{"as_of":"2026-08-12T15:19:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a86057edc4ad13d89dc7e59f5eeca63579edb29b63c12bc87eeb0f74e59fa28c","coverage":[{"denominator":43,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":43,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-11T12:52:28.654949Z","state":"measured"},{"denominator":43,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":43,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2607.04828/citation-record","integrity":"/paper/2607.04828/integrity","json":"/paper/2607.04828/citation-record.json","paper":"/paper/2607.04828"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"nvidia, may 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:5044f5b877c231e5980271c7d66cb1ef95080fa1ebf23091806eae83b3f54794","observation_id":"0bfc68d1-b081-4195-8fd6-9827c4913324","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"IEEE Std 754-2019 (Revision of IEEE 754-2008), pages 1–84, July 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:ae1d68e63bd3b1297bcae7608222a6e58ea5df18ecb3611506607559a95b122d","observation_id":"1534c31a-cf4c-4a5e-9c8a-4cf0e1e31a5b","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:b90cb0878f5def0fa99d251e48feec2682d5e790494aabebc1d3a818eabf34fa","observation_id":"042cec3e-2a6e-4a5e-8a14-aeed5903a7b0","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:e14f0f4fe7d7c9cfbc60c7af68f2695642af0d53fd5fc20a7198a2366c465bb6","observation_id":"00b8cbb8-d609-4b56-877e-0763d4435619","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"A Levenberg–Marquardt method for large nonlinear least-squares problems with dynamic accuracy in functions and gradients","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:f1225f05e66b20718ee61643676685ae09d05d1b481e80dbfccc22034f4578d8","observation_id":"aa25efb8-cc57-40ba-8a34-31e3438764b6","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1093/imanum/drz076","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Adaptive cubic regularization methods with dynamic inexact hessian information and applica- tions to finite-sum minimization","venue":"IMA Journal of Numerical Analysis","work_id":"656ab9b0-7729-4a5d-94f9-9c3642809b7f","year":2021},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:262d4af21a80825b9423ae240ef144382d6a7348c196c11c0216b34c16bb6c2e","observation_id":"6d8ae56e-f454-4f9e-90e5-538d38044fcf","resolution":{"observed_at":"2026-07-11T12:58:01.021494Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-07-12T01:21:38.199303+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-12T01:21:38.199303+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1093/imanum/drz027","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Subsampled inexact Newton methods for minimizing large sums of convex functions","venue":"IMA Journal of Numerical Analysis","work_id":"e59d15aa-d39d-4be6-8d08-ad630bf17deb","year":2020},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:bf690164dd3cc749791b575f4e5bb7736a45da4d6928da0c94ad2cd752bca43e","observation_id":"4199e5eb-118b-4d8a-a5df-6c284d20cd9a","resolution":{"observed_at":"2026-07-11T12:58:00.978957Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-07-12T01:21:38.701202+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-12T01:21:38.701202+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"Inexact Newton methods with matrix approximation by sampling for nonlinear least-squares and systems, August 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:192a9a22c0e98869a0c31f8456949deaba097accf8b5902bc9e8c5eee7c76077","observation_id":"5981e44a-ccf1-4ed0-a5e6-1f7329e2e284","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/20m1366253","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"SIAM/ASA Journal on Uncertainty Quantification","work_id":"74070e88-c744-479b-a7a5-4160ae27d477","year":2022},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:7f5ee8aa2bf1b8190c25f4df2b499fbf03e87b5e70cb0042bbf230c2631d4e89","observation_id":"4fd39a2a-79a1-4826-b656-aee44a2e4ce4","resolution":{"observed_at":"2026-07-11T12:58:00.973664Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-07-12T01:21:39.138403+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-12T01:21:39.138403+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"Convex Optimization","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:eaaaf2b819894a8c98a79fbbbd9d2c5d24ba279ef6da66f23faf20322a900a22","observation_id":"7ec42522-d7a9-47a9-ae32-73c2b4f1be90","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:b83c7043185aa5053b95c77e0c84f239331879b8d4cfd0b4e61e2652a5657a39","observation_id":"744770d5-ba0f-42df-bbbb-d86fe16c6bc0","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/140954362","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"SIAM Journal on Optimization","work_id":"6e061af5-1bb5-4850-9d47-5ca1e81e2476","year":null},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:3515ad877e400e0d6df61150843d89db3aaa5e9892625f0cc926eae1d77966f6","observation_id":"5ddf8437-f389-4231-ac13-dc27d8e119ca","resolution":{"observed_at":"2026-07-11T12:58:00.992246Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-07-12T01:21:39.621201+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-12T01:21:39.621201+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"Evaluation Complexity of Algorithms for Nonconvex Optimization: Theory, Computation and Perspec- tives","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:efaf3ff8b7d5b0aaf80c902a576a626032a19526650be345609c97cfa55f826e","observation_id":"40cf9f00-27ee-4255-91a5-036bf8fe94e1","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:5ea95d4a3f2ba5468f1468cf52a46dea6341910d12e13793d4a8a1c231164e12","observation_id":"7633dcdc-7250-4222-a091-9bb7c1696302","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:d3be5bf9b04a3fae4f92a031f1236cb190c65bc2d12744a2c41a12f816c61114","observation_id":"bd6f7f69-6547-4885-909e-2a54e1d4b184","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"Dembo, Stanley C","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:293ff89a2724f2219555a2bf5e954c86a00118c276fb3a2f22dd9a7289603e03","observation_id":"fd9cdeb3-eead-4dc3-9f04-f80d74243401","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/1.9781611971200","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Society for Industrial and Applied Mathematics eBooks","work_id":"a2fb8a38-51d1-4fa1-a951-9ef6c8295285","year":1996},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:fa7f51f6d384ddae35afa27d6f455828498705f42928f5b939e15b5c8464a251","observation_id":"842156a4-cbc1-44c9-847a-489b9afa5ce9","resolution":{"observed_at":"2026-07-11T12:58:00.998819Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-07-12T01:21:40.88325+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-12T01:21:40.88325+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"Dolan and Jorge J","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:b039c6eee3683121602ba6ffaec502ebe1d05fd5b08a95826a1f6919b2ab96c6","observation_id":"8b6d4343-21cb-4ebd-acb2-35d51a3ecd10","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"Gratton and Ph","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:a89746e8a0516ae9b4d470e6091cd4fd4b0ddbec91fa298816a91a0395b89a0c","observation_id":"a45e4f97-4a7b-40cc-8e33-093e831e4ddc","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"Gratton and Ph","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:7eb82e49c768c9e658428e9e0eba2e34d36501a8e033077b682ac99451471f85","observation_id":"baee3a97-8317-484e-9019-8b4849846f31","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"Hestenes and Eduard Stiefel","venue":null,"work_id":null,"year":1952},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:0495914558bc2453919247b86c8dee628c7aa2e81163fae19465d4b79f62c611","observation_id":"aa710f04-62a4-4f87-8432-bbf5f9ce8022","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:78499da9024726859aa5220fdca3750e24e03b8a927205e7c947f781c71e090a","observation_id":"1f620ffd-b9da-46a8-9a87-10a04f4233c2","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:773a407ead3273c1298771b378ef7c4e2074ebee751603022c8cfdc6a68e94e1","observation_id":"b4821342-bc4c-4e51-9be9-df947a0cf169","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"Higham and Theo Mary","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:03fa25c15ccd151d0c094ee97766ce3227554a2f214cc8e859c40bf92cedc831","observation_id":"de6527a1-bafb-478e-a5e8-4bad98589575","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"Higham and Theo Mary","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:6216e4110b262a950b07a797a7a424e18024067cbac469c8dc92347d340ae846","observation_id":"474317d5-67ba-4c16-abf0-ac640c5c5eba","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"Horn and Charles R","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:45f37f142962326ab0dcde37ac153bbe10479f7bf32e2a142ce89ce380d693eb","observation_id":"bc8b85bb-0e5f-46d0-951a-70f2cc7adf8f","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:770d8d769843a9e62d5f0fc2139455e918481850968741da9fb3a58bd2420d05","observation_id":"353cfedd-68b3-45e2-a7ba-f52681b262a0","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:2157f47bffad012f16a18d27a55495c51c553146fb9feace4b138883077d5a65","observation_id":"73b436c5-a989-4d0e-b970-e6f8644dc010","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.16051","last_updated":"2023-10-09T19:05:54Z","snapshot_observed_at":"2026-08-09T04:48:09.515573Z","submitted_at":"2023-07-29T19:00:56Z","title":"Newton's Method in Three Precisions","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.16051","snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"cited_paper":"/paper/2307.16051","citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:82ba9228eafc622647885de43690ef691a0c1e903d621d74354dfd968ed81840","observation_id":"5b14b95e-6af6-4e39-af4b-9fc0a9f0974c","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf02165230","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Lancaster","venue":"Numerische Mathematik","work_id":"0c09d315-8fcb-48d6-90f0-33ee73c318ce","year":1966},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:106cd5a6a0abbe50de6c20bee3c629e0df40d45bbde1b0bd8b8d8a010391772a","observation_id":"802c81a9-8588-4e29-9856-b0458cc0957e","resolution":{"observed_at":"2026-07-11T12:58:01.035553Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-07-12T01:21:43.41073+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-12T01:21:43.41073+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"Practical quasi-newton methods for solving nonlinear systems","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:0642b9ccee802db090664a3099fe506f34ded04035cc7d71961b365ab1cd5744","observation_id":"6bb73288-c420-40e6-86dc-8b41c5c499f1","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"A multi-precision quadratic regularization method for unconstrained optimization with rounding error analysis","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:566b037a1f0f32d81f9f91589985bfe88bcc18852ae9e1c7189db628fad39387","observation_id":"0a3591a0-9b04-409c-bdd8-56a7c123afc1","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:418f516c68dfa12ceed088cfa201bb9c5e48400d973ea56972a6a73998099aef","observation_id":"d15144dd-a82f-40e5-a97d-899a95c66b3e","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.19720","last_updated":"2025-05-26T09:08:46Z","snapshot_observed_at":"2026-08-08T21:20:33.298017Z","submitted_at":"2025-05-26T09:08:46Z","title":"A Structured Tour of Optimization with Finite Differences","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.19720","snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"A structured tour of optimization with finite differences, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"cited_paper":"/paper/2505.19720","citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:ebf8c58ca5453ef63812c961f0ded1831c8705d1aef40bb6a5e530a4f285e6fd","observation_id":"fd2c17c1-bd67-457a-a78b-826f8a7ed6c1","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:6dc3bf627d64162e5f2c81ec66f5ec132fdef89065418104020c1a52ded42553","observation_id":"20899bc9-f3bb-4a36-be13-047808bc27de","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/s0895479899359837","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Newton’s method in floating point arithmetic and iterative refinement of generalized eigenvalue problems","venue":"SIAM Journal on Matrix Analysis and Applications","work_id":"bfd0479d-1360-400c-aea9-b650314bfacf","year":2001},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:22a39c9f412bd9b0a1d155e9a293e3f1e7a13aeb76e2c75ec96b37de7d970be8","observation_id":"6434424f-6aa3-4005-a02f-6098f1df5b06","resolution":{"observed_at":"2026-07-11T12:58:01.023979Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-07-12T01:21:44.34106+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-12T01:21:44.34106+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"Lower and upper bounds of the con- vergence rate of gradient methods with composite noise in gradient, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:500ce62d8ac41a023496222f3f313127353c8e569d976ed3ab32d70c45bc4c14","observation_id":"914e03bb-c9ea-489c-9738-f09e0c84a007","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf01399601","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Wo´ zniakowski","venue":"Numerische Mathematik","work_id":"411edb11-d8d9-4c3e-8d53-c96b9c076ab9","year":1977},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:47ffbcfa23f12e36a3e6b5bae32e56cedb7fe31bcec2266fea850165297645d8","observation_id":"70fdab8f-02ad-4de4-830e-843424a76ec6","resolution":{"observed_at":"2026-07-11T12:58:00.987041Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-07-12T01:21:44.793545+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-12T01:21:44.793545+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10107-019-01405-z","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Mathematical Programming","work_id":"62a1ba55-131b-43be-bbc0-6fae37bf4e16","year":2020},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:537632fd38af8210a2a0780c3c7cc464572795c3a5863e6fa7be163fb395b8fd","observation_id":"b5eb6764-102d-40d9-82c4-87837bc2409d","resolution":{"observed_at":"2026-07-11T12:58:01.011717Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-07-12T01:21:45.316908+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-12T01:21:45.316908+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1093/imanum/drac043","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Yao, Peng Xu, Fred Roosta, Stephen J","venue":"IMA Journal of Numerical Analysis","work_id":"16da9234-e736-4a91-972a-5701832c8eb4","year":2021},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:624923ca706e86c654572950d43e5b0c2ccad2f805f21f7cb6cee6b147930863","observation_id":"dd69a28d-b0b3-4692-b006-31406a679dba","resolution":{"observed_at":"2026-07-11T12:58:00.986304Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-07-12T01:21:45.851089+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-12T01:21:45.851089+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T12:52:28.654949Z","title":"Inexact nonconvex Newton-type methods","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:fb9d27d80b244ea1c026f2c2887efdfeb0151fbf568b74f02b4887dc811ab1cf","observation_id":"33190c68-e0de-4c5e-bd06-49fe8424a69c","resolution":{"observed_at":"2026-07-11T12:52:28.654949Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1093/imanum/3.1.109","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"IMA Journal of Numerical Analysis","work_id":"9bd73fe0-b753-43d3-b133-960a0eb18b70","year":1983},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:e823ea64f74a9c5249d3bcadb230def53e5f5b12a9c22f9d3248c1beab869a9e","observation_id":"c1769c62-dd5b-40f0-b185-9603b7270a6d","resolution":{"observed_at":"2026-07-11T12:58:00.965606Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-07-12T01:21:46.224438+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-12T01:21:46.224438+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/0721040","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"SIAM Journal on Numerical Analysis","work_id":"2f2d8224-3e48-4a12-aef4-f8036343600d","year":1984},"citing_paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-07-11T12:52:28.654949Z"},"links":{"citing_paper":"/paper/2607.04828"},"observation_digest":"sha256:1e17afbf6850e93db4b35a7e68225e04c846ee0ac8b65894b6990464da0f2d03","observation_id":"0d5dadd0-1df8-4a16-904d-e1bfa44d9168","resolution":{"observed_at":"2026-07-11T12:58:01.003898Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-07-12T01:21:46.641189+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-12T01:21:46.641189+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2607.04828","last_updated":"2026-07-06T09:02:09Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-12T09:57:05.646876Z","submitted_at":"2026-07-06T09:02:09Z","title":"Mixed precision Newton's method for optimization"},"reference_resolution":{"displayed":43,"state_counts":{"malformed_identifier":5,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":26,"verified_exact":12,"verified_fuzzy":0},"total_outbound_references":43},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2607.04828."}