{"as_of":"2026-08-24T02:06:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a02a736af2fe2d50d0ea6c940beff0d5be4957f1367ce109aa4c1dcb3b919103","coverage":[{"denominator":30,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":30,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T23:48:30.997733Z","state":"measured"},{"denominator":31,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":31,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T05:09:49.886165Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.04084","snapshot_observed_at":"2026-08-02T05:09:49.886165Z","title":"Lupoian , Modular U nits on X_ 1 ( p) and Q uotients of the C uspidal G roup, Preprint (2025), arXiv:2502.04084v1 [math.NT] https://arxiv.org/abs/2502.04084v1","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13536","last_updated":"2026-07-15T07:40:49Z","snapshot_observed_at":"2026-08-22T08:31:22.805598Z","submitted_at":"2026-07-15T07:40:49Z","title":"Bernoulli determinants and cuspidal subgroups","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-02T05:09:49.886165Z"},"links":{"cited_paper":"/paper/2502.04084","citing_paper":"/paper/2607.13536"},"observation_digest":"sha256:c6c8617babc593e3db366b4a80eaf27cada781f9e5aa9d067520b1c2221f60aa","observation_id":"c8bc8488-e1db-4767-85ac-3472196cbebd","resolution":{"observed_at":"2026-08-02T05:09:49.886165Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2502.04084/citation-record","integrity":"/paper/2502.04084/integrity","json":"/paper/2502.04084/citation-record.json","paper":"/paper/2502.04084"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T23:48:31.902488Z","title":"9, 1997–2027","venue":null,"work_id":"d325d6db-7d10-43be-853f-bd71336460f8","year":2011},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.683258Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:f19bbb0c2f9813484ae6e39d3a8cf8f1eed613982f9a1c17e19ff714e4d42eae","observation_id":"1427f2e4-6132-433b-9b04-777e38afa1ec","resolution":{"observed_at":"2026-08-08T23:48:31.904985Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.895334Z","title":null,"venue":null,"work_id":"eff6cf1e-6551-4f76-808d-1030ac4b4d99","year":2011},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.714126Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:c92e625dde4c0c231a8634d4666bde4d75715dab1cc66ac3f072a7eb2012392f","observation_id":"35ff203a-d31a-4def-9c6d-0c14813cf5df","resolution":{"observed_at":"2026-08-08T23:48:31.897741Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.886866Z","title":"8, 2255–2263","venue":null,"work_id":"a16acd2a-b6a5-4fc7-9f14-11e026d54bab","year":1997},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.718077Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:0e665ff78faeac8c6dc60e78a46f78ef7f0b75f9d006445e9f4868fd42152a01","observation_id":"6cbd0b18-1a70-4be0-9301-0138c61c0a55","resolution":{"observed_at":"2026-08-08T23:48:31.890621Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.833451Z","title":null,"venue":null,"work_id":"8eaee8b2-03f4-4462-8278-026d95ebf23b","year":2014},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.721292Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:c35d46e633d5f241182cf64e86e9d74c98801783732cbe1b1a17053d9f10cee0","observation_id":"d92885b2-b2d6-478d-843d-39b381fbdc10","resolution":{"observed_at":"2026-08-08T23:48:31.880838Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.730690Z","title":null,"venue":null,"work_id":"2dde65a5-a411-4454-9ac0-5f2ab74a747f","year":2005},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.725298Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:e6223e4880eb9fad16afd5c945d4d496c3c8ea7ec476f13254e7900b940cf3d2","observation_id":"a9528018-ed5d-4774-bfbd-a4cff4fbf3c0","resolution":{"observed_at":"2026-08-08T23:48:31.786022Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.723449Z","title":null,"venue":null,"work_id":"b7cea8cc-446f-4a94-98d8-1d3336d6f8fc","year":1973},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.728936Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:c74ae852e23d14c23ff01c04117992c6b9a3572b98f3f46802c1358784b8ae47","observation_id":"f52ea00b-be8d-41c9-b957-38d51c9d9c45","resolution":{"observed_at":"2026-08-08T23:48:31.726056Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.715491Z","title":null,"venue":null,"work_id":"3153a3f9-701b-47c2-9de3-88965414e1b7","year":1984},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.732645Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:0df68ccd1efba12172db0b5bb1a45013f201a805bc5e4fa8038b100c056343a3","observation_id":"c480b8f8-f94c-48ad-89c2-3e1ab45ab7d5","resolution":{"observed_at":"2026-08-08T23:48:31.718329Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.707330Z","title":null,"venue":null,"work_id":"0fe09eb7-d612-48e9-a94b-d64b7a8346a3","year":2018},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.735423Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:d59e2e7953bafa5c94ad77eb80bf68ea7209cd06443c04438cc8e09624c160e0","observation_id":"20532a3b-fb3f-43d8-9ea5-d31b24064a91","resolution":{"observed_at":"2026-08-08T23:48:31.709993Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.699310Z","title":"1, 3, 3.1, 3.1, 3.2","venue":null,"work_id":"e7015543-6478-4e13-852b-1dcd0ed0b959","year":1981},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.738417Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:f1f6d8c10293e600452527851c59b074119e7e7d8bde4974ca4d7914d6699815","observation_id":"6cf60c4f-1571-4946-8ec8-7769f9094315","resolution":{"observed_at":"2026-08-08T23:48:31.702105Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.690568Z","title":null,"venue":null,"work_id":"242060e2-8f29-484e-95b5-571870445937","year":1997},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.741583Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:b974d51adb1622f8075a77da2d793027b5c65b64d3380b19b04ee592fb532d0c","observation_id":"5b8507d5-061c-4de9-be99-d2066bf62699","resolution":{"observed_at":"2026-08-08T23:48:31.693329Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.674544Z","title":"2, 149–172","venue":null,"work_id":"1a2b54e4-6779-48bd-9303-64f2e7a3fc93","year":1995},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.744620Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:d72a418cab3e32f063e0572c8bc957ee3f6a291948cdde76fa199bcf3fcc2012","observation_id":"9930b4ff-efaa-4bb9-a0a8-f15a907f0fc7","resolution":{"observed_at":"2026-08-08T23:48:31.684867Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.552920Z","title":null,"venue":null,"work_id":"001d02a8-8a9e-454a-ab71-49fb57e791c1","year":1972},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.747653Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:11cf751c3e3e42dcb0ee30079f4aba182b97f1356bffa9a6b84bcf97592d114e","observation_id":"f01e51c9-7f86-487b-b40f-992e6bd63cde","resolution":{"observed_at":"2026-08-08T23:48:31.621847Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.450186Z","title":"1, 33–186","venue":null,"work_id":"356eecee-48b8-4400-b48e-5b2468c469a0","year":1977},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.750705Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:30969d33e6a148ec9a9bcab576ee8a0c188d060e312f7b6e9b603c353cf732ad","observation_id":"a57447bb-1257-4fc3-a72d-2224ab800c7e","resolution":{"observed_at":"2026-08-08T23:48:31.453029Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.441947Z","title":"1, 334–350","venue":null,"work_id":"9c8aa128-2068-41f7-b4a1-324b65c1c5af","year":1957},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.753788Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:65368e4e3b2d608769f2b8b464a48190185cc34c7c8f0ddd24dafd917c259fc5","observation_id":"4470bb5c-8e8f-4d71-b590-25a3be1d4f41","resolution":{"observed_at":"2026-08-08T23:48:31.445089Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.433987Z","title":"3, 373–387","venue":null,"work_id":"02ebefcf-f00a-4cfd-9585-27999adf645a","year":1959},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.757111Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:17553737e40a95b28c7a5f53d8426a3fa33b43d7030c2fd90cbb0023ede0f44d","observation_id":"b3e7facd-284c-4a4d-b42f-f48d1cc3eb36","resolution":{"observed_at":"2026-08-08T23:48:31.437010Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.425317Z","title":null,"venue":null,"work_id":"9940bf2d-1bce-45c3-8872-763715ce5d08","year":1972},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.759983Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:16c85fb87232a93b8cdbc9567d214f4f42dc5189c5f8c7c1e6330ceca8637ee9","observation_id":"57dbc248-abc3-4bc6-8fb8-c1647e81c960","resolution":{"observed_at":"2026-08-08T23:48:31.428672Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.416814Z","title":null,"venue":null,"work_id":"5fccf2a8-8747-4bf7-8dd6-0ef510728905","year":1974},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.762929Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:9273f83396254704d60c2225c53428b65c9f772b1e9095696a9f227eba9585de","observation_id":"91036337-9c50-4b40-860a-1e5a76a75b7c","resolution":{"observed_at":"2026-08-08T23:48:31.420071Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.407608Z","title":"3, 733–772","venue":null,"work_id":"37a6757f-c283-43e7-8c13-cff9671297f8","year":2013},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.765780Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:1b41557c32aae94ae3aace0a6c3681a2a99591bab80b2ca4cd6d206f94951c84","observation_id":"5e21612b-9e2b-458e-b499-ed23d4a071cf","resolution":{"observed_at":"2026-08-08T23:48:31.411204Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.355109Z","title":"2, 273–318","venue":null,"work_id":"ff858dfe-eadf-4c9d-b01d-146d30c42e9b","year":2014},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.768767Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:ae61b0c9c35860b86b7c7eda5e4569f860cbc8f2990ee268551c9c890a94dc7d","observation_id":"9921b1d6-7baa-479f-a595-a01c19da4806","resolution":{"observed_at":"2026-08-08T23:48:31.392946Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.261392Z","title":null,"venue":null,"work_id":"136e21a7-4fd9-4022-a915-013b781ca6c1","year":2015},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.771129Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:97c6a8d96646a5d51dbd940f0061cf14654c7d5bf52f7e31cadbc74066d0d1a1","observation_id":"8d2b223e-2187-424a-9adb-7ef478498b6d","resolution":{"observed_at":"2026-08-08T23:48:31.310411Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.238133Z","title":"1, Princeton university press,","venue":null,"work_id":"930349f6-55bc-4360-9f0c-cdb0b46121d7","year":null},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.774198Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:ba3b152fef9243644565a3f2e65c0d91844a64e0aa0a6d40a88619cc9d1bc2f2","observation_id":"af6a4ff6-f207-4158-b56e-401bce196d70","resolution":{"observed_at":"2026-08-08T23:48:31.241081Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.229284Z","title":"2, 348–374","venue":null,"work_id":"ff0978fa-f278-4adf-8f11-cefdb59743df","year":1992},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.777403Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:6b13fb598694456bf3adbdeafff594f80b0e5f42f547e6d2c25ac4c4b666911f","observation_id":"f8ae7363-4876-4fcb-9665-48b9773e669f","resolution":{"observed_at":"2026-08-08T23:48:31.232642Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.220391Z","title":"2, 515–549","venue":null,"work_id":"671bea06-585b-475f-ad5e-722d16b426a6","year":1993},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.780403Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:2e214f30f4e83a0de4e0e9de7abdf92016a4e81413e0e39d8656d14c3606dd1a","observation_id":"2f9e729c-27a9-4e7a-aabc-f5ece053ed32","resolution":{"observed_at":"2026-08-08T23:48:31.223677Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.212203Z","title":"4, 671–686","venue":null,"work_id":"d62841d3-2ed7-4d44-ac6a-d15d6c531702","year":1995},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.783164Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:2fc9720c44348ea72b224c762511733f267fddf09170f58325311fe66a77c597","observation_id":"b225ae44-931e-4494-9858-b255680f3610","resolution":{"observed_at":"2026-08-08T23:48:31.215324Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.202695Z","title":"1, 180–213","venue":null,"work_id":"48b91bbf-30e7-405f-bc7c-f6c264b23429","year":1997},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.785997Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:ff8518b56f2f1d3a43b78b82c94d21504b17d601861c35a42fef8b5ad12ff66b","observation_id":"9d9acd73-3951-4716-a576-982420d9f585","resolution":{"observed_at":"2026-08-08T23:48:31.205786Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.183725Z","title":"1, 5, 5, 6.1","venue":null,"work_id":"0f1715f9-6ed7-41fd-bc44-90773d99289f","year":2007},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.817159Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:bbe60088333670a7e4e2c61c107825114a2ea7d895221929a4420ee84e8f60e7","observation_id":"ee7e1693-b3c6-4a22-8a48-7a3160e3de6e","resolution":{"observed_at":"2026-08-08T23:48:31.196301Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.057424Z","title":"1, 203–228","venue":null,"work_id":"920bca6f-8e64-4a8e-8051-af3bed172714","year":2010},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.888498Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:8b5d54e7ebb386c246d3f4349fcb8b572e0ee857b39dcc100f7098b2153705df","observation_id":"6547f02d-8d6c-4f97-b0ef-880b8fe04ff3","resolution":{"observed_at":"2026-08-08T23:48:31.106419Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.048420Z","title":null,"venue":null,"work_id":"8bdcec80-23aa-4730-8a32-a1ee8e122911","year":2023},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.917251Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:0a2db69907b286ee3b569ccd15c83594277962b601ae010fa84b4d5294a47dfe","observation_id":"6160fa26-3c00-496d-9d0d-fe0c04ad690f","resolution":{"observed_at":"2026-08-08T23:48:31.051775Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.039041Z","title":null,"venue":null,"work_id":"b3fc7a09-028e-4e8a-853d-727f3653c8ca","year":2023},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.993700Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:765d672562efcc7af8de82ae89832cc5d600baa44609fd123398fca3b8eeb732","observation_id":"b6240116-be88-4ce6-9c85-931ecab7de7f","resolution":{"observed_at":"2026-08-08T23:48:31.042294Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-08T23:48:31.026478Z","title":"1, 5, 5 Depar tment of Ma thema tics, University College London, Lon don, WC1H 0AY, UK Email address : e.lupoian@ucl.ac.uk 25","venue":null,"work_id":"05081484-ed6a-411f-bac2-013e52f2e224","year":1980},"citing_paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-08T23:48:30.997733Z"},"links":{"citing_paper":"/paper/2502.04084"},"observation_digest":"sha256:ee768889608b2f14ee8f764b66b01fe35b13ef13afc2bbc3754eebb62a1aae13","observation_id":"e2f4d4ef-f2e4-4e78-8756-06890785ea6f","resolution":{"observed_at":"2026-08-08T23:48:31.031754Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2502.04084","last_updated":"2025-02-06T13:53:17Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-14T05:37:17.073322Z","submitted_at":"2025-02-06T13:53:17Z","title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group"},"reference_resolution":{"displayed":30,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":13,"verified_exact":0,"verified_fuzzy":17},"total_outbound_references":30},"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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 24 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2502.04084."}