{"as_of":"2026-08-09T13:45:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:dac41c2eb21cc7878facc294bd89dde358187cb2dd30b6fcab973b623b1a506a","coverage":[{"denominator":63,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":63,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T17:57:21.013316Z","state":"measured"},{"denominator":64,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":64,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-15T19:01:40.879901Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":1,"source":"arxiv_reference","source_observed_at":"2026-08-05T02:28:24.338817Z","state":"measured"}],"external_citation_measurements":[{"count":0,"observed_at":"2026-08-05T02:28:24.338817Z","source":"arxiv_reference"}],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"cited_work":{"arxiv_id":"2509.10378","doi":"10.48550/arxiv.2509.10378","metadata_source":"arxiv_reference","pith_arxiv_id":"2509.10378","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"ArXiv.org","work_id":"bad845fa-84a2-437c-bd99-f7165e912cdf","year":2025},"citing_paper":{"arxiv_id":"2602.23840","last_updated":"2026-02-27T09:21:48Z","snapshot_observed_at":"2026-07-06T22:47:15.482910Z","submitted_at":"2026-02-27T09:21:48Z","title":"A novel gauge-equivariant neural-network architecture for preconditioners in lattice QCD","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-15T19:01:40.879901Z"},"links":{"cited_paper":"/paper/2509.10378","citing_paper":"/paper/2602.23840"},"observation_digest":"sha256:2b8f09d89a2577a26f73a396c85d8833b52767570bfaa54e42fe602de7d32865","observation_id":"6e61cee8-5daa-4925-ade1-b0a6b244fdb9","resolution":{"observed_at":"2026-05-15T19:06:30.469466Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2509.10378/citation-record","integrity":"/paper/2509.10378/integrity","json":"/paper/2509.10378/citation-record.json","paper":"/paper/2509.10378"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T17:57:17.393828Z","title":"Hadrons and nuclei.The European Physical Journal A, 55:1–27, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:17.393828Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:73cea1f748572ac07c1ead65ef42c96fdef8ac405b69e6dc965b60354150d042","observation_id":"b7ac2844-0d9a-4bc4-8e1a-093041974c6c","resolution":{"observed_at":"2026-08-04T17:57:17.393828Z","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":"2026-08-04T17:57:17.456758Z","title":"Review of particle physics.Progress of Theoretical and Experimental Physics, 2020(8):083C01, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:17.456758Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:fda36e9fd5b3290c9237b194f3e36474c1dc00b5662511df45f2a423ca59c7ca","observation_id":"8f7ce356-f6c0-4b76-ba8f-37b58adf9874","resolution":{"observed_at":"2026-08-04T17:57:17.456758Z","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":"2026-08-04T17:57:17.487284Z","title":"Hot-dense lattice qcd.The European Physical Journal A, 55:1–11, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:17.487284Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:3328179ee8839998830eaa79c314b3cb8d9a61283ac5aeadd96a09f9f59ead9e","observation_id":"61370699-7351-4ecd-b67f-5bfc1ddcef64","resolution":{"observed_at":"2026-08-04T17:57:17.487284Z","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":"2026-08-04T17:57:17.552383Z","title":"Status and future perspectives for lattice gauge theory calculations to the exascale and beyond.The European Physical Journal A, 55:1–26, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:17.552383Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:be9cf0d0dff64ca4e7059ae803687c80a60c13f3be8f6887b9e5f03124b05fb3","observation_id":"9b9ceee5-0ebd-42b1-998f-6ab671b73631","resolution":{"observed_at":"2026-08-04T17:57:17.552383Z","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":"2026-08-04T17:57:17.587641Z","title":"SIAM, 2003","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:17.587641Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:e30b496ddc9700028664fc2d51fc71467008f6008b36463987159ffbaec2e47d","observation_id":"cd3eaa0a-d681-4569-99b7-a3db6f57743c","resolution":{"observed_at":"2026-08-04T17:57:17.587641Z","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":"2026-08-04T17:57:17.653210Z","title":"Hackett, Yin Lin, Phiala E","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:17.653210Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:5c6fa9198e36c7150c51afe82a25fb92a05b87e0e9711295b6e954c00d9cc844","observation_id":"d49d99bb-fd72-4454-8c21-6f0424a6cc44","resolution":{"observed_at":"2026-08-04T17:57:17.653210Z","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":"2026-08-04T17:57:17.756146Z","title":"Brannick and K","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:17.756146Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:e9d9df1229dac81632c1efe7058b7497c0881540c72bacf4769fad5ed1f4f74f","observation_id":"03a2fad4-7dcf-4909-a4ea-da6ea6d36b92","resolution":{"observed_at":"2026-08-04T17:57:17.756146Z","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":"2026-08-04T17:57:17.857627Z","title":"Adaptive multigrid algorithm for lattice qcd.Physical review letters, 100(4):041601, 2008","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:17.857627Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:bff3c872796ba3c41952012d54589c5f9d64f37f4a8886b563c6a96705897856","observation_id":"9985c440-5392-4f31-b5ea-402423677851","resolution":{"observed_at":"2026-08-04T17:57:17.857627Z","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":"2026-08-04T17:57:17.900338Z","title":"Adaptive multigrid algorithm for the lattice wilson-dirac operator.Physical review letters, 105(20):201602, 2010","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:17.900338Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:0b6b4ae7aef8226ee3996a259503ad93b0204acdadee361c86f1145520b08335","observation_id":"ff58cc9a-9cbd-4b1c-bf4d-46c37d9e5af7","resolution":{"observed_at":"2026-08-04T17:57:17.900338Z","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":"2026-08-04T17:57:17.987659Z","title":"Brower, M","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:17.987659Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:66bc6b146c29848d103900394c55885fe1071b506c5fb88eea7ef7b9ea22ae0d","observation_id":"0cf95e60-e331-41f6-9396-43c5b3c122b0","resolution":{"observed_at":"2026-08-04T17:57:17.987659Z","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":"2026-08-04T17:57:18.054385Z","title":"Brower, M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.054385Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:aa47577e3f335afcbe18a533e6843bc910d73af5e3f8ed5b007135f215ebbf6a","observation_id":"c37547e7-31f7-4403-bfcb-532f99968fb3","resolution":{"observed_at":"2026-08-04T17:57:18.054385Z","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":"2026-08-04T17:57:18.097788Z","title":"Babich, M","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.097788Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:e1a519322f57563cd2424cf2d15bb1f7a32aa113efb9d6a199e48a83ba8b5c5b","observation_id":"6ad4b193-7bb3-4c25-8f0c-b43167640208","resolution":{"observed_at":"2026-08-04T17:57:18.097788Z","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":"2026-08-04T17:57:18.142433Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.142433Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:af575eb992dddee40e55d7c78df844077445709e80ffffa91e7a4decb1f760ac","observation_id":"fc01b4bc-2947-4c6a-982c-6ed4ef7be95f","resolution":{"observed_at":"2026-08-04T17:57:18.142433Z","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":"2026-08-04T17:57:18.212767Z","title":"Adaptive Aggregation-Based Domain Decomposition Multigrid for the Lattice Wilson–Dirac Operator.SIAM J","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.212767Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:4b21d30612d2b5c7587e44493adefa1c7792b32901e1464ed2227f2772cb51b4","observation_id":"8f5660a9-e595-43cf-8921-36aa6435b610","resolution":{"observed_at":"2026-08-04T17:57:18.212767Z","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":"2026-08-04T17:57:18.245535Z","title":"Comparison of Domain Wall Fermion Multigrid Methods","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.245535Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:d7d3f855da15cad65a2b29e122f0c89e4f11e3c7e202ec5d9682b384b2788e64","observation_id":"45725ede-54d0-4ac6-b26d-7806749e2455","resolution":{"observed_at":"2026-08-04T17:57:18.245535Z","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":"2026-08-04T17:57:18.285929Z","title":"Adaptive Aggregation-based Domain Decomposition Multigrid for Twisted Mass Fermions.Phys","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.285929Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:20725a87dccd6acf54091c5c4199da58d7645a2f74ff192c629bd53a35c53f54","observation_id":"4c1f2e02-909a-4558-a795-8398a5e0cdd6","resolution":{"observed_at":"2026-08-04T17:57:18.285929Z","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":"2026-08-04T17:57:18.329759Z","title":"Multigrid Preconditioning for the Overlap Operator in Lattice QCD.Numer","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.329759Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:43f34c653f3a8e2c4ab98c597afab30551a675c3991e0e49d7f16de07834f8f4","observation_id":"9f8e128c-6d11-4448-9c3a-307346cbd2da","resolution":{"observed_at":"2026-08-04T17:57:18.329759Z","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":"2026-08-04T17:57:18.374377Z","title":"Brower, Robert G","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.374377Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:c8a67babfafcdb2958f1619434c445750d4a68b9c916bd2caa52ccb6fee50e2c","observation_id":"cce5dae0-8cc8-4503-9776-0cfbc3578f30","resolution":{"observed_at":"2026-08-04T17:57:18.374377Z","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":"2026-08-04T17:57:18.496583Z","title":null,"venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.496583Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:9a615984beecbecb3bca8d2665ae215d6dbbd3f8096aed819b6650144f3595a3","observation_id":"4b0b3d20-9dad-4e83-a139-4916478709b6","resolution":{"observed_at":"2026-08-04T17:57:18.496583Z","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":"2026-08-04T17:57:18.566319Z","title":"Accelerating multigrid with streaming chiral SVD for Wilson fermions in lattice QCD","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.566319Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:b8341d8f9b75c5d19ddcb6e6b3689f4d348a806b3888649b0191dd97eaee247d","observation_id":"f439b463-449e-439b-908f-6dc1cb82132d","resolution":{"observed_at":"2026-08-04T17:57:18.566319Z","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":"2026-08-04T17:57:18.669204Z","title":"Multigrid low-mode averaging.Phys","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.669204Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:56349ccd218c15f0689c08a4cced734d4e53fd82fd3cfe40ac6c51e7937803d3","observation_id":"e973157c-d0c6-43ad-99b8-eb5e5c341400","resolution":{"observed_at":"2026-08-04T17:57:18.669204Z","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":"2026-08-04T17:57:18.744104Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.744104Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:e3bbc40964139e7cbf027b812fbb1255f308b3eaa0c3e24d8c0f6861f0d323d8","observation_id":"72c45520-8d4a-45d3-95dc-b92998b50ca4","resolution":{"observed_at":"2026-08-04T17:57:18.744104Z","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":"2026-08-04T17:57:18.764610Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.764610Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:fcfb16760ee9c5e7b29f4bb9f3b09ba0d7797af916296bfe0d7bfd7f44db732e","observation_id":"e1ff44e6-9ba4-4276-90c8-bb457a554586","resolution":{"observed_at":"2026-08-04T17:57:18.764610Z","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":"2026-08-04T17:57:18.803646Z","title":"Deflated Multigrid Multilevel Monte Carlo.PoS, LAT- TICE2022:030, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.803646Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:83d85c363fabc81f3224645acfd76eaa14e861474fd9d2b767350a58e9039a4d","observation_id":"de8a5503-e15a-4f7f-bf46-d1b869b6e1d9","resolution":{"observed_at":"2026-08-04T17:57:18.803646Z","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":"2026-08-04T17:57:18.907402Z","title":"MRHS multigrid solver for Wilson-clover fermions.PoS, LATTICE2022:285, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.907402Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:f9f6fa15bf54725f55b0f01cc1f531f58acbf9ee28fe2ce035a7d436f7abad7d","observation_id":"b6ab81d9-79fa-4850-bc04-e2bee18c44eb","resolution":{"observed_at":"2026-08-04T17:57:18.907402Z","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":"2026-08-04T17:57:18.981377Z","title":"Boyle, and Tilo Wettig","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:18.981377Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:f0c69990dc0ad67926470edcacdc1ad9be9daddefe2919e2ebbd8d49fdb911e8","observation_id":"fd623212-087d-42b0-a1df-cbf327c61bad","resolution":{"observed_at":"2026-08-04T17:57:18.981377Z","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":"2026-08-04T17:57:19.069269Z","title":"Coarsest-level improvements in multigrid for lattice QCD on large-scale computers.Comput","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.069269Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:0e051356abe22e93964095d64b71ee29dedb14e7960b17642aa1cd9923b9d1ee","observation_id":"2904fd62-ab54-4cb6-b3aa-ce64886151e7","resolution":{"observed_at":"2026-08-04T17:57:19.069269Z","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":"2026-08-04T17:57:19.112908Z","title":"SIAM, 1994","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.112908Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:ceec912f50133686519339c09324091a323659f52fda9c709f400f5ada7b7b49","observation_id":"2ea98213-b69c-45fd-a1bc-edea50e83f32","resolution":{"observed_at":"2026-08-04T17:57:19.112908Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.16368","last_updated":"2024-10-24T14:06:40Z","snapshot_observed_at":"2026-08-07T15:58:04.205013Z","submitted_at":"2023-05-25T11:45:46Z","title":"Neural incomplete factorization: learning preconditioners for the conjugate gradient method","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.16368","snapshot_observed_at":"2026-08-04T17:57:19.156833Z","title":"Neural incomplete factorization: learning preconditioners for the conjugate gradient method, October 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.156833Z"},"links":{"cited_paper":"/paper/2305.16368","citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:cf29b10d5fedbaa06664c1cd40c526fec7ba9f19c77e8b70a5dce89eb2c37a4b","observation_id":"98e6596f-6f8b-4333-b0a2-b47dde1ddc3f","resolution":{"observed_at":"2026-08-04T17:57:19.156833Z","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":"2026-08-04T17:57:19.203087Z","title":"Hicken, and Shaowu Pan","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.203087Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:347666b038506ee2ec3afaa088d2db5a1355298b504f398e3b0cc0a1d2122950","observation_id":"738b8ca1-b875-4b96-8bb7-a7d8930efd9e","resolution":{"observed_at":"2026-08-04T17:57:19.203087Z","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":"2026-08-04T17:57:19.276449Z","title":"NeuralPCG: Learning Preconditioner for Solving Partial Differential Equations with Graph Neural Network","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.276449Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:6e801bf1ac664d80a9c83a62dd5e170f70a48ec27d63d0cb9fe905b7d6dfa6f7","observation_id":"82a86da8-34e4-42ea-b777-758ed8a8e767","resolution":{"observed_at":"2026-08-04T17:57:19.276449Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2203.11025","last_updated":"2022-03-14T10:31:11Z","snapshot_observed_at":"2026-07-06T12:50:15.089729Z","submitted_at":"2022-03-14T10:31:11Z","title":"Multigrid-augmented deep learning preconditioners for the Helmholtz equation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2203.11025","snapshot_observed_at":"2026-08-04T17:57:19.308453Z","title":"Multigrid-augmented deep learning preconditioners for the Helmholtz equation, March 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.308453Z"},"links":{"cited_paper":"/paper/2203.11025","citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:c7016bca6d9d8231a3e3194ee998ecba1d7da85de5d03a072a3dc599616218a3","observation_id":"ea6f0652-2164-40a3-b535-77e3e207cdbb","resolution":{"observed_at":"2026-08-04T17:57:19.308453Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.06925","last_updated":"2019-06-17T09:57:06Z","snapshot_observed_at":"2026-07-06T08:00:46.942504Z","submitted_at":"2019-06-17T09:57:06Z","title":"Deep Learning of Preconditioners for Conjugate Gradient Solvers in Urban Water Related Problems","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.06925","snapshot_observed_at":"2026-08-04T17:57:19.373838Z","title":"Deep Learning of Preconditioners for Conjugate Gradient Solvers in Urban Water Related Problems, June 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.373838Z"},"links":{"cited_paper":"/paper/1906.06925","citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:f431c4d0cf0960d70cb933693b79dc2d484cad55f599de61412020f619af5205","observation_id":"ba4500fb-f824-49a1-bab1-1825041e712a","resolution":{"observed_at":"2026-08-04T17:57:19.373838Z","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":"2026-08-04T17:57:19.410881Z","title":"Graph Neural Networks for Selection of Preconditioners and Krylov Solvers","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.410881Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:00919ac91a8403686a96c650553ae88d809141d7519076489cad099c2c0e9e39","observation_id":"4fc7f783-9950-4b2d-8f6a-56dd357c4ab5","resolution":{"observed_at":"2026-08-04T17:57:19.410881Z","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":"2026-08-04T17:57:19.454354Z","title":"Preconditioning.Acta Numerica, 24:329–376, 2015","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.454354Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:27de41825f134c4ee614acd950e4faa7116511eb42819c0287be1957fe44514e","observation_id":"fea59815-d952-4dc7-9790-c46108e595ea","resolution":{"observed_at":"2026-08-04T17:57:19.454354Z","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":"2026-08-04T17:57:19.499631Z","title":"SIAM, 1997","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.499631Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:5f937d39943b0385e6c38d24b07f27254bd6f6e405d83520e6cbd6ec92505ea4","observation_id":"c9d8b8ef-d203-4812-b3e7-fbefdc7ac930","resolution":{"observed_at":"2026-08-04T17:57:19.499631Z","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":"2026-08-04T17:57:19.591980Z","title":"Number 13","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.591980Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:6cca29b115b91c0fa4d7936cfdd25f7fa9920991fec328a438dc768a53023bce","observation_id":"fd1082a1-0472-4794-b376-ac4993f59bb6","resolution":{"observed_at":"2026-08-04T17:57:19.591980Z","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":"2026-08-04T17:57:19.664482Z","title":"SIAM, 2014","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.664482Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:e9cee252df75282153b3e77ed1123af69843c8a1be1325b4b84a46ee400a4bdd","observation_id":"18a5e21c-9c34-4ba9-bb26-e85b3e812924","resolution":{"observed_at":"2026-08-04T17:57:19.664482Z","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":"2026-08-04T17:57:19.711612Z","title":"Preconditioning discretizations of systems of partial differential equations","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.711612Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:e3dfb65c4efc3801f51433e7cda78517069a36c024abd9e68f16e15a4fb694ce","observation_id":"a045c1a9-0a7c-4f40-b2da-db2d49b1d85d","resolution":{"observed_at":"2026-08-04T17:57:19.711612Z","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":"2026-08-04T17:57:19.722967Z","title":"A note on preconditioners and scalar products in krylov subspace methods for self-adjoint problems in hilbert space.Electron","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.722967Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:4b67f295ffa4da6a1827c4c1d846a68f3f5d4daf9de1a22e9b51df01239219b3","observation_id":"6de0469a-bec1-4020-b5f7-26c3bd47da8a","resolution":{"observed_at":"2026-08-04T17:57:19.722967Z","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":"2026-08-04T17:57:19.777599Z","title":"SIAM, 2014","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.777599Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:f63eab92d0e665f975af426e2d701f9d3cee92281cd45805d24e2da5ccc9f349","observation_id":"7eda7a7c-500a-49d8-bdae-77a5d1c1a6f5","resolution":{"observed_at":"2026-08-04T17:57:19.777599Z","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":"2026-08-04T17:57:19.834732Z","title":"Preconditioning techniques for large linear systems: a survey.Journal of computational Physics, 182(2):418–477, 2002","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.834732Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:7dbf7ffc0eb6a6d04b616f8053575f6c5432a899c58cbc9da03b89fd160c4088","observation_id":"74ceed8a-26f9-4f45-9433-39cd3527d83c","resolution":{"observed_at":"2026-08-04T17:57:19.834732Z","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":"2026-08-04T17:57:19.863566Z","title":"Graph Networks as a Universal Machine Learning Framework for Molecules and Crystals.Chemistry of Materials, 31(9):3564–3572, May 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.863566Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:c662c8009e8504ee018769d473051f90339243008a1a2d3cd6ac873614e1ccbe","observation_id":"d8b8b388-b667-4348-a79b-ac332af27236","resolution":{"observed_at":"2026-08-04T17:57:19.863566Z","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":"2026-08-04T17:57:19.917221Z","title":"Düben, Tim N","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.917221Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:b91bd14ef0a7d51d041fcd77d257564d8687e8cae5e428c9fffca201c64867a5","observation_id":"475334d4-4f1b-402d-a590-ddd048d9af36","resolution":{"observed_at":"2026-08-04T17:57:19.917221Z","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":"2026-08-04T17:57:19.945878Z","title":"Graph neural preconditioners for iterative solutions of sparse linear systems, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.945878Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:6ef64cf50fb2a3db1c0089b618f6ba654f7e3649994bb11470c222a37a1b81ed","observation_id":"c8b5fc91-8e28-4e11-a338-2d61dc3d78ee","resolution":{"observed_at":"2026-08-04T17:57:19.945878Z","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":"2026-08-04T17:57:19.999622Z","title":"Gauge-equivariant neural networks as preconditioners in lattice QCD, February","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:19.999622Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:30224ff103b5a0830341d8ab198496eee2fa4723559a4ebd0754e232c513085c","observation_id":"b2aff152-1347-4db1-8d0a-6a6406c83925","resolution":{"observed_at":"2026-08-04T17:57:19.999622Z","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":"2026-08-04T17:57:20.121022Z","title":null,"venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.121022Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:cc42ecafe82231647e54b7d91245ec1bd19ee8450873daa8e0decfbfe008030a","observation_id":"e7cd1070-643f-418f-92dd-2419c4796271","resolution":{"observed_at":"2026-08-04T17:57:20.121022Z","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":"2026-08-04T17:57:20.135578Z","title":"Multilayer feedforward networks are universal approxi- mators.Neural Networks, 2(5):359–366, January 1989","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.135578Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:0b6a19d8e95e035913a4e29463dd2bc080220f8467a881acb654bf2ff4c9eb0c","observation_id":"f6c47d63-abc5-496a-96fc-36ba4a0cd871","resolution":{"observed_at":"2026-08-04T17:57:20.135578Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2010.08895","last_updated":"2021-05-17T03:12:33Z","snapshot_observed_at":"2026-07-06T10:05:26.653366Z","submitted_at":"2020-10-18T00:34:21Z","title":"Fourier Neural Operator for Parametric Partial Differential Equations","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.08895","snapshot_observed_at":"2026-08-04T17:57:20.158538Z","title":"Fourier Neural Operator for Parametric Partial Differential Equations, May 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.158538Z"},"links":{"cited_paper":"/paper/2010.08895","citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:ca5ae1cb7360ab00b7b5a50b91434af64810aa9d1896585b48a25af218662406","observation_id":"40d557cf-7f1f-46b6-8767-31800bc71187","resolution":{"observed_at":"2026-08-04T17:57:20.158538Z","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":"2026-08-04T17:57:20.242978Z","title":"Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.Nature Machine Intelligence, 3(3):218–229, March 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.242978Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:4f88e5d1c5d8b5a6ba29c66962196c29de42ff83cd00e940359738184cf527e1","observation_id":"bf460760-d032-4861-be29-319c63d24ae5","resolution":{"observed_at":"2026-08-04T17:57:20.242978Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-09T04:16:11.013437Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-04T17:57:20.298639Z","title":"Neural Operator: Learning Maps Between Function Spaces, April 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.298639Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:e92d5af8cfe3f087b549015359f658a9645b3649117b441d3b4615e575b7a6f1","observation_id":"70de1d89-488e-413b-9b55-ae4160e23cfc","resolution":{"observed_at":"2026-08-04T17:57:20.298639Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2009.11992","last_updated":"2020-09-25T01:13:51Z","snapshot_observed_at":"2026-07-06T09:58:38.280271Z","submitted_at":"2020-09-25T01:13:51Z","title":"A physics-informed operator regression framework for extracting data-driven continuum models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2009.11992","snapshot_observed_at":"2026-08-04T17:57:20.352204Z","title":"Patel, Nathaniel A","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.352204Z"},"links":{"cited_paper":"/paper/2009.11992","citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:f20756cc728661c8e24e2db4e2c840b3db1a1e6cb8813fd1323ee43f90a509d0","observation_id":"899cac90-a1f2-4dcf-8f3c-7109cb27c280","resolution":{"observed_at":"2026-08-04T17:57:20.352204Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.06905","last_updated":"2021-09-13T06:33:30Z","snapshot_observed_at":"2026-07-06T11:38:32.437113Z","submitted_at":"2021-08-16T05:31:05Z","title":"A physics-informed variational DeepONet for predicting the crack path in brittle materials","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.06905","snapshot_observed_at":"2026-08-04T17:57:20.412216Z","title":"A physics-informed variational Deep- ONet for predicting the crack path in brittle materials.arXiv:2108.06905 [cs, math], September 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.412216Z"},"links":{"cited_paper":"/paper/2108.06905","citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:54de28c98856d190cd8e2b4a2e80e428b53240dffbc1723d1f351e3dfe787c02","observation_id":"96ac513b-eac1-46a8-9595-8050a48b01ee","resolution":{"observed_at":"2026-08-04T17:57:20.412216Z","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":"2026-08-04T17:57:20.466461Z","title":"DeepGraphONet: A Deep Graph Operator Network to Learn and Zero-Shot Transfer the Dynamic Response of Networked Systems.IEEE Systems Journal, 17(3):4360– 4370, September 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.466461Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:8fcd1504cd10033643f200ac9f314738e46ebf1012b2b0fa60e20d0e0a8eb4ab","observation_id":"d02475b3-f7f5-47c6-aaf3-94a8d2b8e3c3","resolution":{"observed_at":"2026-08-04T17:57:20.466461Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.14688","last_updated":"2023-12-22T13:43:57Z","snapshot_observed_at":"2026-07-06T17:07:06.073336Z","submitted_at":"2023-12-22T13:43:57Z","title":"A Mathematical Guide to Operator Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.14688","snapshot_observed_at":"2026-08-04T17:57:20.511261Z","title":"A Mathematical Guide to Operator Learning, December 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.511261Z"},"links":{"cited_paper":"/paper/2312.14688","citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:6b9c629a2f4f30b5882fd72e53d493856cc5b1e72a349ab1e86fb6c87acbf725","observation_id":"570f73eb-9b3e-4883-b6c7-bb59819b0fbe","resolution":{"observed_at":"2026-08-04T17:57:20.511261Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1411.4038","last_updated":"2015-03-08T22:16:40Z","snapshot_observed_at":"2026-07-06T04:00:38.324755Z","submitted_at":"2014-11-14T20:46:03Z","title":"Fully Convolutional Networks for Semantic Segmentation","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1411.4038","snapshot_observed_at":"2026-08-04T17:57:20.595607Z","title":"Fully Convolutional Networks for Semantic Segmentation","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.595607Z"},"links":{"cited_paper":"/paper/1411.4038","citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:fe4036f11dc1d4ae81e01e01f6ab0778ec75db71549c3228557542d64d1d15a1","observation_id":"1b701174-d1ea-4074-bba2-9f5577032701","resolution":{"observed_at":"2026-08-04T17:57:20.595607Z","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":"2026-08-04T17:57:20.689632Z","title":"Confinement of quarks.Physical review D, 10(8):2445, 1974","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.689632Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:26c34fdf9fffcedf40437247c40b6e5f9ba591241994c6ea77da5bf6e725705e","observation_id":"37af0b93-d2af-4f23-8510-6b223051f9aa","resolution":{"observed_at":"2026-08-04T17:57:20.689632Z","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":"2026-08-04T17:57:20.731624Z","title":"CASK: A Gauge Covariant Transformer for Lattice Gauge Theory","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.731624Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:5dfeb1832a7901a621604ad86209bf155f6eb1644e2834f66b74cfa6e16aa479","observation_id":"928862ae-9b82-4e11-9caf-38e03977ee42","resolution":{"observed_at":"2026-08-04T17:57:20.731624Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.17039","last_updated":"2024-05-06T19:15:43Z","snapshot_observed_at":"2026-07-06T18:05:51.085146Z","submitted_at":"2024-04-25T21:05:01Z","title":"Differentiating Through Linear Solvers","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.17039","snapshot_observed_at":"2026-08-04T17:57:20.822268Z","title":"Differentiating through linear solvers.arXiv preprint arXiv:2404.17039, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.822268Z"},"links":{"cited_paper":"/paper/2404.17039","citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:c7403cc520d0db46b7e3bcd769b358472345ba69432fb398dfbc77816ad71040","observation_id":"e9c813a4-887b-438d-b496-fa05abf8af1c","resolution":{"observed_at":"2026-08-04T17:57:20.822268Z","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":"2026-08-04T17:57:20.873221Z","title":"A taxonomy of automatic differentiation pitfalls.Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 14(6):e1555, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.873221Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:ef85c874630970cc0e7f6ee3cdd586177a6d30f5c06bc1286733c2595af944f1","observation_id":"e4ea6fc1-76a1-4323-a1cd-416684f89605","resolution":{"observed_at":"2026-08-04T17:57:20.873221Z","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":"2026-08-04T17:57:20.955592Z","title":"Scaling test of fermion actions in the schwinger model","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.955592Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:499611de97ee64255ecce86d76bc9b8b9ab68344c6fb17ce4ad6442847679978","observation_id":"8563001a-673a-454f-a342-0b815417db9d","resolution":{"observed_at":"2026-08-04T17:57:20.955592Z","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":"2026-08-04T17:57:21.013316Z","title":"Cambridge University Press, 2003","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:21.013316Z"},"links":{"citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:9b4cbe507459a0deb23049b66ffb48514c098cee419f08e426d54d4b91436311","observation_id":"2cbc072f-8b33-4edf-b82c-5b0d38bd46b7","resolution":{"observed_at":"2026-08-04T17:57:21.013316Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2302.05419","last_updated":"2023-02-10T18:34:54Z","snapshot_observed_at":"2026-07-06T14:50:33.453443Z","submitted_at":"2023-02-10T18:34:54Z","title":"Gauge-equivariant neural networks as preconditioners in lattice QCD","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2302.05419","snapshot_observed_at":"2026-08-04T17:57:20.081997Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.081997Z"},"links":{"cited_paper":"/paper/2302.05419","citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:d8686639c6bfca14826d078c823ec60173e19499773f5f1703af927782e09601","observation_id":"c4a89151-39b2-4cc8-b7b8-5be5c8c47114","resolution":{"observed_at":"2026-08-04T17:57:20.081997Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","latest_version":1,"primary_category":"hep-lat","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory"},"reference_resolution":{"displayed":63,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":63,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":63},"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 63 of 63 outbound references and 1 inbound Pith citation observation for arXiv:2509.10378."}