{"as_of":"2026-08-12T11:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7525e135ee01117cbc2d6071ce5afbebc7e8b9f5fc4a9cae2b24f8c6acd7c685","coverage":[{"denominator":67,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":67,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T16:14:11.585761Z","state":"measured"},{"denominator":68,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":68,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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":"2026-08-02T19:05:04.966848Z","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":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.10340","snapshot_observed_at":"2026-08-02T19:05:04.966848Z","title":"[Fur26] Lorenzo Furio","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2603.04021","last_updated":"2026-06-08T12:33:01Z","snapshot_observed_at":"2026-08-12T05:00:20.329765Z","submitted_at":"2026-03-04T12:57:05Z","title":"Explicit p-adic Hodge theory for elliptic curves and non-split Cartan images","version":2},"reference_index":1994,"source":"pdf_text","source_observed_at":"2026-08-02T19:05:04.966848Z"},"links":{"cited_paper":"/paper/2412.10340","citing_paper":"/paper/2603.04021"},"observation_digest":"sha256:45369341026ded77d6426d3ca25e9501896b0ee8df9da1e33a69e04699d36163","observation_id":"2b2db2c1-f3e0-4d8c-ab90-e6f4e08a4cd1","resolution":{"observed_at":"2026-08-02T19:05:04.966848Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2412.10340/citation-record","integrity":"/paper/2412.10340/integrity","json":"/paper/2412.10340/citation-record.json","paper":"/paper/2412.10340"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:14:12.422017Z","title":"Bajolet, Yu","venue":null,"work_id":"60c9ba41-3cd9-4000-b9a2-3b3b5577fad1","year":2021},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.355877Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:52f284c5a392f2e3b6dc099ba831beb433b97d6e69c60b01faa4d3f2de48b81e","observation_id":"6f0dda37-14be-42c7-bfa2-6fa5d189f303","resolution":{"observed_at":"2026-08-11T16:14:12.425267Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.413008Z","title":"Balakrishnan, N","venue":null,"work_id":"247e8766-cffa-406d-af63-8a42be9a5a12","year":2019},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.359937Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:95426230dba1daeee1467a2019373e1e20569b67302a0f90fdc558a35931b158","observation_id":"a6d6df51-0910-4deb-9bcf-d30a1ad80bc6","resolution":{"observed_at":"2026-08-11T16:14:12.416226Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.403157Z","title":null,"venue":null,"work_id":"d4abb63b-2ceb-410b-9aa0-1d7b6d322cab","year":2023},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.363654Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:c2aa99b2b4c83b55ff00054174eb659dc1e76936568d016aebb9012088fc064c","observation_id":"b3af3fd5-9e1b-436d-a06d-e5011828d9eb","resolution":{"observed_at":"2026-08-11T16:14:12.406576Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.393451Z","title":null,"venue":null,"work_id":"ef1ee7b6-3a9a-4138-824d-ed909dc8d9ed","year":2009},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.368827Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:a66ae502a9b77ebf207f1d33a27568a70ad358a418c70590171b92fc3ed3f712","observation_id":"1212ccd2-0bed-4df0-910d-3db27e767c21","resolution":{"observed_at":"2026-08-11T16:14:12.397340Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.384447Z","title":null,"venue":null,"work_id":"58a1a5cc-6d5e-44f6-8977-31c47889c779","year":2010},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.372453Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:809b55fcb0aba1f87d8bb3de57cd2014abf8479d7c8dd4b97f432c6f4f4cd5d7","observation_id":"f587c0b6-2fe7-40a9-8279-64cab0d215b6","resolution":{"observed_at":"2026-08-11T16:14:12.387430Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.375388Z","title":"Bilu and P","venue":null,"work_id":"2a1be261-e2a9-4743-bbd3-8e88fe75fcc9","year":2011},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.376551Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:e83c4e5f17b57616fb9b0a68ef57a8b901058afe01888afa82323e08ce803181","observation_id":"08a782b8-df07-4ad1-add5-30cdc480fe22","resolution":{"observed_at":"2026-08-11T16:14:12.378604Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.366405Z","title":"Bilu and P","venue":null,"work_id":"0e6102dc-a2f6-42ed-bc93-1f6cdcb0e9ee","year":2011},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.380099Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:222c8de9efdae97f11b53ffa8b9a78fd14282fceae7d3f723ec1abd4d6b06e06","observation_id":"3d1822d2-a45e-42b2-8a24-f056eff18b8e","resolution":{"observed_at":"2026-08-11T16:14:12.369655Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.357599Z","title":null,"venue":null,"work_id":"1511d299-2f6a-441a-8404-31ff8ae056f1","year":2013},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.383456Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:0ab302a42a63bf34b951121f9fa31425d40a888634522cde6456f0ad7bbba0d0","observation_id":"333b99fc-5e0b-428a-a73e-98567072103d","resolution":{"observed_at":"2026-08-11T16:14:12.360711Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.348433Z","title":null,"venue":null,"work_id":"0fd54d35-e659-4036-8783-7f9f6b9939e2","year":1972},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.386888Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:b9f173a89fe7fb3affc929cc46330fdd365338fda07efb85c4c1c062baa181af","observation_id":"af6a45a4-ad2b-4d6e-ac2e-aa64b1e95aec","resolution":{"observed_at":"2026-08-11T16:14:12.351492Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.339286Z","title":"Brau and N","venue":null,"work_id":"7f23cffb-83c5-4037-a870-c91077ad2812","year":2016},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.390555Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:0490e9af7d5591726007d52a65343a6b91fb4f3ca61bf5102d1770cab2ee4b6d","observation_id":"fa15b06d-750b-49ca-acbf-2720cd45b754","resolution":{"observed_at":"2026-08-11T16:14:12.342494Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.330113Z","title":"Breuil, B","venue":null,"work_id":"9bf11eb3-7608-460b-b4d2-8b521bc1950b","year":2001},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.393867Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:d998f267b8358421282d8b6b1f8ee34882be1e7eb0dca822786cbb62276b5e05","observation_id":"c9bcdab6-3872-4565-80c3-ad71fc308bcb","resolution":{"observed_at":"2026-08-11T16:14:12.333591Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.320351Z","title":null,"venue":null,"work_id":"7089c232-a106-4942-8a0e-ca0677b94c9a","year":1999},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.398466Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:b6f67a944a37c07ebd0464de7ef52245e5947f58738a0ca2b898a93c885fa241","observation_id":"a7b54d41-f2fb-43f6-8d66-8306aa5dff8c","resolution":{"observed_at":"2026-08-11T16:14:12.324517Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.311201Z","title":null,"venue":null,"work_id":"5d4dd923-b1d0-4ab4-be63-5144b097e895","year":null},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.401757Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:7c332e601eeeeefa177706cd44ab976e1199fe3bd5111b22e2e665790ac9b2be","observation_id":"60ace70d-8a0a-4225-a598-26b34c032aab","resolution":{"observed_at":"2026-08-11T16:14:12.314588Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.291528Z","title":null,"venue":null,"work_id":"065545c3-d4ba-4171-b7c0-1b3cf9882ba0","year":2005},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.409222Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:1f1373566ae6e48ccd2203412153f116409e4652c8fdd13b2f4917a33b4cb812","observation_id":"9c5df87f-a582-4adc-9df3-6d9226d86613","resolution":{"observed_at":"2026-08-11T16:14:12.295535Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.282512Z","title":null,"venue":null,"work_id":"172ad4f3-15de-4500-911d-01097a863b4d","year":2023},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.412695Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:f32f571c643b5ea14fe35636dba6c2c92aaa53e0d0e4506d48df840acf7f8a8a","observation_id":"2af78c76-f807-4ff0-b2bc-35d8422a9723","resolution":{"observed_at":"2026-08-11T16:14:12.285831Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.273068Z","title":null,"venue":null,"work_id":"25646961-07d0-45de-a396-b19c51736923","year":2022},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.415960Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:a162a27655f1a8dc3ec3224800c58c441607373753652ea2e3c72217c20c61c7","observation_id":"536e44c1-1cbf-4bea-97c9-d84d529ecd58","resolution":{"observed_at":"2026-08-11T16:14:12.276474Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.264259Z","title":null,"venue":null,"work_id":"2f7c6da8-a933-4c06-b035-653ceaf04f18","year":2014},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.419185Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:5c7849be758e0da8abcadb522ecef5bec2611748e5d42b6ebe6b53df4bb827c1","observation_id":"eeb816e9-efba-4073-92b4-2c5d2b4faae3","resolution":{"observed_at":"2026-08-11T16:14:12.267484Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.254932Z","title":null,"venue":null,"work_id":"c90b7da2-6208-4f41-9747-d119b3392dfc","year":1985},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.422363Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:8df9de5e3b6cf6abeaf2a4d2e11253d674d64f09d0e648b6dc0908ba39437972","observation_id":"91eee355-c352-4baa-8bae-4f1abb1e2cda","resolution":{"observed_at":"2026-08-11T16:14:12.258235Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.244664Z","title":null,"venue":null,"work_id":"e10061ee-49b4-4425-b023-0ed7fd3d3799","year":1985},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.425873Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:f740cb330cb41ff399ab5d290182993e6f93a8c854c2c45053d0e201b19a1051","observation_id":"a22475b3-e08b-4a8e-8770-82a60185c7e8","resolution":{"observed_at":"2026-08-11T16:14:12.248698Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.235730Z","title":null,"venue":null,"work_id":"93e812e0-ed56-4047-a3ac-3bfce5bbe341","year":2022},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.428915Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:76a64925d2d00b39fecdc4dabba9462c483c233546ab5b163401359bb7324cba","observation_id":"5ceb45dd-af57-40f2-b3b5-1780759117ec","resolution":{"observed_at":"2026-08-11T16:14:12.238861Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.226545Z","title":null,"venue":null,"work_id":"fa8cd8ed-a40a-4412-be4e-aa37851d7759","year":1999},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.432106Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:eca7e2a4049b770629d7b58b785c702720bf273564dff8e9a3b0043fd91742b5","observation_id":"ba38f5f0-2f4a-49de-9ad3-dc8227f37308","resolution":{"observed_at":"2026-08-11T16:14:12.229841Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.435113Z","title":"Furio and D","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.435113Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:3b85f29d473b7a9da9b9576dc0081a75f61a88a7011f88d2e8a2114c269928ce","observation_id":"e21bba08-900f-4b2f-9466-fe15832a921a","resolution":{"observed_at":"2026-08-11T16:14:11.435113Z","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":"2026-08-11T16:14:12.216830Z","title":null,"venue":null,"work_id":"c33c50b7-4b9b-415c-b0c0-09604a05b345","year":2002},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.438303Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:51c77704e5e205f2f8738c00864ebd7ec9be9fe0f6810d840515745767c8d6d8","observation_id":"c770975a-238c-46e6-8906-a7d2fbb56a3b","resolution":{"observed_at":"2026-08-11T16:14:12.220227Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.206920Z","title":"Gaudron and G","venue":null,"work_id":"21be8e14-deaa-400b-af1e-7d8888e5e13c","year":2014},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.442100Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:b3a030e7c229807f6b6ab4711b3ac079166a146f90eeded59b6b9b9066dec5bc","observation_id":"89c9c8cd-2b81-4485-a22c-628d00dab968","resolution":{"observed_at":"2026-08-11T16:14:12.211143Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.197298Z","title":"Greenberg","venue":null,"work_id":"97f4f827-f607-43ce-bd56-c7ecbbef2e59","year":2012},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.445189Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:99f94a33622dbe04b10e056b4f3f6baee1935752f1eb56cf8c6c91301e8b5f85","observation_id":"a77e665c-db8b-4269-9096-ac6b851fc25e","resolution":{"observed_at":"2026-08-11T16:14:12.200396Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.187850Z","title":"Greenberg, K","venue":null,"work_id":"cb69f3e8-2304-4102-a113-96c9a9511b34","year":2014},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.448337Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:e96d126e8c149b57bd15221e3394b82f43f6ae5099c8b909bc95de4ef1e6e09a","observation_id":"7aefc3d3-ed92-4f3d-bdd9-d799e3ba7b14","resolution":{"observed_at":"2026-08-11T16:14:12.191147Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.178099Z","title":"Hoorfar and M","venue":null,"work_id":"9fae5fde-5ef8-467f-9958-2066168abed5","year":2008},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.451643Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:1a9a0ad79ba5509c97f850c8735a597a90fc5aba3bcd64d98280c381c52f1472","observation_id":"c7df2f45-91b9-422d-95a7-47a53e2ec0c3","resolution":{"observed_at":"2026-08-11T16:14:12.181593Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.168728Z","title":"Jones and K","venue":null,"work_id":"66b937f7-e869-4c3e-93e7-df048e51eebc","year":2022},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.454815Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:7c4aab253ad551965e733ed587e6e6d681b7a2a46498c61a6b6207bc6a052564","observation_id":"15602f08-1e6e-420d-a83f-b0e0aee7b73b","resolution":{"observed_at":"2026-08-11T16:14:12.172045Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.158840Z","title":null,"venue":null,"work_id":"d6f4c39c-7a11-485d-8106-00fee19a09be","year":1985},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.457859Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:7a17fbeba3e66c6f41fe1b8c924d07ddbe7f36c3febaeda7308fd5cce52d2f43","observation_id":"88ebe55b-ce44-4eec-99f6-58b9c08c9bc5","resolution":{"observed_at":"2026-08-11T16:14:12.162318Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.148280Z","title":null,"venue":null,"work_id":"b1993101-fa5d-4476-a8cd-a018e0a11387","year":1990},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.461216Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:9db6ecb1352712642ca28d9ed477eff6ac58aba650b9ef5c8fa831e19a3a713c","observation_id":"f3a42606-7056-4127-868b-2fd3be3c67f3","resolution":{"observed_at":"2026-08-11T16:14:12.151608Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.137893Z","title":null,"venue":null,"work_id":"188eb7a8-ee78-4aea-8e3f-e3efb3e31a0a","year":1995},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.464349Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:ad52a32b8ffefcfd63cd09374b9f9f40ed27673cada83468850821c0984db46c","observation_id":"0e692287-efa4-4768-a2c3-09156c455700","resolution":{"observed_at":"2026-08-11T16:14:12.142112Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.023200Z","title":"Le Fourn","venue":null,"work_id":"792384e8-18ca-4a2f-ba50-a750ce436930","year":2016},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.468029Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:6a2b89cf9fa5be22ec0e013292fb6e22167f0eebd5cacb7b531a6e47e70e3f91","observation_id":"c3bba292-7476-4015-9e65-f28e9b6d9cc4","resolution":{"observed_at":"2026-08-11T16:14:12.131094Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.012424Z","title":"Le Fourn and P","venue":null,"work_id":"1ed18293-0ea3-4ebd-bd90-fdd3f28f3992","year":2021},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.471661Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:f3c3fe1a48aa714b4db477025a92b2759ada681e250af3aebac267bd0ec9c3c6","observation_id":"0dcb9f9f-11bb-4683-b0ec-858751476902","resolution":{"observed_at":"2026-08-11T16:14:12.016271Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:12.002858Z","title":null,"venue":null,"work_id":"d9368f5c-d3bc-429f-9053-5246735fb3f2","year":2019},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.474746Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:ba46e2dfa60c3314854e563598df2ca5dfe8546707646c31cf6556ca83cb1060","observation_id":"47b4bb90-f9a7-45c6-bad7-11658e8e6f78","resolution":{"observed_at":"2026-08-11T16:14:12.006088Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.478759Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.478759Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:1abd10188aad151dabfe454f8dca605ed817ff6345c951c953bb1ad3406c1d7e","observation_id":"1274b5ae-2827-453e-8267-02c5f6290d2f","resolution":{"observed_at":"2026-08-11T16:14:11.478759Z","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":"2026-08-11T16:14:11.986433Z","title":"The L-functions and modular forms da tabase","venue":null,"work_id":"370b9672-6ec6-47cd-b383-cec90fde8cec","year":2024},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.481927Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:5cb552e85dae76b098ed52e4d884eda30d216b6bd090c6f3539cbded7f9f2385","observation_id":"0bfa4c3b-789a-4316-898e-f7c82dbfe14b","resolution":{"observed_at":"2026-08-11T16:14:11.989776Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.977659Z","title":"Lombardo","venue":null,"work_id":"b05ff04e-08c7-4755-a83f-15237a28c75d","year":2015},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.485872Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:7637913ba1bb0ac1cb1c1ff0dc2d59933bbdf10a65f9c6a493809893f9e92781","observation_id":"f7dd6cad-a527-4c89-9928-0745763ae2a7","resolution":{"observed_at":"2026-08-11T16:14:11.980733Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.968418Z","title":"Lombardo and S","venue":null,"work_id":"5006566f-0ad1-45f3-92b3-9488f9539927","year":2022},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.489340Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:e47d602f8142a04e1759bdd4a736bad080ec8b3823e605fbd2d1fe6694ebcb82","observation_id":"60a6ef02-f6a8-4b8e-95e9-ff5c697f2f6c","resolution":{"observed_at":"2026-08-11T16:14:11.971641Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.959247Z","title":"Lozano-Robledo","venue":null,"work_id":"df915eee-4c90-4b8b-87bb-bc3e6cab0d77","year":2016},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.493369Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:3ee0d41a155eda9683785cebe5a8072d6c1c9d36e303fa6796d1bba5450316a3","observation_id":"4659194b-bc1f-48cc-ba67-a443ae85c5d8","resolution":{"observed_at":"2026-08-11T16:14:11.962550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.949009Z","title":"Masser and G","venue":null,"work_id":"ba21dc9a-d4f7-4650-80b0-501b42b05c80","year":1993},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.496586Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:b623bdcb97cfa74e9ba2dde9eab813726fe0be8f812a8792a246630e9a0386f3","observation_id":"3cd869cd-4b6c-4010-ad98-daa5c9ac7fc0","resolution":{"observed_at":"2026-08-11T16:14:11.952686Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.939745Z","title":null,"venue":null,"work_id":"47e4bd52-1471-4759-8b3f-e9d6c60fd8df","year":1993},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.499751Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:bb7a153a580632363af8fa90a971c2b2e662ab5923e31ddeb1ea31e50e593d94","observation_id":"6dd07d89-9b25-4a64-8d72-3961201a85d0","resolution":{"observed_at":"2026-08-11T16:14:11.943076Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.929459Z","title":"Mayle and T","venue":null,"work_id":"116f6b52-c767-4d7c-9bd4-7956c2e88ba9","year":2024},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.503019Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:7c19e5ae265ad58e8fd8c2704e018f21c288d36d8fbe41b1ea4a3b0a87790bf5","observation_id":"cc5c7d4a-2b3d-40f9-bda7-3b012b15cc7a","resolution":{"observed_at":"2026-08-11T16:14:11.932657Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.919146Z","title":null,"venue":null,"work_id":"7ab39f5b-0b01-41d4-8a0e-f2efb578c3e2","year":1976},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.506402Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:5685b429395fe812ff7f036e45a9af7f2fe0fa004fe1c3b0c2faf8c2dd50f472","observation_id":"cf6c079f-6750-4824-91cf-73826d5d3f7e","resolution":{"observed_at":"2026-08-11T16:14:11.923483Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.909797Z","title":null,"venue":null,"work_id":"3f2f8a4f-2298-4442-9e03-187a3b573149","year":1978},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.509906Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:96c8de0bddf81336046f2d9a3f1a626c042c54caf59a66d23ae6bc6e61d3c23e","observation_id":"a164f638-02a4-4518-b0ae-e0cc9594dbd2","resolution":{"observed_at":"2026-08-11T16:14:11.913054Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.899850Z","title":null,"venue":null,"work_id":"a2b08362-52ed-4cbc-ad96-b441a4b63e89","year":1987},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.513015Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:95101c3cdaa4c89625e981cc04557484a2955df5318238fc9a0d704d9fc75b3b","observation_id":"032d43a8-3158-4190-bbe9-080681708935","resolution":{"observed_at":"2026-08-11T16:14:11.903841Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.889741Z","title":"Momose and M","venue":null,"work_id":"e4453864-51a2-46a2-b9b8-648cd6d4fc80","year":2002},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.516033Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:1cb68875aba3766e437975cc29d457cff18f98019704fc963cb6a580ed5bab5e","observation_id":"9873a738-8294-4ec7-b124-07c921b7e700","resolution":{"observed_at":"2026-08-11T16:14:11.893674Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.880098Z","title":null,"venue":null,"work_id":"8049936a-b882-4400-b470-db704cfa43f3","year":2019},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.519181Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:25f71331d67ec911994966ff0e5120e9d3ec003a21dbd2c845761fdf31c87c94","observation_id":"557266f1-0efc-4455-b414-138d9f6c6891","resolution":{"observed_at":"2026-08-11T16:14:11.883222Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.871018Z","title":null,"venue":null,"work_id":"262b2b51-8309-49f3-9241-609e0a935efa","year":1966},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.523170Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:4381a13738455de81e4bd4e79cbb0393e96097491f9f19665b9f9285dcd2b0d2","observation_id":"6169f5e1-163a-48a0-8ea9-cf06b0c0d7e7","resolution":{"observed_at":"2026-08-11T16:14:11.874351Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.861506Z","title":null,"venue":null,"work_id":"a251e34c-32fa-4f0c-8e1b-f4bdefa78a99","year":2019},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.527015Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:f7add90f3045f0e4c9904091f5deda077495c4faf12c090a21d72913f8313efb","observation_id":"6474dac0-d035-4ca2-8663-9bb94518aada","resolution":{"observed_at":"2026-08-11T16:14:11.864760Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.852513Z","title":null,"venue":null,"work_id":"3fcdfd3e-d544-4b98-84c4-cc3941a8edfd","year":1983},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.530823Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:4cbdaeb1847a6b27d13c8eb959d43e849262d603d25724485b66984107d7a2b5","observation_id":"cf0bae70-05e2-4e19-9537-3fb9539c9a54","resolution":{"observed_at":"2026-08-11T16:14:11.855639Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.842943Z","title":"Rouse, A","venue":null,"work_id":"2661cfce-99aa-4bf5-8790-bacfe7d6c946","year":null},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.534156Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:87178946f7132dce931ef66984241bfce099a8fe8ae3e1549f4af97404172e08","observation_id":"af08ebe0-1dae-43c9-9bff-e161354954ad","resolution":{"observed_at":"2026-08-11T16:14:11.846480Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.824201Z","title":"Rouse and D","venue":null,"work_id":"2f2576ff-c5bc-4d47-905a-1fcd19fe67d7","year":2015},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.541587Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:0d021d126feb2fdd7fb7e0fcdc5f62649af754124d58769cd65db3e8fc47bf82","observation_id":"b9850424-b4cf-454c-bc36-3b061e9c17e9","resolution":{"observed_at":"2026-08-11T16:14:11.827761Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.813910Z","title":"Schoof and N","venue":null,"work_id":"1d2d4206-4d53-4042-ab0d-c91bcc14b8e9","year":2012},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.544863Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:1af8de684738b477531b1a9d50507e3291966ffae58a2ac5932d49519830a75a","observation_id":"0aa96c3b-b023-493b-8951-47c85b32b2a6","resolution":{"observed_at":"2026-08-11T16:14:11.817584Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.804762Z","title":null,"venue":null,"work_id":"4769df1b-b097-459b-8251-b458799edffa","year":1972},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.548126Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:917818fcba325a2660b31fc1ebbe011313f20a8d4d1bd72552b7a7ff3f60d38b","observation_id":"8d5da33a-515a-48d0-9045-1e7232540680","resolution":{"observed_at":"2026-08-11T16:14:11.807721Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.795303Z","title":null,"venue":null,"work_id":"4490a45f-bfce-44dc-b650-344a296fe13f","year":1981},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.551525Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:dc0e69c3ce22ef8413f4055046274a8a2c00a22c01c0d55d9a6c13cac7e629a2","observation_id":"c9d5619e-acb5-434d-8286-4956f13435ff","resolution":{"observed_at":"2026-08-11T16:14:11.798691Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.784628Z","title":null,"venue":null,"work_id":"667d0caf-db7f-4a37-a3b7-31804ea2906e","year":1998},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.554679Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:5fba93abd12889fb42f85c6d8702f56b2d23c0e079c4a437d22f2c6502eb5e21","observation_id":"6b60ca41-91f7-4df3-8fb5-b5a99cf1ef9d","resolution":{"observed_at":"2026-08-11T16:14:11.788529Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.774027Z","title":null,"venue":null,"work_id":"396c8678-f3ce-4bb0-ae7f-d4ce820950c9","year":1998},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.558417Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:1a5bc3831d3e4cfdadf8bc24a5cf08c4871c0d528ed4bbfdd73fb6209c790ee4","observation_id":"e83005b5-7f73-4668-a14c-0d018f46c2e3","resolution":{"observed_at":"2026-08-11T16:14:11.777267Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.764294Z","title":null,"venue":null,"work_id":"643879f8-7a13-4f57-9b04-042ca5823a05","year":2023},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.562304Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:889cb979004e851895cd1aa3f95e65dea5a7fc6b06c72ee6894d3afd2bf56859","observation_id":"6b639ad2-f183-425b-ae32-077d1b893dcd","resolution":{"observed_at":"2026-08-11T16:14:11.767721Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.753681Z","title":"Sol´ e and M","venue":null,"work_id":"345a5b56-01da-466b-94ab-27f148f4543c","year":2011},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.565387Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:51192a8c23a16577aa593a6379cae8b08347cabb58a07a62b8e4b991bfc12164","observation_id":"b1719d3b-dc18-42ab-b13e-b820bd876407","resolution":{"observed_at":"2026-08-11T16:14:11.757866Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.743723Z","title":null,"venue":null,"work_id":"64f7a095-5ebc-488f-93a3-267dd1eed350","year":2017},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.568676Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:a8a36d8301fb6cb86f0f596e94ef226d7a23a66605c709b3bf126156230e1632","observation_id":"7ed2ae69-4ac7-4bc6-a8e5-bcdb52f48902","resolution":{"observed_at":"2026-08-11T16:14:11.747142Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.732039Z","title":null,"venue":null,"work_id":"4d979c10-ff86-4188-bade-dd5a3928b1a4","year":1998},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.571856Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:811ca1f47063be0368d032f108f2c8b6674730cc445adabc88572124fa828652","observation_id":"e3fd4c0c-9da5-4516-a43e-1659c74befc2","resolution":{"observed_at":"2026-08-11T16:14:11.735455Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1102.4656","last_updated":"2011-02-23T02:56:44Z","snapshot_observed_at":"2026-07-06T02:23:56.159752Z","submitted_at":"2011-02-23T02:56:44Z","title":"Bounds for Serre's open image theorem","version":1},"cited_work":{"arxiv_id":"1102.4656","doi":null,"metadata_source":"pith","pith_arxiv_id":"1102.4656","snapshot_observed_at":"2026-08-11T16:14:11.643199Z","title":"Bounds for Serre's open image theorem","venue":"math.NT","work_id":"2cba81b1-6c21-45d5-800c-2cb9f65316c2","year":2011},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.574821Z"},"links":{"cited_paper":"/paper/1102.4656","citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:18fddb14c121bfa5b4cab6fb0d8ae7f4e70a054faafc27a2f420f515251bef9e","observation_id":"ec0ee588-7b01-4259-98f1-2b955c29e311","resolution":{"observed_at":"2026-08-11T16:14:11.649275Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1508.07660","last_updated":"2015-08-31T01:28:58Z","snapshot_observed_at":"2026-07-06T04:28:10.687091Z","submitted_at":"2015-08-31T01:28:58Z","title":"On the possible images of the mod ell representations associated to elliptic curves over Q","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1508.07660","snapshot_observed_at":"2026-08-11T16:14:11.578342Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.578342Z"},"links":{"cited_paper":"/paper/1508.07660","citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:8c95d90d494f82447cbf05aac3940e0028b213fa153df75701f6acde76e1e754","observation_id":"42e4e153-0995-4fc7-8c3b-af779b5021dc","resolution":{"observed_at":"2026-08-11T16:14:11.578342Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1508.07663","last_updated":"2022-01-18T18:26:22Z","snapshot_observed_at":"2026-08-12T02:17:27.149314Z","submitted_at":"2015-08-31T02:06:05Z","title":"Possible indices for the Galois image of elliptic curves over Q","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1508.07663","snapshot_observed_at":"2026-08-11T16:14:11.582004Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.582004Z"},"links":{"cited_paper":"/paper/1508.07663","citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:7fba425f92def1a9687449a3be037dcc5184d0d5dc93166eb73fb1980120a15a","observation_id":"5e98ef47-01a0-4aab-86ae-128dd7da2f54","resolution":{"observed_at":"2026-08-11T16:14:11.582004Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2206.14959","last_updated":"2024-03-22T00:25:05Z","snapshot_observed_at":"2026-08-12T08:02:05.922946Z","submitted_at":"2022-06-30T00:34:50Z","title":"Explicit open images for elliptic curves over $\\mathbb{Q}$","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2206.14959","snapshot_observed_at":"2026-08-11T16:14:11.585761Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.585761Z"},"links":{"cited_paper":"/paper/2206.14959","citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:3d6f1e857c37615481f51008d1f45dca02e2282913a593bcfaed37bf0c6ce741","observation_id":"9cc13c75-5459-4bbe-998a-99370d97121a","resolution":{"observed_at":"2026-08-11T16:14:11.585761Z","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":"2026-08-11T16:14:12.301613Z","title":null,"venue":null,"work_id":"ee95ad63-fc8f-4152-8a52-826833c282b9","year":null},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":1967,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.405290Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:2bfc3c1f5fa6ce04c7dda2805b7f1c078a710fa7616d87255886268d5dd03226","observation_id":"23189e37-d5d8-4f00-866e-902fea8b5885","resolution":{"observed_at":"2026-08-11T16:14:12.305040Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T16:14:11.833835Z","title":null,"venue":null,"work_id":"c31712ff-2c5e-4cad-8393-04113133514b","year":null},"citing_paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals","version":4},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-11T16:14:11.537480Z"},"links":{"citing_paper":"/paper/2412.10340"},"observation_digest":"sha256:e0a1ab079f6093c7b139561ffe7b5725e0d548846eb0044a13cc807e04e2da01","observation_id":"c27805b3-2c3e-43ce-becd-1f3b5d6cfcff","resolution":{"observed_at":"2026-08-11T16:14:11.837092Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.10340","last_updated":"2026-06-05T16:27:58Z","latest_version":4,"primary_category":"math.NT","snapshot_observed_at":"2026-08-12T03:15:52.841365Z","submitted_at":"2024-12-13T18:37:45Z","title":"Effective bounds for adelic Galois representations attached to elliptic curves over the rationals"},"reference_resolution":{"displayed":67,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":42,"verified_exact":1,"verified_fuzzy":24},"total_outbound_references":67},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 67 of 67 outbound references and 1 inbound Pith citation observation for arXiv:2412.10340."}