{"as_of":"2026-08-09T13:54:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4dc8933f3bbb08af510db039d1844f26065f4b57afdf7ab70ba91d995d71d8e7","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T15:40:06.587257Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+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/2507.15452/citation-record","integrity":"/paper/2507.15452/integrity","json":"/paper/2507.15452/citation-record.json","paper":"/paper/2507.15452"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.806182Z","title":"application to tissue perfusion problems","venue":null,"work_id":"70b56b74-b636-4fdc-9382-12f456ebe10c","year":2008},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.519816Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:cdf4ebfab5adecea89f299df90668d5fac211082073d8f74d51fba15601ba738","observation_id":"8319e4e3-e9cf-48ac-9943-67647c753fd1","resolution":{"observed_at":"2026-08-06T15:40:06.808551Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.798495Z","title":null,"venue":null,"work_id":"d98febb6-2f23-40a4-9919-fa79348d4435","year":2021},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.523327Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:a281b11b76dc36f528e3f9bb3659250b0d70c3b88f967bc62dfa50b3eea5cc55","observation_id":"68d9daab-bfde-499a-99c7-8a98fb341110","resolution":{"observed_at":"2026-08-06T15:40:06.801156Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.791440Z","title":"SIAM Journal on Numerical Analysis 59(1), 558–582 (2021)","venue":null,"work_id":"af510f6b-73c8-441c-be28-de191f6b2496","year":2021},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.526027Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:031aba623153dacb0ef44c264f455c46c589d29c330e71b70a386ecf9e033960","observation_id":"c03a3379-f99a-4e9e-9386-72456e010ab0","resolution":{"observed_at":"2026-08-06T15:40:06.793851Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.783768Z","title":"Mathematical Models and Methods in Applied Sciences 33(12), 2425–2462 (2023)","venue":null,"work_id":"ea5208d2-1b94-49f6-bd33-ae555069c57c","year":2023},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.529405Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:9fb76e5e93e2f72db8909a2b1007d636c04b9c78846e545adf051ab4b3165156","observation_id":"3df6f3ed-795e-427c-9fb4-f708103db6d7","resolution":{"observed_at":"2026-08-06T15:40:06.786413Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.776262Z","title":"Applied Mathematics","venue":null,"work_id":"8128bcf0-1859-4688-9693-a2ccc250b514","year":2003},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.532161Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:3301b72a9942089361bdfe87a0ea3395d69d8e66dccda42a752f9f9b89629ea6","observation_id":"58c97b85-952d-4b35-835c-08de217193cb","resolution":{"observed_at":"2026-08-06T15:40:06.778709Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.768824Z","title":"Numerical Linear Algebra with Applications 18(1), 1–40 (2011)","venue":null,"work_id":"6cf11b67-450a-49e7-861c-b797f14eeb3a","year":2011},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.536392Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:369063234cbcc374a314f3ed9dd2197254802036c89cf13a990c2c49e1b00177","observation_id":"6e413fd5-d5fd-422f-9efc-094d593904a7","resolution":{"observed_at":"2026-08-06T15:40:06.771257Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.761383Z","title":null,"venue":null,"work_id":"bd6e6896-8daf-499c-af1c-06c8e4fbe1d8","year":2005},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.539588Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:94c7a390967b567468b24541793c50b2bdca539ee39368489cd70db36aaa901d","observation_id":"34582ead-111b-41f8-9eeb-8ce0ca1e47c8","resolution":{"observed_at":"2026-08-06T15:40:06.763912Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.752834Z","title":"Elsevier, Amsterdam, The Netherlands (2000)","venue":null,"work_id":"964f567d-300b-46bd-8e21-e16f2d70ab54","year":2000},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.542443Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:087342795db677500682bda644733cbc06bde8c0bec1c573321c5af9afa0a0b1","observation_id":"68c88171-4b22-47e4-8282-dcbe5152cc5e","resolution":{"observed_at":"2026-08-06T15:40:06.755781Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.744465Z","title":"Oxford University Press, Oxford, UK (1999)","venue":null,"work_id":"d4276f6d-4934-4636-8fe9-7543c9372623","year":1999},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.544741Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:c8376e3578618b8e88875ed42b46e911f71ccad9eb0066adbf4cd6ae2fd0daf0","observation_id":"8924bae7-9ad9-40dd-bce5-9496c65496b6","resolution":{"observed_at":"2026-08-06T15:40:06.747410Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.735651Z","title":"SIAM Journal on Scientific Computing 38(6), 962–987 (2016)","venue":null,"work_id":"232d7d3b-8101-4402-ae99-3c12d371d11f","year":2016},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.547762Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:4df2951e22b339d3fffabfc79d3dbf082516ea1a6aff152adf1e23a7481e2cb2","observation_id":"5e8784da-b8c8-4bfb-bde0-20528d1505f8","resolution":{"observed_at":"2026-08-06T15:40:06.738757Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.727468Z","title":"SIAM Journal on Scientific Computing 46(3), 1461–1486 (2024) 22","venue":null,"work_id":"9547c70b-975c-4d34-b304-d43f74cedc63","year":2024},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.550342Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:db202f3133dcebb77c8671638ed22b29be16648bb0b05694057501228fb88174","observation_id":"3ebd3db7-caf0-4903-97a2-8c4d93f6073b","resolution":{"observed_at":"2026-08-06T15:40:06.730280Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.718940Z","title":"Computer Methods in Applied Mechanics and Engineering 431, 117256 (2024)","venue":null,"work_id":"c4e4af99-d0b0-4a53-a141-0460ab5d9a97","year":2024},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.552919Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:84361b0819c6c2f3f020b07bf57f419836d6e1f7ab563533dc4ad6898fc143ee","observation_id":"bc3e3c95-3ea2-45c2-9ce4-70da82eb6e60","resolution":{"observed_at":"2026-08-06T15:40:06.722023Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.709955Z","title":"SIAM Journal on Scientific Computing 45(3), 127–151 (2023)","venue":null,"work_id":"d76bb0cd-0110-4c67-af5d-44ae65446a9c","year":2023},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.555192Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:a917e19c7d0f6443a6b81d2fbd9d2d7a08cb1832d32182931bc836cfa5f8c568","observation_id":"5ece6ea9-1987-4745-ac30-dfe9df28e3e5","resolution":{"observed_at":"2026-08-06T15:40:06.712675Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.558491Z","title":"SIAM Journal on Scientific Computing 47(1), 151–181 (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.558491Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:2a742b253ab5dfc4a4dedc51664a069a6be64efaf77b45c18b79b39e1e374bc0","observation_id":"05da9e44-e045-4e6e-90ce-28a16e6954ca","resolution":{"observed_at":"2026-08-06T15:40:06.558491Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.697856Z","title":"Nature Machine Intelligence 3, 218–229 (2021)","venue":null,"work_id":"f385b978-c3c7-4f9a-b287-e271bc26173d","year":2021},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.560903Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:b0a3523bf335f7fd8f3bb65f13266d1218268b650b54a62c37abcbd9ed694ba6","observation_id":"67d29e4c-4ecb-4c11-b75e-6dd6de57e739","resolution":{"observed_at":"2026-08-06T15:40:06.700219Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.689930Z","title":"Communications on Applied Mathematics and Computation, 1–38 (2024)","venue":null,"work_id":"00328b51-d37e-4e36-a3af-e4c1b85da8b7","year":2024},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.563588Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:b11a28a320a78558f1bb82f90d14f31f70c75285a2c45f8d57a93f73d4e3c91a","observation_id":"b255d5c0-0dec-4875-bcbd-fa6f754f825a","resolution":{"observed_at":"2026-08-06T15:40:06.692763Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.08491","last_updated":"2025-05-13T12:22:08Z","snapshot_observed_at":"2026-08-07T15:45:46.813761Z","submitted_at":"2025-05-13T12:22:08Z","title":"Numerical Solution of Mixed-Dimensional PDEs Using a Neural Preconditioner","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.08491","snapshot_observed_at":"2026-08-06T15:40:06.566254Z","title":"https://arxiv.org/abs/2505.08491","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.566254Z"},"links":{"cited_paper":"/paper/2505.08491","citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:501fa06ae4c2a5d5e6b8edea6f2b4b3206489bfad8c0c8bbe817ba5f7a1e2f7f","observation_id":"4c4dae05-fea4-4874-af7f-491fdba2d29a","resolution":{"observed_at":"2026-08-06T15:40:06.566254Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.19638","last_updated":"2024-01-10T14:55:22Z","snapshot_observed_at":"2026-08-04T09:05:47.294364Z","submitted_at":"2023-05-31T08:07:44Z","title":"A Unified Framework for U-Net Design and Analysis","version":2},"cited_work":{"arxiv_id":"2305.19638","doi":null,"metadata_source":"pith","pith_arxiv_id":"2305.19638","snapshot_observed_at":"2026-08-06T15:40:06.623388Z","title":"A Unified Framework for U-Net Design and Analysis","venue":"stat.ML","work_id":"65d5bf32-42fa-4659-abbd-6bb0744355b4","year":2023},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.569291Z"},"links":{"cited_paper":"/paper/2305.19638","citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:1be593e78c23b6dbd1f8c5bcd9e7acb99df668c26322bb417c3bbb6eea590286","observation_id":"888804d2-fd0e-4bb4-9d57-34e726d2c3a3","resolution":{"observed_at":"2026-08-06T15:40:06.628091Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.681367Z","title":"arXiv e-prints, 1502 (2015)","venue":null,"work_id":"7b40d5ef-a5d4-4833-b568-67bdb94009ae","year":2015},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.572111Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:97ed9628fb09ff6c64ca38e75cc8d2fb845847e284e626191fd4e43327a35d80","observation_id":"fa49b704-fd2c-4aaa-b2dc-c0ff98175c46","resolution":{"observed_at":"2026-08-06T15:40:06.684002Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.672895Z","title":"SIAM Journal on Scientific Computing 14(2), 461–469 (1993)","venue":null,"work_id":"b06681bd-efd5-4a72-9fe7-82aa72963d94","year":1993},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.574878Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:09a6e502c3a51e9190a4934abe67b58af01c4f6ce59c20f3f052c3265308e769","observation_id":"256460b1-4d4c-4757-ba04-39c48bb87cb1","resolution":{"observed_at":"2026-08-06T15:40:06.675697Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.665118Z","title":"ESAIM: Mathematical Modelling and Numerical Analysis 53(6), 2047–2080 (2019)","venue":null,"work_id":"abe29d11-99cf-4a22-b143-8c2f004c0d55","year":2019},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.577286Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:6a20f72eb48e974e38f4e4feb4a66d446854f154c66c99bacd955da3def14f9c","observation_id":"343d9082-ffbc-4f77-ad3a-49d38b838950","resolution":{"observed_at":"2026-08-06T15:40:06.667771Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.657924Z","title":"Acta Numerica 10, 251–312 (2001)","venue":null,"work_id":"a719e0e5-53ea-4937-85e7-4301157697a5","year":2001},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.579481Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:a72ae74a4d237ec63506ee7389e730c4c035aecb839267e176809c7862ac50c0","observation_id":"ed04aa51-2417-4c49-aa0a-16a9b08c552d","resolution":{"observed_at":"2026-08-06T15:40:06.660295Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1912.01703","last_updated":"2019-12-03T22:06:05Z","snapshot_observed_at":"2026-07-06T08:41:49.632205Z","submitted_at":"2019-12-03T22:06:05Z","title":"PyTorch: An Imperative Style, High-Performance Deep Learning Library","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1912.01703","snapshot_observed_at":"2026-08-06T15:40:06.582330Z","title":"arXiv preprint arXiv:1912.01703 (2019)","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.582330Z"},"links":{"cited_paper":"/paper/1912.01703","citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:1104d7b5899c63a831d5a8ad13796a2f5db847fe3803df7a8e6566b90eadc68c","observation_id":"2d921174-a838-4f3e-bb8c-b93cc5f8a23e","resolution":{"observed_at":"2026-08-06T15:40:06.582330Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.650195Z","title":"Journal of Scientific Computing 97(35) (2023) 23","venue":null,"work_id":"25a822de-a49c-42f8-94fe-96678cd77dd6","year":2023},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.584832Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:7056ff182087e8cf840f53b01c5834086eb1128d78368000c9c3112a7a33e2dc","observation_id":"35833f9c-1d93-4d26-9666-e1f90d1ac4e5","resolution":{"observed_at":"2026-08-06T15:40:06.652655Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:40:06.642583Z","title":"arXiv (2018) 24","venue":null,"work_id":"95541481-ea3e-4ed4-bf88-dd3b445db5f6","year":2018},"citing_paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T15:40:06.587257Z"},"links":{"citing_paper":"/paper/2507.15452"},"observation_digest":"sha256:64e8e18343c6b564dcdb8b3821b1d5480f25ae10ca2847d65e6d2ffcc5960cd4","observation_id":"5d6a3f3a-b684-4796-9d3a-ff3c04630351","resolution":{"observed_at":"2026-08-06T15:40:06.645240Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.15452","last_updated":"2025-07-21T10:03:55Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-07T21:01:48.394631Z","submitted_at":"2025-07-21T10:03:55Z","title":"Neural Preconditioning via Krylov Subspace Geometry"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":5,"verified_exact":0,"verified_fuzzy":19},"total_outbound_references":25},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2507.15452."}