8b","observation_id":"09718049-7558-4a05-a7a7-285c4b7ba070","resolution":{"observed_at":"2026-08-07T10:44:33.540935Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T10:44:33.254341Z","title":"Элементы теории функций и функционального анализа // М.: ФИЗМАТЛИТ, 2004","venue":null,"work_id":"4900c1e8-e851-42dd-bdcb-25d2db246342","year":2004},"citing_paper":{"arxiv_id":"2506.04866","last_updated":"2025-06-05T10:37:43Z","snapshot_observed_at":"2026-08-07T10:29:10.268821Z","submitted_at":"2025-06-05T10:37:43Z","title":"On the construction of a gradient method of quadratic optimization, optimal from the point of view of minimizing the distance to the exact solution","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-07T10:44:30.077401Z"},"links":{"citing_paper":"/paper/2506.04866"},"observation_digest":"sha256:2342b97abd8140764df95c24280cfcfec08181ae25405728a2306f0b0c218939","observation_id":"645f8a0a-6398-44ed-9673-a19ddb70dfd5","resolution":{"observed_at":"2026-08-07T10:44:33.367632Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T10:44:32.982872Z","title":"Применение градиентных методов оптимизации для решения задачи Коши для уравнения Гельмгольца // Компьютерные исследования и моделирование, 2022, т","venue":null,"work_id":"d9928620-9d91-4e47-a9f6-2faad959dfc7","year":2022},"citing_paper":{"arxiv_id":"2506.04866","last_updated":"2025-06-05T10:37:43Z","snapshot_observed_at":"2026-08-07T10:29:10.268821Z","submitted_at":"2025-06-05T10:37:43Z","title":"On the construction of a gradient method of quadratic optimization, optimal from the point of view of minimizing the distance to the exact solution","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-07T10:44:30.293074Z"},"links":{"citing_paper":"/paper/2506.04866"},"observation_digest":"sha256:5136d8426cff3b846c66d4eaec9d183038e51000841bbdd7fca16b294919f4fd","observation_id":"d43dcaa6-c916-4887-a6f7-dac8a04bc4f2","resolution":{"observed_at":"2026-08-07T10:44:33.062929Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T10:44:32.808981Z","title":"О модификации метода покомпонентного спуска для решения некоторых обратных задач математической физики // Компьютерные исследования и моделирование, 2023, т","venue":null,"work_id":"4a476b04-c15d-4de6-bdd1-a486155b9d09","year":2023},"citing_paper":{"arxiv_id":"2506.04866","last_updated":"2025-06-05T10:37:43Z","snapshot_observed_at":"2026-08-07T10:29:10.268821Z","submitted_at":"2025-06-05T10:37:43Z","title":"On the construction of a gradient method of quadratic optimization, optimal from the point of view of minimizing the distance to the exact solution","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-07T10:44:30.446682Z"},"links":{"citing_paper":"/paper/2506.04866"},"observation_digest":"sha256:7921637cd4320f9d73a4d6d51fd921b61b6e622140ffa90ecb275cf475a56a61","observation_id":"79718f6b-4c78-447f-bf3b-cf191b109bc0","resolution":{"observed_at":"2026-08-07T10:44:32.873589Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T10:44:32.463235Z","title":"Минимизация негладких функционалов // Журнал вычислительной математики и математической физики, 1969, т","venue":null,"work_id":"9117e6f8-61dd-4025-8e0c-f45fe81b92a7","year":1969},"citing_paper":{"arxiv_id":"2506.04866","last_updated":"2025-06-05T10:37:43Z","snapshot_observed_at":"2026-08-07T10:29:10.268821Z","submitted_at":"2025-06-05T10:37:43Z","title":"On the construction of a gradient method of quadratic optimization, optimal from the point of view of minimizing the distance to the exact solution","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-07T10:44:30.592188Z"},"links":{"citing_paper":"/paper/2506.04866"},"observation_digest":"sha256:47818f19e2c9557e816a335a94cf5d57eae038fee07b412aee724e448400615e","observation_id":"832ac142-fc0c-4503-a001-1e8649163e6e","resolution":{"observed_at":"2026-08-07T10:44:32.641265Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2310.07922","last_updated":"2024-04-03T15:24:47Z","snapshot_observed_at":"2026-08-07T15:40:29.115226Z","submitted_at":"2023-10-11T22:31:42Z","title":"Polyak Minorant Method for Convex Optimization","version":4},"cited_work":{"arxiv_id":"2310.07922","doi":null,"metadata_source":"pith","pith_arxiv_id":"2310.07922","snapshot_observed_at":"2026-08-07T10:44:31.680998Z","title":"Polyak Minorant Method for Convex Optimization","venue":"math.OC","work_id":"09049a34-9631-4dfc-907e-32329353a3cb","year":2023},"citing_paper":{"arxiv_id":"2506.04866","last_updated":"2025-06-05T10:37:43Z","snapshot_observed_at":"2026-08-07T10:29:10.268821Z","submitted_at":"2025-06-05T10:37:43Z","title":"On the construction of a gradient method of quadratic optimization, optimal from the point of view of minimizing the distance to the exact solution","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-07T10:44:30.732726Z"},"links":{"cited_paper":"/paper/2310.07922","citing_paper":"/paper/2506.04866"},"observation_digest":"sha256:c28e347f7d2e2910db22b20067d4f8dec6b4e8f3b7489328a15abd3968726c9c","observation_id":"8eba5296-f12f-41b8-a70d-e49da117685b","resolution":{"observed_at":"2026-08-07T10:44:31.869054Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2210.06367","last_updated":"2022-10-12T16:18:27Z","snapshot_observed_at":"2026-07-06T14:04:16.634759Z","submitted_at":"2022-10-12T16:18:27Z","title":"Quadratic minimization: from conjugate gradient to an adaptive Heavy-ball method with Polyak step-sizes","version":1},"cited_work":{"arxiv_id":"2210.06367","doi":null,"metadata_source":"pith","pith_arxiv_id":"2210.06367","snapshot_observed_at":"2026-08-07T10:44:31.282664Z","title":"Quadratic minimization: from conjugate gradient to an adaptive Heavy-ball method with Polyak step-sizes","venue":"math.OC","work_id":"4c6a95ff-c39a-4345-becb-df9595f8e658","year":2022},"citing_paper":{"arxiv_id":"2506.04866","last_updated":"2025-06-05T10:37:43Z","snapshot_observed_at":"2026-08-07T10:29:10.268821Z","submitted_at":"2025-06-05T10:37:43Z","title":"On the construction of a gradient method of quadratic optimization, optimal from the point of view of minimizing the distance to the exact solution","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T10:44:30.900562Z"},"links":{"cited_paper":"/paper/2210.06367","citing_paper":"/paper/2506.04866"},"observation_digest":"sha256:67ce9c20366a41b2fd3fa5c9db1c9b042ebffa3d1f060f4c20ebc43de0ee3025","observation_id":"f907969e-3be9-462e-aeb5-6f42b875cf25","resolution":{"observed_at":"2026-08-07T10:44:31.432355Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T10:44:32.033369Z","title":"Inverse and ill-posed problems: theory and applications // Berlin: Walter de Gruyter GmbH & Co, 2012","venue":null,"work_id":"6e71fe37-f152-4e26-a1ec-18a7102fc7e3","year":2012},"citing_paper":{"arxiv_id":"2506.04866","last_updated":"2025-06-05T10:37:43Z","snapshot_observed_at":"2026-08-07T10:29:10.268821Z","submitted_at":"2025-06-05T10:37:43Z","title":"On the construction of a gradient method of quadratic optimization, optimal from the point of view of minimizing the distance to the exact solution","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T10:44:31.060172Z"},"links":{"citing_paper":"/paper/2506.04866"},"observation_digest":"sha256:c14a481b0c51fc276ca3fc84407b586244d98d0d7d570f34cb4d1e12f1d25e34","observation_id":"c2ede430-1fea-4f21-9dec-4a2774d71bf3","resolution":{"observed_at":"2026-08-07T10:44:32.213809Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.04866","last_updated":"2025-06-05T10:37:43Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-07T10:29:10.268821Z","submitted_at":"2025-06-05T10:37:43Z","title":"On the construction of a gradient method of quadratic optimization, optimal from the point of view of minimizing the distance to the exact solution"},"reference_resolution":{"displayed":8,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":2,"verified_fuzzy":6},"total_outbound_references":8},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 8 of 8 outbound references and 0 inbound Pith citation observations for arXiv:2506.04866."}