{"as_of":"2026-08-16T10:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f49b0473734b70050975f3d72483c49bf8a335122fa44f659c41d8433d56139f","coverage":[{"denominator":19,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":19,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T18:38:00.513987Z","state":"measured"},{"denominator":19,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":19,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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/2502.10335/citation-record","integrity":"/paper/2502.10335/integrity","json":"/paper/2502.10335/citation-record.json","paper":"/paper/2502.10335"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T18:38:01.553248Z","title":"Adleman and Kevin S","venue":null,"work_id":"3800cd45-aa5c-41ab-858d-d50dcf400024","year":1994},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.297628Z"},"links":{"citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:298c8427687be78c56f1b2bc7bda32cbf9525b38943780bc1284c95e88e9d626","observation_id":"70e075f7-5238-4ac9-9178-e21e962ec893","resolution":{"observed_at":"2026-08-07T18:38:01.558259Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-07T18:38:01.509053Z","title":"Booker, Ghaith A","venue":null,"work_id":"1c5b38ac-e101-4717-ac6c-eef195aa0d17","year":2015},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.307526Z"},"links":{"citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:419fe23be658901fc6cd2c23969d99b4b6ee433b5a7ff36734f18cbb01ae556d","observation_id":"7881e815-f105-408e-8f52-48e5ca918a85","resolution":{"observed_at":"2026-08-07T18:38:01.531441Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.23948","last_updated":"2024-10-31T14:03:37Z","snapshot_observed_at":"2026-08-15T12:36:16.259681Z","submitted_at":"2024-10-31T14:03:37Z","title":"Transformers to Predict the Applicability of Symbolic Integration Routines","version":1},"cited_work":{"arxiv_id":"2410.23948","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.23948","snapshot_observed_at":"2026-08-07T18:38:00.821316Z","title":"Transformers to Predict the Applicability of Symbolic Integration Routines","venue":"cs.LG","work_id":"1f81bff5-a9c6-4433-afd0-62cf905cdf15","year":2024},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.312707Z"},"links":{"cited_paper":"/paper/2410.23948","citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:3c35a20f724cd92c142b6ce8e0bb15935b223467eb3ca4963a2a827cd6a419ec","observation_id":"dbc79bef-4808-4aa1-9601-330704abedae","resolution":{"observed_at":"2026-08-07T18:38:00.852822Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-07T18:38:01.447227Z","title":"Computing the roots of polynomials","venue":null,"work_id":"7324cbaf-339c-420f-a922-ac02fc5a183e","year":2022},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.321932Z"},"links":{"citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:499516e1a5f55875a44ee7327f6907d2b04ceab87c20fd93c2b7261aa4968572","observation_id":"4500b7f2-97ab-4231-8590-fbea7f8b7934","resolution":{"observed_at":"2026-08-07T18:38:01.473916Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-07T18:38:01.356869Z","title":"Linear algebra with transformers","venue":null,"work_id":"39eaf27e-9629-4710-8330-ebdf441b9e99","year":2022},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.327482Z"},"links":{"citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:ed190c2a26237543d0f9b48ac353a6161dc4d2dcd06ed414b4cf17ed984460c4","observation_id":"ced92f47-5370-489f-81b7-7f70c5719c37","resolution":{"observed_at":"2026-08-07T18:38:01.391571Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-07T18:38:01.257951Z","title":"Int2int, 2024","venue":null,"work_id":"b7c54895-3006-4d0c-9143-564ce3457f08","year":2024},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.332386Z"},"links":{"citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:73100944b47f374834c8cab93569f59b4ca31f03ab300ec126f5d0887894884f","observation_id":"88a74714-73ad-46a7-a4a8-4ff9276ba9cb","resolution":{"observed_at":"2026-08-07T18:38:01.285922Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-07T18:38:01.215182Z","title":"Learning the greatest common divisor: explaining transformer predictions","venue":null,"work_id":"ea2acd8f-14b7-4fdc-9660-af582f410cdc","year":2024},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.341504Z"},"links":{"citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:21002ae46459bc218bcd8e42854e10bac1e5f7d225ef23ab7786b55cbdd49095","observation_id":"42c39f16-e0ac-4bd4-87d9-76df95a08f2f","resolution":{"observed_at":"2026-08-07T18:38:01.227082Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-07T18:38:01.159203Z","title":"What does machine learning have to offer number theory? Available at https://youtu.be/jjA2CqY5Ang, 2024","venue":null,"work_id":"afd2ca08-d547-4e0b-8b4f-1fb328b34650","year":2024},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.351486Z"},"links":{"citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:f99c349356357c72d7a3bde07e8be5ff7217fbe8f85d4b44d3923a609526ce01","observation_id":"03faf340-ec85-4180-a69f-04109e665f0f","resolution":{"observed_at":"2026-08-07T18:38:01.177354Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-07T18:38:01.139587Z","title":"The M \\\"obius function is strongly orthogonal to nilsequences","venue":null,"work_id":"69d0f8af-d9a0-44c1-aa20-01d05d4804e2","year":2012},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.367535Z"},"links":{"citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:720b06108f16843faf1a36fdb908e5cc5fbd90353ab2e91bc2753a38aab94678","observation_id":"00853063-03dd-4322-889c-e7fe46e9afdd","resolution":{"observed_at":"2026-08-07T18:38:01.144703Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-07T18:38:01.102856Z","title":"Kreber, Markus Norman Rabe, and Bernd Finkbeiner","venue":null,"work_id":"a9185f30-e868-4c57-b520-cc5f134ae929","year":2021},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.393926Z"},"links":{"citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:3194ac0a596924127b5338ba8a304d786455e34ca02c830b960abda60080c63a","observation_id":"8a93d238-3e02-4267-ad65-228869172e97","resolution":{"observed_at":"2026-08-07T18:38:01.117641Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1412.6980","last_updated":"2017-01-30T01:27:54Z","snapshot_observed_at":"2026-08-14T18:51:16.666127Z","submitted_at":"2014-12-22T13:54:29Z","title":"Adam: A Method for Stochastic Optimization","version":9},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1412.6980","snapshot_observed_at":"2026-08-07T18:38:00.407640Z","title":"Adam: A method for stochastic optimization","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.407640Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:4fdb003d826c4c3193a0dddabf2024d1fa2129d1580196513beae7bebdbe8e49","observation_id":"252c5ce3-081b-4e0e-aa35-f30a17baef9b","resolution":{"observed_at":"2026-08-07T18:38:00.407640Z","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":"2026-08-07T18:38:01.077435Z","title":"Neural GPUs learn algorithms","venue":null,"work_id":"08d8af9e-a18d-4249-90ac-707c31e7a4b0","year":2016},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.420025Z"},"links":{"citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:2150718fb251131d37ed5100b1c321fbf8dcb70ff3a3290cdd7f5e1caaa1d1ca","observation_id":"441634d8-1522-425a-a505-8c9aa0cc70c4","resolution":{"observed_at":"2026-08-07T18:38:01.087356Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-07T18:38:01.048208Z","title":"Code accompanying ``Studying number theory with deep learning: a case study with the M\\\" o bius and squarefree indicator functions'' , 2025","venue":null,"work_id":"0eefbf9c-7e3b-4b79-828c-b4e777f6802f","year":2025},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.429105Z"},"links":{"citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:b7059d815a383ebf91bd7f08b2341d8ebcd6a6f9b6766bb6b4cc659c00b6c0ec","observation_id":"d0614185-442e-49eb-b504-2756a45af32b","resolution":{"observed_at":"2026-08-07T18:38:01.053893Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-07T18:38:00.446289Z","title":"Montgomery and Robert C","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.446289Z"},"links":{"citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:1432f039f06e11cc6c3e33353f833a792cb8b69ac9e773ddd606cb15b6c24b72","observation_id":"974c0862-186d-4b87-9095-3484d494f813","resolution":{"observed_at":"2026-08-07T18:38:00.446289Z","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":"2026-08-07T18:38:00.993259Z","title":"Investigating the ability of neural networks to learn simple modular arithmetic","venue":null,"work_id":"61d46ccf-d546-4509-81ac-f7b8ab129fd2","year":2017},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.466124Z"},"links":{"citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:9a12c0b9a713ddb54064f6c5883e39520c9cc1b7216a9e9e25823fa29f1d26d0","observation_id":"26f74712-452e-43c9-b5f8-f98c45e1f0ec","resolution":{"observed_at":"2026-08-07T18:38:01.001832Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2009.03393","last_updated":"2020-09-07T19:50:10Z","snapshot_observed_at":"2026-08-15T02:27:43.801647Z","submitted_at":"2020-09-07T19:50:10Z","title":"Generative Language Modeling for Automated Theorem Proving","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2009.03393","snapshot_observed_at":"2026-08-07T18:38:00.487359Z","title":"Generative language modeling for automated theorem proving","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.487359Z"},"links":{"cited_paper":"/paper/2009.03393","citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:3d2d476065186e1163538e5caab3916afa74a96c53f94a7de158f06061184d79","observation_id":"0b44bf4c-d91f-4965-8401-5d09c16a50bd","resolution":{"observed_at":"2026-08-07T18:38:00.487359Z","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":"2026-08-07T18:38:00.963086Z","title":"Three lectures on M öbius randomness","venue":null,"work_id":"e8003c2f-f958-4ace-aeb1-05b057066d37","year":2011},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.492585Z"},"links":{"citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:7a5744dadfad204e822e28181e07b7e9888796a996f9b68f85754ac8106f4419","observation_id":"da5f9b78-b22c-4087-9dee-802c750f9e76","resolution":{"observed_at":"2026-08-07T18:38:00.969053Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2107.07116","last_updated":"2021-07-15T04:47:35Z","snapshot_observed_at":"2026-08-15T16:13:00.708079Z","submitted_at":"2021-07-15T04:47:35Z","title":"Transformer-based Machine Learning for Fast SAT Solvers and Logic Synthesis","version":1},"cited_work":{"arxiv_id":"2107.07116","doi":null,"metadata_source":"pith","pith_arxiv_id":"2107.07116","snapshot_observed_at":"2026-08-07T18:38:00.610120Z","title":"Transformer-based Machine Learning for Fast SAT Solvers and Logic Synthesis","venue":"cs.NE","work_id":"dc5ddfd0-0259-4755-a320-d23a5e9666c3","year":2021},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.498786Z"},"links":{"cited_paper":"/paper/2107.07116","citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:5610b8d969af239bf6796b7c3e05e3429d6c9d55ec15bbd6d836035ada343103","observation_id":"6facfc28-7978-4fb0-9167-64dcde37d017","resolution":{"observed_at":"2026-08-07T18:38:00.629392Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-07T18:38:00.897270Z","title":"Number-theoretic functions which are equivalent to number of divisors","venue":null,"work_id":"74b5488a-cba5-44be-ba05-ae6375e62dcf","year":1985},"citing_paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-07T18:38:00.513987Z"},"links":{"citing_paper":"/paper/2502.10335"},"observation_digest":"sha256:b39678dd4cc57a6b9e7aa0685eeeabb9b5ebe0735bfdcd7a55c5179fddfe5608","observation_id":"b9a2d851-7f53-40ef-8f7a-1b8872e79a1b","resolution":{"observed_at":"2026-08-07T18:38:00.926526Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2502.10335","last_updated":"2025-07-25T18:48:48Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-16T04:22:55.448543Z","submitted_at":"2025-02-14T17:50:00Z","title":"Studying number theory with deep learning: a case study with the M\\\"obius and squarefree indicator functions"},"reference_resolution":{"displayed":19,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":2,"verified_fuzzy":14},"total_outbound_references":19},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2502.10335."}