{"as_of":"2026-08-10T15:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d4f8f0dfd2059c8fc284f402fb96f8e0a82d5436810d531097a01ae2cb1ee6ae","coverage":[{"denominator":36,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":36,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T10:22:36.015100Z","state":"measured"},{"denominator":36,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":36,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+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/2508.00247/citation-record","integrity":"/paper/2508.00247/integrity","json":"/paper/2508.00247/citation-record.json","paper":"/paper/2508.00247"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:22:36.430144Z","title":"fkan: Fractional kolmogorov-arnold networks with trainable jacobi basis functions, 2024","venue":null,"work_id":"ef38feb0-6fc6-4a80-985b-c997bc005467","year":2024},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.885868Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:a38d46f3d75f00733a4e8dae11f4b2102f939c883bfd4112a4dbe320b4fde33e","observation_id":"0782c68f-8c93-4f93-bbe2-0a8a3cd9bbb7","resolution":{"observed_at":"2026-08-06T10:22:36.434013Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.419219Z","title":"rkan: Rational kolmogorov-arnold networks, 2024","venue":null,"work_id":"bc790e8c-663b-4195-9943-a9ac753d69ec","year":2024},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.889814Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:6e8146568938326ec99c5a8c39fa0064ccf4a9c15b9386370d4ee2af45825b7a","observation_id":"aae34488-3ff3-44c8-8cbf-c40d02b9fe15","resolution":{"observed_at":"2026-08-06T10:22:36.423116Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.406315Z","title":"A theory of adaptive pattern classifiers.IEEE Transactions on Elec- tronic Computers, (3):299–307, 2006","venue":null,"work_id":"cc884302-13f4-4178-b49b-366552d9f0ba","year":2006},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.894051Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:b603f91dab7f7429b28fbfcd519ed9d93053c57efa8f9d30edcfb0bc1e4017ad","observation_id":"245822e9-df73-42ce-ba7b-3a1e6e98c3ae","resolution":{"observed_at":"2026-08-06T10:22:36.410917Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:35.898795Z","title":"Wav-kan: Wavelet kolmogorov-arnold networks, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.898795Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:41b7a219092ba39123459c9d35b3f3a3f34ac27f9ce7a7065d361d68ed72429d","observation_id":"813b0d34-b668-4438-8f43-6bf6a3f09507","resolution":{"observed_at":"2026-08-06T10:22:35.898795Z","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":"2026-08-06T10:22:36.386996Z","title":"Coleman and Yuying Li","venue":null,"work_id":"95f2dc0e-4cd5-4673-8f13-64c2f31498d9","year":1996},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.902896Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:cc39334f9a774d18b1bdd25fc547abd8cef1aea8fd8d0e2cb31a8d11848afbf5","observation_id":"9cad226b-0824-4fc5-bd8b-518df92d1dbf","resolution":{"observed_at":"2026-08-06T10:22:36.390184Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.377114Z","title":"Approximation by superpositions of a sigmoidal function.Mathemat- ics of control, signals and systems, 2(4):303–314, 1989","venue":null,"work_id":"5018629e-3bf6-4c84-96d9-61af2d73492a","year":1989},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.907564Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:a6b8002f23defcdf4d88aa2d2100a6342dfd5ef3f01e3f4cf5724d537eb210d5","observation_id":"13942aac-32f1-45ba-9d21-a1bbfb1c81f4","resolution":{"observed_at":"2026-08-06T10:22:36.380502Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.367454Z","title":"The weierstrass approximation theorem.Journal of Mathematics and Physics, 4(1-4):148–152, 1925","venue":null,"work_id":"d21de9db-42ab-42cd-8233-d240fc4d58e1","year":1925},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.911647Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:cf8b2d4c346bb09cf1799f4e636cb6cd58096b555dd10dd96d1b2cbbd09e0f42","observation_id":"997ef08d-94f6-4114-930d-d06a84f57059","resolution":{"observed_at":"2026-08-06T10:22:36.371091Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.356348Z","title":"Representation properties of networks: Kol- mogorov’s theorem is irrelevant.Neural Computation, 1(4):465–469, 1989","venue":null,"work_id":"1ac7ea86-e05e-4ee9-bf33-78770e74ad03","year":1989},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.915444Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:a63092482390a623c6747c180437e03747bc121633de337238bac18826f8a14c","observation_id":"966320f6-812a-46f1-b3b4-5fb19701527b","resolution":{"observed_at":"2026-08-06T10:22:36.359809Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.344253Z","title":"Kolmogorov’s mapping neural network existence theorem","venue":null,"work_id":"0b2edbb1-ea99-439b-b191-0922537d2152","year":1987},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.918481Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:e4a22c8d5bacbbfb0ee9d9dd67e1dc551e751fa4fd14b79f47769dc429556687","observation_id":"569a5a36-9cd3-423c-a198-6003656ed484","resolution":{"observed_at":"2026-08-06T10:22:36.348653Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.332100Z","title":"Addison-Wesley Longman Publishing Co., Inc., 1989","venue":null,"work_id":"79ef68f6-db0b-43b6-b800-66be5ced7fea","year":1989},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.921871Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:584e528a5f9d1767a0ad39b86ab4870bf45db943d978e1ea8d12b72d83012137","observation_id":"ebdcc51b-c212-4e91-9671-a73c393e6208","resolution":{"observed_at":"2026-08-06T10:22:36.336148Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.321969Z","title":null,"venue":null,"work_id":"62feb973-6f4d-43a6-8961-7bf8bb582701","year":1927},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.925166Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:eb46aed67aaa1bfe57f0dd1b441628dd721dacd449e2a5eab6d3541bc6750f4a","observation_id":"0b72fed7-5db3-48e6-af7d-35d609547bd8","resolution":{"observed_at":"2026-08-06T10:22:36.325528Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.311527Z","title":"Multilayer feedforward net- works are universal approximators.Neural networks, 2(5):359–366, 1989","venue":null,"work_id":"708f4ac3-7b53-45ba-b634-fee71bccbaa0","year":1989},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.928128Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:72f3f12055d8f56184380e0abbf4ac8512d0846ccd225abadeb06054c6f5ad6c","observation_id":"889780ea-1769-4fa0-beee-34a91e5c9fa7","resolution":{"observed_at":"2026-08-06T10:22:36.314944Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.300691Z","title":null,"venue":null,"work_id":"ae930af3-315e-40c3-bdd6-cdb2dd3a7319","year":1941},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.931784Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:20008b0caf17ec84c6f88331eec6f2e74487040e4bc241f671e9bb85d8ce6175","observation_id":"f0011aff-1c52-4af3-9080-16e9da313f67","resolution":{"observed_at":"2026-08-06T10:22:36.304987Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.289342Z","title":"On the representations of continuous functions of many variables by superposition of continuous functions of one variable and addition","venue":null,"work_id":"42783e61-3f36-4ee0-a11f-06808cd02060","year":1957},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.935773Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:2a9bceabefed1d677355663160d80e0667b285d247b5123b64e29da0d86bfa62","observation_id":"5141c854-ffed-43aa-8f8b-fccbfd34be0c","resolution":{"observed_at":"2026-08-06T10:22:36.293009Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.278101Z","title":"American Mathematical Society, 1961","venue":null,"work_id":"94017371-76de-43ea-97b4-6e9663004032","year":1961},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.939104Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:5fae5ebadcae0c306ec8dfe422f7ca446075b6ec2e99aed8745193532802e753","observation_id":"cd946f17-a2bc-439f-b1fc-605871c3c8e8","resolution":{"observed_at":"2026-08-06T10:22:36.281791Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.265423Z","title":"Kolmogorov’s theorem is relevant.Neural Computation, 3(4):617–622, 1991","venue":null,"work_id":"fff1b9ea-5752-4eb6-8a33-4d23cd175c28","year":1991},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.942414Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:a19a005efcfc2bf0aacc91086ff2779f8caead86ac8050535ae54032df3f249f","observation_id":"36234b14-c511-4c16-b1fa-a13491762a7d","resolution":{"observed_at":"2026-08-06T10:22:36.269429Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.254770Z","title":"Kolmogorov’s theorem and multilayer neural networks.Neural Networks, 5(3):501–506, 1992","venue":null,"work_id":"a28f4646-8e06-4f54-abdc-a17aeab840ec","year":1992},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.945978Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:f15c365a0ca7bae5012ca1ae93157654f4f9f78bedb881f52b1efab9aa9fd6d3","observation_id":"33caf5b6-eb5a-4a8d-9128-af3f2c40d4d1","resolution":{"observed_at":"2026-08-06T10:22:36.258116Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.06721","last_updated":"2024-05-10T06:03:45Z","snapshot_observed_at":"2026-08-04T21:06:56.482139Z","submitted_at":"2024-05-10T06:03:45Z","title":"Kolmogorov-Arnold Networks are Radial Basis Function Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.06721","snapshot_observed_at":"2026-08-06T10:22:35.949097Z","title":"Kolmogorov-arnold networks are radial basis function networks.arXiv preprint arXiv:2405.06721, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.949097Z"},"links":{"cited_paper":"/paper/2405.06721","citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:2133f27927f76169ac6c31fe52e5450e55284e94a4561d071344d185dca58ed0","observation_id":"f8e44a88-436c-43d8-9ecf-777207506d22","resolution":{"observed_at":"2026-08-06T10:22:35.949097Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.10205","last_updated":"2024-08-19T17:59:04Z","snapshot_observed_at":"2026-08-09T18:26:15.186638Z","submitted_at":"2024-08-19T17:59:04Z","title":"KAN 2.0: Kolmogorov-Arnold Networks Meet Science","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.10205","snapshot_observed_at":"2026-08-06T10:22:35.953387Z","title":"Kan 2.0: Kolmogorov-arnold networks meet science.arXiv preprint arXiv:2408.10205, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.953387Z"},"links":{"cited_paper":"/paper/2408.10205","citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:7fc0c8b5c7ae59d35e559141f7f19d8af69cfaaf670c7150ecb51025430f45bb","observation_id":"75616422-fc30-406f-8351-53ac3afabc9e","resolution":{"observed_at":"2026-08-06T10:22:35.953387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.19756","last_updated":"2025-02-09T21:09:09Z","snapshot_observed_at":"2026-07-06T18:07:47.744531Z","submitted_at":"2024-04-30T17:58:29Z","title":"KAN: Kolmogorov-Arnold Networks","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.19756","snapshot_observed_at":"2026-08-06T10:22:35.957334Z","title":"Kan: Kolmogorov-arnold networks.arXiv preprint arXiv:2404.19756, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.957334Z"},"links":{"cited_paper":"/paper/2404.19756","citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:e52d18dba9fc4902f764bee76c6ad2d483d52a9650f6ec280dfcdd810eb938db","observation_id":"7a9905b3-1e15-4dcb-852d-60cdba9be6fb","resolution":{"observed_at":"2026-08-06T10:22:35.957334Z","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":"2026-08-06T10:22:36.242175Z","title":"Approximation of functions, athena series.Selected Topics in Mathematics, 1966","venue":null,"work_id":"500d3588-62ee-4f43-9d42-c3f051ab73c5","year":1966},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.961745Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:3c403ef1b408a51113c215797debbce73500854cddb6606b712087997e814a1f","observation_id":"c0fc408e-d93c-4345-9cf4-e18aa937da30","resolution":{"observed_at":"2026-08-06T10:22:36.245824Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.232024Z","title":"MIT press, 2017","venue":null,"work_id":"1389f4fe-304c-4ed3-875f-fd63053e3b98","year":1988},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.964872Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:8e808c7485a461e3b045dad76a1dead5f5c342e41471724fb968c53244f96ff9","observation_id":"b600c162-4011-4b7d-8131-9580a83b3570","resolution":{"observed_at":"2026-08-06T10:22:36.235133Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.02075","last_updated":"2024-08-12T17:17:00Z","snapshot_observed_at":"2026-08-10T03:59:12.991590Z","submitted_at":"2024-06-04T07:54:31Z","title":"ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLU","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.02075","snapshot_observed_at":"2026-08-06T10:22:35.968460Z","title":"Relu-kan: New kolmogorov-arnold networks that only need matrix addition, dot multiplication, and relu.arXiv preprint arXiv:2406.02075, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.968460Z"},"links":{"cited_paper":"/paper/2406.02075","citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:b3c8ff8daf8807815028ccbde9d69c091daab95f9e866655069879898e099c42","observation_id":"aff49614-3e8d-4ef3-8320-accb55048504","resolution":{"observed_at":"2026-08-06T10:22:35.968460Z","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":"2026-08-06T10:22:36.221153Z","title":"Sinekan: Kolmogorov- arnold networks using sinusoidal activation functions.Frontiers in Artificial Intelligence, Volume 7 - 2024, 2025","venue":null,"work_id":"1395b18a-14a4-4bb5-94ae-22a1b29c3b28","year":2024},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.972414Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:9fcddf2fa363af6aa3a7bceccbed287793da44ad9d86722ff5394aa050eef2aa","observation_id":"977d68dd-862c-4c58-bc7e-fd45e3672dc5","resolution":{"observed_at":"2026-08-06T10:22:36.225085Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:35.975868Z","title":"The perceptron: a probabilistic model for information storage and organization in the brain.Psychological review, 65(6):386, 1958","venue":null,"work_id":null,"year":1958},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.975868Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:37adb2cec00f9f70170e0d6278d0242fc5ee557a43a18538f59cd3c1e2076d92","observation_id":"b7ba7ea4-1cc8-452c-a425-005d94160529","resolution":{"observed_at":"2026-08-06T10:22:35.975868Z","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":"2026-08-06T10:22:36.201179Z","title":"Rumelhart, Geoffrey E","venue":null,"work_id":"18ba0d4d-ac64-4e32-a877-591638bc0617","year":1986},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.979257Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:65f54c378e8a4b81c947ebb87338d5fbea74659db45ec1da203fccc9b1284d0e","observation_id":"ffbcda8f-7c25-4562-bf87-9bc5b5e8ed57","resolution":{"observed_at":"2026-08-06T10:22:36.205093Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.190864Z","title":"Learning representa- tions by back-propagating errors.nature, 323(6088):533–536, 1986","venue":null,"work_id":"f246257a-15fb-4f3f-a06c-1082ab361bb5","year":1986},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.982249Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:e33c8c7fba3553bf53307c41b100192217f4c643b25b7d1be80c9c86b3b5511c","observation_id":"5de53efb-5177-404b-b8e5-535c89fe1381","resolution":{"observed_at":"2026-08-06T10:22:36.194050Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.179712Z","title":null,"venue":null,"work_id":"0820e1ce-a059-436b-b284-7bc4a61afbb0","year":2024},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.985522Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:826c560123856374ae8499d9985874a0a6f975a5ebe184ea10454f18b95cb854","observation_id":"0585a3f9-e42e-4789-8f1a-4c300fcf1fda","resolution":{"observed_at":"2026-08-06T10:22:36.183386Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.167548Z","title":"A comprehensive and fair comparison between mlp and kan representations for differential equations and operator networks, 2024","venue":null,"work_id":"bf518845-eb01-449e-8820-8bf22c9bcda6","year":2024},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.989642Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:6118df391e62c5f44f1ad71912c61307ae2569d6f9ddd4071bfb4211a6b31179","observation_id":"48ccc8df-ae32-4437-bd03-ddef7fba3194","resolution":{"observed_at":"2026-08-06T10:22:36.170940Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.155584Z","title":null,"venue":null,"work_id":"e2ad787d-b46a-40df-8082-59f4ade6689c","year":2020},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.993450Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:5794d6a7ac6bb3ebc6df487aa8e845affd9b7b26373f3aeb7dc07ec6fbeb68cd","observation_id":"e4dd546c-fef0-45fc-b836-346984e38050","resolution":{"observed_at":"2026-08-06T10:22:36.159546Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.141883Z","title":"On the structure of continuous functions of several variables.Trans- actions of the American Mathematical Society, 115:340–355, 1965","venue":null,"work_id":"e9c18579-925c-4309-954a-f6698f5653d5","year":1965},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:35.996906Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:bf5645d199bfcfaac9c5a08215ae2130ded1962eb4e6fe0cfa5bd2ce526806b3","observation_id":"9d295a87-99f1-45b0-a408-9629f986037c","resolution":{"observed_at":"2026-08-06T10:22:36.146747Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.07200","last_updated":"2024-06-14T15:46:11Z","snapshot_observed_at":"2026-08-08T21:02:58.042224Z","submitted_at":"2024-05-12T07:55:43Z","title":"Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.07200","snapshot_observed_at":"2026-08-06T10:22:36.000359Z","title":"Chebyshev polynomial-based kolmogorov- arnold networks: An efficient architecture for nonlinear function approximation.arXiv preprint arXiv:2405.07200, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:36.000359Z"},"links":{"cited_paper":"/paper/2405.07200","citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:57344410318f315e625add7a46f04b3185158dd35c1fcb2f5843c1e6ae82d6ce","observation_id":"41b32f68-3a17-4895-ba31-3d78a875de44","resolution":{"observed_at":"2026-08-06T10:22:36.000359Z","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":"2026-08-06T10:22:36.129352Z","title":"Chebyshev polynomial-based kolmogorov-arnold networks: An efficient architecture for nonlinear function approxi- mation, 2024","venue":null,"work_id":"2b671676-0e97-4c84-af49-c70073221310","year":2024},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:36.004589Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:1be3af41f2c4cd5d2db43a5e0050c0caad33899be499a26c94a3f5f94aa8176c","observation_id":"9a377140-17a8-45b5-b1bb-c80040193542","resolution":{"observed_at":"2026-08-06T10:22:36.133568Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T10:22:36.115717Z","title":"Bsrbf-kan: A combination of b-splines and radial basic functions in kolmogorov-arnold networks, 2024","venue":null,"work_id":"a1c89941-5368-4c8d-bb4b-176f0dcc5d3e","year":2024},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:36.008476Z"},"links":{"citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:b0845900626881b954207cf57603946fe1905201687aed87cddca00f9666c8a0","observation_id":"36db5f1d-3081-4190-86c5-66067a85c439","resolution":{"observed_at":"2026-08-06T10:22:36.121115Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.01034","last_updated":"2025-08-14T10:41:49Z","snapshot_observed_at":"2026-08-05T02:05:56.574184Z","submitted_at":"2024-06-03T06:36:04Z","title":"Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformation","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.01034","snapshot_observed_at":"2026-08-06T10:22:36.011666Z","title":"Fourierkan-gcf: Fourier kolmogorov-arnold network–an effective and efficient fea- ture transformation for graph collaborative filtering.arXiv preprint arXiv:2406.01034, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:36.011666Z"},"links":{"cited_paper":"/paper/2406.01034","citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:c8dc6520120b32010591142bb2148ae7b8bb4626a106896e541151ef9aae2023","observation_id":"c600179b-0b1e-43df-bff1-d33fd72e7b7c","resolution":{"observed_at":"2026-08-06T10:22:36.011666Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.16674","last_updated":"2024-08-17T15:20:31Z","snapshot_observed_at":"2026-08-08T05:23:01.070427Z","submitted_at":"2024-07-23T17:43:35Z","title":"KAN or MLP: A Fairer Comparison","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.16674","snapshot_observed_at":"2026-08-06T10:22:36.015100Z","title":"Kan or mlp: A fairer comparison.arXiv preprint arXiv:2407.16674, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T10:22:36.015100Z"},"links":{"cited_paper":"/paper/2407.16674","citing_paper":"/paper/2508.00247"},"observation_digest":"sha256:c0ada7cba6de96e5eca50447156b8142f661bdf4a675ab4c530c2a1fb1cf1b20","observation_id":"1bf6fc30-20e3-4c9e-b95b-1463b01c2a95","resolution":{"observed_at":"2026-08-06T10:22:36.015100Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2508.00247","last_updated":"2025-08-01T01:16:09Z","latest_version":1,"primary_category":"stat.ML","snapshot_observed_at":"2026-08-07T07:05:38.679850Z","submitted_at":"2025-08-01T01:16:09Z","title":"Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks"},"reference_resolution":{"displayed":36,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":13,"verified_exact":0,"verified_fuzzy":23},"total_outbound_references":36},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2508.00247."}