{"as_of":"2026-08-12T22:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2c9af4719ead5169bd7c4d0ccdc4bc0b764ec048184fbf6cf66087e24ce216c9","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T10:12:48.881527Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"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/2510.11379/citation-record","integrity":"/paper/2510.11379/integrity","json":"/paper/2510.11379/citation-record.json","paper":"/paper/2510.11379"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1177/10943420211003313","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Abdelfattah, H","venue":"The International Journal of High Performance Computing Applications","work_id":"aad7f63b-413c-4d38-acb7-e55f2b69972a","year":2021},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:45.981549Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:b54f2a9e9e19a3d83c37c516adbf4532d607f79482d18c460295658b6edaa631","observation_id":"a3f1b183-4cb3-4447-9f04-a9ddeb09e1cd","resolution":{"observed_at":"2026-08-04T10:14:08.653683Z","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":"2026-08-12T06:34:36.333875+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":"2026-08-04T10:12:46.060417Z","title":"Bj¨ orck, T","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:46.060417Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:51437565264405add201b2d46cbe5e7e0a35487ebc29dc36c0463d9f4474a9db","observation_id":"e05ae203-8685-47f2-a4f5-f24ad30f3eb2","resolution":{"observed_at":"2026-08-04T10:12:46.060417Z","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":"2026-08-04T10:12:46.167286Z","title":"Carson and J","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:46.167286Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:059043e1b4103296b935cf1112153cace8ac6d46916e19658fa2475187c11df6","observation_id":"dc5b320f-45c0-430b-89bf-fc1d75e1ec47","resolution":{"observed_at":"2026-08-04T10:12:46.167286Z","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":"2026-08-04T10:12:46.255937Z","title":"Carson, J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:46.255937Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:e6de0abe5bcaab38395bd9563a2c9df554a4547ed26ddcd4fe07f9e2e2483897","observation_id":"d18c8958-828f-4910-84b3-2c30f881e110","resolution":{"observed_at":"2026-08-04T10:12:46.255937Z","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":"2026-08-04T10:12:46.413731Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:46.413731Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:86592e231db761472e6e0dd9adf37c6d48cda90510b1eed02fb2fd5d5cd0538c","observation_id":"d0c8ec15-bf56-4cd6-b7b9-643049e2d262","resolution":{"observed_at":"2026-08-04T10:12:46.413731Z","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":"2026-08-04T10:12:46.594015Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:46.594015Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:599f2680dd7783ff32569781036ffdfc35a92ada8e3d5982b7871421dc15d790","observation_id":"47a8c5f8-415f-4465-b990-1413c1ffd80c","resolution":{"observed_at":"2026-08-04T10:12:46.594015Z","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":"2026-08-04T10:12:46.685122Z","title":"El Arar, D","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:46.685122Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:8213718122a249137d059190236f09047d8c576493896a6885f6bc7a7d46c109","observation_id":"e7788c17-d31b-4770-b779-90b9bd998e51","resolution":{"observed_at":"2026-08-04T10:12:46.685122Z","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":"10.1016/0024-3795(89)90285-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Greenbaum","venue":"Linear Algebra and its Applications","work_id":"89b175c6-1d65-4dc6-a68a-9b62df10a279","year":1989},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:46.857832Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:0cfa88bd0e035fc08dfbc1dddefa16e0960a4339f2935b19d6bfe621d6a48ae3","observation_id":"5248de52-5f43-4d2a-a601-dcaf85aa4996","resolution":{"observed_at":"2026-08-04T10:14:08.397075Z","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":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/s0895479895284944","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Greenbaum","venue":"SIAM Journal on Matrix Analysis and Applications","work_id":"bebd54dc-013e-47e8-b405-861a0f54d0af","year":1997},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:47.036898Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:3b448dd843fc61c06a458ac4a30a1a1c80470c730989f3efbf3104f0359dd5a6","observation_id":"a0640046-5142-44ea-986d-a4e51a9d4112","resolution":{"observed_at":"2026-08-04T10:14:08.221333Z","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":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.04155","last_updated":"2025-05-07T06:11:49Z","snapshot_observed_at":"2026-08-07T15:49:18.290643Z","submitted_at":"2025-05-07T06:11:49Z","title":"An Adaptive Mixed Precision and Dynamically Scaled Preconditioned Conjugate Gradient Algorithm","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.04155","snapshot_observed_at":"2026-08-04T10:12:47.149191Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:47.149191Z"},"links":{"cited_paper":"/paper/2505.04155","citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:2ef8163f4a20211be9ee3dbae3099d3a8e5a2f7f782348a6a48af24db9d94e09","observation_id":"af3d0bb7-cc60-4985-a369-7559fd3159ba","resolution":{"observed_at":"2026-08-04T10:12:47.149191Z","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":"2026-08-04T10:12:47.292368Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:47.292368Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:5d007d7d7518afb2061e173a38328b1b2598c6a8569e41f19870c02dbc537a2f","observation_id":"006c9d89-bb7a-409f-a49b-c56495ccb0c2","resolution":{"observed_at":"2026-08-04T10:12:47.292368Z","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":"2026-08-04T10:12:47.398963Z","title":null,"venue":null,"work_id":null,"year":1952},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:47.398963Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:24ca036e09614e07d6c2661fe46cdffd78370107346a465c3e6fa36d74248c09","observation_id":"7cfcf3d1-60f2-48cf-9764-3a1e06737e5f","resolution":{"observed_at":"2026-08-04T10:12:47.398963Z","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":"2026-08-04T10:12:47.579750Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:47.579750Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:4378311906a44cae39e6f77c758dab12d83706be9c1606b685792c8087189ca5","observation_id":"a98c4cd1-5b5c-4c81-ba4c-7063f42a684d","resolution":{"observed_at":"2026-08-04T10:12:47.579750Z","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":"2026-08-04T10:12:47.688921Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:47.688921Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:e7e222823292a8f83aa85eeab88588ab0256d233433090631f7fc04a1dd79952","observation_id":"a74ee9ab-6a56-4250-9953-37a59f8c8e10","resolution":{"observed_at":"2026-08-04T10:12:47.688921Z","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":"10.1137/19m1270434","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"SIAM Journal on Matrix Analysis and Applications","work_id":"8fec6e78-b585-4e14-bf7b-283a6c2aa4eb","year":2020},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:47.810628Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:e3766bf73b65cd42b4e97e5f46fc46822e7f2a2119b7715012bff1050b3c0139","observation_id":"895860f1-ff46-4015-8d0b-3c428ef5cf3e","resolution":{"observed_at":"2026-08-04T10:14:08.039363Z","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":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/060659727","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Jir´ anek and M","venue":"SIAM Journal on Matrix Analysis and Applications","work_id":"93f32791-8293-4b1f-a2be-270d226ee9b5","year":2008},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:47.889573Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:295b676bc9212a61af47a92637b936a4c17aa8cae51af1d22e53d986c49e043e","observation_id":"f12172e3-9613-4589-bf07-4afe6da1a9aa","resolution":{"observed_at":"2026-08-04T10:14:07.889873Z","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":"2026-08-12T06:34:36.333875+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":"2026-08-04T10:12:47.961135Z","title":"Liesen and Z","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:47.961135Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:442f4015481e502dd9b000589faea7ac75b0edc612892436d0d8c1c304064e31","observation_id":"966a1332-eea2-4169-b6f6-417c2e9776fd","resolution":{"observed_at":"2026-08-04T10:12:47.961135Z","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":"10.1017/s096249290626001x","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Meurant and Z","venue":"Acta Numerica","work_id":"8a419cca-c1f8-43f3-9213-06145275c772","year":2006},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:48.030445Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:f34eea7eeb1070cef968267e7a8187f87075bf68273edc1c32a09c34175710e1","observation_id":"5b8022fc-45f2-4cc0-b832-537572157269","resolution":{"observed_at":"2026-08-04T10:14:07.784655Z","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":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/050630416","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"SIAM Journal on Matrix Analysis and Applications","work_id":"d2f0f448-9721-4164-aa59-557a1cf1e71e","year":2006},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:48.126585Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:6230bfe19e32152de6369303a27d6c386bfcf2939c63a454f847298881bbe093","observation_id":"24c121c4-c8e9-4992-9795-00989e9c0f57","resolution":{"observed_at":"2026-08-04T10:14:07.680653Z","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":"2026-08-12T06:34:36.333875+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":"2026-08-04T10:12:48.209213Z","title":null,"venue":null,"work_id":null,"year":1923},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:48.209213Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:a05f861e4ba63d0cc2f20eddca4d82340535706bfb4fbb27a6c8079bd29cee6e","observation_id":"9e741fdc-4712-4d48-b5dc-c7ed6a874816","resolution":{"observed_at":"2026-08-04T10:12:48.209213Z","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":"2026-08-04T10:12:48.341987Z","title":"Saad.Iterative methods for sparse linear systems","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:48.341987Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:9f689b6e3058fa69d64293d4ce6fcccd64afff9d2a8945effb6a7b85d27a0033","observation_id":"07205157-db76-400e-bd62-5a6277de3c23","resolution":{"observed_at":"2026-08-04T10:12:48.341987Z","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":"10.1145/3651155","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Scott and M","venue":"ACM Transactions on Mathematical Software","work_id":"f446ab98-153f-4dff-84cb-36dd6507973a","year":2024},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:48.488315Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:7080db5bde88a260ecfab30a42fcb9a8b9b26247627d9160ae1132f6bd4bc47c","observation_id":"e8b7f146-f518-4c5b-9a72-ca44ebe1d624","resolution":{"observed_at":"2026-08-04T10:14:07.360008Z","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":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/s0895479897323087","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"SIAM Journal on Matrix Analysis and Applications","work_id":"d3f24f55-9edf-40c4-bbf4-c60368a5568a","year":2001},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:48.603522Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:d752eff60a8460c56771f56bb5c3cada9a17a668c1a9f33462aa41f5645195a1","observation_id":"a75a3094-3cf4-4d8e-8917-2842639f7a53","resolution":{"observed_at":"2026-08-04T10:14:07.237644Z","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":"2026-08-12T06:34:36.333875+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":"2026-08-04T10:12:48.672343Z","title":"Strakoˇ s and P","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:48.672343Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:4b6dc211032459e73b594af87a34dee7cc1f09f25e2f6964d5de319489936b27","observation_id":"cc3646b4-307f-430d-8d15-840880908668","resolution":{"observed_at":"2026-08-04T10:12:48.672343Z","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/s10543-005-0032-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Strakoˇ s and P","venue":"BIT Numerical Mathematics","work_id":"44ebf0a2-8e24-4c12-9efe-8efa3a211f27","year":2005},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:48.749979Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:3352b6dee16a9d82a432369eda2b520ceba7fdbf69d346d41f12979a60696e06","observation_id":"14dc6cbb-4510-4aa3-bb8d-eb03e01e6a76","resolution":{"observed_at":"2026-08-04T10:14:06.989973Z","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":"2026-08-12T06:34:36.333875+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":"2026-08-04T10:12:48.881527Z","title":"Vieubl´ e.Mixed precision iterative refinement for the solution of large sparse linear sys- tems","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-04T10:12:48.881527Z"},"links":{"citing_paper":"/paper/2510.11379"},"observation_digest":"sha256:7255a98e1daa7c7d95f33a82aa95a297888304f4a6a1a5f291c0046b01b9bcd1","observation_id":"fd61105d-1389-45b2-b5c5-9648121ee341","resolution":{"observed_at":"2026-08-04T10:12:48.881527Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2510.11379","last_updated":"2026-07-21T08:39:38Z","latest_version":3,"primary_category":"math.NA","snapshot_observed_at":"2026-08-08T10:10:21.913749Z","submitted_at":"2025-10-13T13:21:02Z","title":"Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":4,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":10,"verified_fuzzy":0},"total_outbound_references":26},"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 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2510.11379."}