{"as_of":"2026-08-08T10:15:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f951b92c9d6b87eda6801caa7ca784ae2ceec3dfbe51592658e3ef82a846a859","coverage":[{"denominator":20,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":20,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:27:27.682085Z","state":"measured"},{"denominator":20,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":20,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2506.08550/citation-record","integrity":"/paper/2506.08550/integrity","json":"/paper/2506.08550/citation-record.json","paper":"/paper/2506.08550"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:27.591319Z","title":"Absil, R","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.591319Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:2a60956d64d34b197b042d0dd53d3f945f200afaa33a1e6a7087c497052e34c9","observation_id":"9391bf56-e6b8-40d4-8257-59f4f7d1b320","resolution":{"observed_at":"2026-08-07T05:27:27.591319Z","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":"2026-08-07T05:27:28.104979Z","title":"Aronszajn,Theory of reproducing kernels, Trans","venue":null,"work_id":"b8263d5e-46f1-4565-9f9a-69eca2217504","year":1950},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.596675Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:1c2e70f0fd408f3ae0455788ba1439d71b261d970c4de0604ba2ae0ce1cc90d6","observation_id":"6d8d8ce1-24f9-4fda-b4d8-eb101b49d3d3","resolution":{"observed_at":"2026-08-07T05:27:28.109527Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:28.091294Z","title":"Bach,Learning Theory from First Principles, MIT Press, 2024","venue":null,"work_id":"1c7e806c-8fcd-40ce-b5da-40426da4e917","year":2024},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.602135Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:cc4bd8a4eff4578facff5c5e942fc35c356e2e60efbf777c30ac882d91932322","observation_id":"22165724-65ce-4904-a017-2a48aaac35c3","resolution":{"observed_at":"2026-08-07T05:27:28.095802Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:28.077000Z","title":"Bach and L","venue":null,"work_id":"80c654de-01c5-4cbf-a87a-7467eb9d8c14","year":2023},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.607997Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:fdb3aba2b816f9f9d9148a359e0d8ae7545bd11c907e5af1a4220788237ca468","observation_id":"fde2f35b-14a0-4f9e-ada1-975de578b530","resolution":{"observed_at":"2026-08-07T05:27:28.081914Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:28.063180Z","title":null,"venue":null,"work_id":"0c7adb0d-16a4-4b2f-9530-4977dd504286","year":1993},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.613044Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:ad862e670a21e94aeac6bc1518065b7b5dee9478d2f79c0f22844f8620e13a9c","observation_id":"1f40180f-a2be-42a6-9da2-bd090dfef24b","resolution":{"observed_at":"2026-08-07T05:27:28.067891Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:28.048386Z","title":"Boumal.An Introduction to Optimization on Smooth Manifolds","venue":null,"work_id":"658365e8-bf4f-4dcd-bf38-e1f6dd2167d9","year":2023},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.617770Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:c8bdd0bc06382ceff7db473b418429db917cab48e023fecf7d6f30c77a49283e","observation_id":"5550b652-efd1-428d-8534-67ed6df5b561","resolution":{"observed_at":"2026-08-07T05:27:28.053439Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:27.622987Z","title":"automati- cally","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.622987Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:abc68072f704f359c58636ed49189d9f684587de4d6f742efc18207168ae69da","observation_id":"d95538f5-1b7f-4b08-bbbf-7964a5ff3579","resolution":{"observed_at":"2026-08-07T05:27:27.622987Z","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":"2026-08-07T05:27:28.034595Z","title":"Cucker and S","venue":null,"work_id":"b85f69fb-8952-4431-845b-3f41263b790a","year":2002},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.628130Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:13d860ae18bfa9e42f208fdd1d07656b60b7c5f4ea2b16bf2605de659f6fd24b","observation_id":"71dbf449-641d-4440-8069-68ed80c03ba7","resolution":{"observed_at":"2026-08-07T05:27:28.038978Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:28.020771Z","title":"Cybenko,Approximation by superpositions of a sigmoidal function, Math","venue":null,"work_id":"60b5330e-b576-46fc-aeb7-88bbcaec6893","year":1989},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.632857Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:02487f691f650f7b56b36eb7779376ad406b57b8e5d39719ceca6c72ce0a637d","observation_id":"62b29daa-d2e6-428d-bb1e-325899b1213c","resolution":{"observed_at":"2026-08-07T05:27:28.025169Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:28.007060Z","title":"Devroye, L","venue":null,"work_id":"36cc31bc-6b41-42bc-8101-89a8a05ba65c","year":1996},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.637307Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:01d359cff95aefe1b04f8f3b478f54d3c4103767fee9582403ff32a275284878","observation_id":"7bdf618c-41b1-44bb-beb9-dfdebb8f1ba9","resolution":{"observed_at":"2026-08-07T05:27:28.011296Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:27.992073Z","title":"Gy¨ orfi, M","venue":null,"work_id":"e6a0d7e2-c8c3-423e-98ed-141527262751","year":2006},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.641596Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:5e671074558b24b5d8e7e1e885a51aab50f3e3db1063bde018177b1a27a02958","observation_id":"c1b6e9b3-2a90-43d7-b513-52a544f941e7","resolution":{"observed_at":"2026-08-07T05:27:27.996521Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:27.976786Z","title":"Helmke and J","venue":null,"work_id":"d383b8c5-3cc8-48e3-8e6b-16af4b4797f5","year":2012},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.645960Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:eb07abdbb1a903ee541d15ed5c7064862692bd1b9500f9b5f45f6b24e8d24b15","observation_id":"11f10d79-b305-4d7b-b91b-9b2f5e581f61","resolution":{"observed_at":"2026-08-07T05:27:27.981627Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:27.962256Z","title":"Ioffe and C","venue":null,"work_id":"74b051ad-3f0c-4dd9-bb19-1de7692c603d","year":2015},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.650433Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:921df27c2ae5c43ead5b2cb7cf5021421606d01967db560889a41b6cf13e2722","observation_id":"a86c2a00-18fd-46b5-af54-401c96f14864","resolution":{"observed_at":"2026-08-07T05:27:27.966961Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:27.946449Z","title":null,"venue":null,"work_id":"1e7c46c6-a8d7-477d-a4d5-d694b715e7f7","year":2003},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.654825Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:46e90635d9f74173c87ccac50f6e0e8f9d9e8268799a39c0c2e4b0ae50804264","observation_id":"07d0d286-09ec-458e-af66-bddf5434cbc6","resolution":{"observed_at":"2026-08-07T05:27:27.951635Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.11665","last_updated":"2025-06-08T21:14:46Z","snapshot_observed_at":"2026-08-07T18:12:57.667700Z","submitted_at":"2025-02-17T10:54:01Z","title":"On the kernel learning problem","version":2},"cited_work":{"arxiv_id":"2502.11665","doi":null,"metadata_source":"pith","pith_arxiv_id":"2502.11665","snapshot_observed_at":"2026-08-07T05:27:27.717799Z","title":"On the kernel learning problem","venue":"stat.ML","work_id":"53ca4853-4351-43a5-826a-88300c48f177","year":2025},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.659466Z"},"links":{"cited_paper":"/paper/2502.11665","citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:775f0565c85269c25c839aff8e0f2d00638b4af11fdea8a403211ec5ef432b19","observation_id":"40f2cf0e-851d-4fda-b41d-dfd1fcc10269","resolution":{"observed_at":"2026-08-07T05:27:27.724147Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:27.930923Z","title":null,"venue":null,"work_id":"2c6b05d4-1a91-4d8e-98a3-d72fcb9cd011","year":2018},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.664532Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:d4637e83c3a7c74991b04eaf27c10a80cc142b679bd31d3e3716dc577425fcd3","observation_id":"1c372ab6-604f-45a9-9b58-5ecf349e25e5","resolution":{"observed_at":"2026-08-07T05:27:27.935389Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:27.916549Z","title":"Misiakiewicz and A","venue":null,"work_id":"4f02531c-7520-4162-bd27-1ffe0bf7767f","year":2024},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.669085Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:d35f108ed4013e6e80124902df2e79bd42882dc6b4c08965922d9a482cc13ab5","observation_id":"107fc3a5-054a-43f9-9d3a-6a4696baa428","resolution":{"observed_at":"2026-08-07T05:27:27.920997Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:27.899708Z","title":"Pemantle,Nonconvergence to unstable points in urn models and stochas- tic approximations, Ann","venue":null,"work_id":"98024c3a-f0dd-40fa-a8d4-613362d809fb","year":1990},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.673356Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:d627081fa5fa163c037bbd22c59aa70eee9086e933a8ed6e94c83a75bca8ef67","observation_id":"3a0a84f4-ef77-435f-ab14-6d9ff13db97f","resolution":{"observed_at":"2026-08-07T05:27:27.905435Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:27.884415Z","title":"Rahimi and B","venue":null,"work_id":"123a69ec-e6ef-4325-97fe-bf7ba87de5dc","year":2007},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.677593Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:fe4cad2fac0e7542d0c67ba2dab845196bfab4b6a4f024991e44d53749abea91","observation_id":"1e1fdbe5-4676-4c29-b8d1-fcf193ec267c","resolution":{"observed_at":"2026-08-07T05:27:27.889114Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:27.868883Z","title":"Rotskoff and E","venue":null,"work_id":"7953527d-d4a5-4b27-8410-c3ddea78901f","year":2022},"citing_paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T05:27:27.682085Z"},"links":{"citing_paper":"/paper/2506.08550"},"observation_digest":"sha256:23fd16efe9b6de91e70b74a808c81e6b7606dc3f5c26255c6b90d54c54d9ebe8","observation_id":"fa746976-b18b-4795-9a0c-ad722feb8d1f","resolution":{"observed_at":"2026-08-07T05:27:27.874399Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.08550","last_updated":"2025-06-10T08:16:03Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-07T05:05:05.317050Z","submitted_at":"2025-06-10T08:16:03Z","title":"Gradient flow in the kernel learning problem"},"reference_resolution":{"displayed":20,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":1,"verified_fuzzy":14},"total_outbound_references":20},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2506.08550."}