{"as_of":"2026-08-06T08:30:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5b33d81140af48a92faf83d0e96ae471df97fd735b146f8602eed094843d0fb0","coverage":[{"denominator":15,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":15,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-19T13:06:11.119310Z","state":"measured"},{"denominator":16,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":16,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-06T06:34:29.942622+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":"2026-08-03T08:37:21.571460Z","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":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.22470","snapshot_observed_at":"2026-08-03T08:37:21.571460Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2601.17142","last_updated":"2026-06-05T18:31:27Z","snapshot_observed_at":"2026-08-05T02:11:46.094825Z","submitted_at":"2026-01-23T19:40:04Z","title":"Logarithmic Density of Rank $\\geq 1$ and Rank $\\geq 2$ Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-03T08:37:21.571460Z"},"links":{"cited_paper":"/paper/2505.22470","citing_paper":"/paper/2601.17142"},"observation_digest":"sha256:3a9879efab57349a7906258baa53f5f6e0037d342d8dd7a13ff6fc9d83130a96","observation_id":"bfe4904c-3789-4f02-afa9-9036d638355e","resolution":{"observed_at":"2026-08-03T08:37:21.571460Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2505.22470/citation-record","integrity":"/paper/2505.22470/integrity","json":"/paper/2505.22470/citation-record.json","paper":"/paper/2505.22470"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2210.10730","last_updated":"2024-10-19T18:46:20Z","snapshot_observed_at":"2026-07-06T14:07:50.468967Z","submitted_at":"2022-10-19T17:14:03Z","title":"Integers expressible as the sum of two rational cubes","version":3},"cited_work":{"arxiv_id":"2210.10730","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2210.10730","snapshot_observed_at":"2026-07-03T07:17:43.853133Z","title":"[BCP97] Wieb Bosma, John Cannon, and Catherine Playoust","venue":null,"work_id":"103b9d5b-332b-437d-9908-96e72bf12a52","year":2020},"citing_paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-19T13:06:11.119310Z"},"links":{"cited_paper":"/paper/2210.10730","citing_paper":"/paper/2505.22470"},"observation_digest":"sha256:389217452e27c778c94e630bd57e3c482690111130e87ccff86660089c038da9","observation_id":"38f609ec-9454-4132-8572-33cc9ec8c925","resolution":{"observed_at":"2026-05-19T13:07:18.141624Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"[BD11] Nils Bruin and Kevin Doerksen","venue":null,"work_id":"412d029f-18e3-428c-8642-9f92615a728a","year":1993},"citing_paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-19T13:06:11.119310Z"},"links":{"citing_paper":"/paper/2505.22470"},"observation_digest":"sha256:07bc12a802490297ffa1d168207364f5c16d2474c9bb58b2595195e24a90ba8b","observation_id":"096f7aa0-d660-494f-a866-b1a373651c30","resolution":{"observed_at":"2026-05-19T13:07:18.396810Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2508.14026","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Galois module structures and the Hasse principle in twist families via the distribution of Selmer groups","venue":null,"work_id":"014e1ee6-3c83-4596-84d7-8f48fa04f2fc","year":null},"citing_paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-19T13:06:11.119310Z"},"links":{"citing_paper":"/paper/2505.22470"},"observation_digest":"sha256:c2bd88048bfcc1ad6de90ae14badb3ac404b834b4f4a5f01d084a843f473613a","observation_id":"f2aae7ae-55cd-4dc6-9def-94afc93ee297","resolution":{"observed_at":"2026-05-19T13:07:18.170120Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Kolyvagin’s work on modular elliptic curves in L-functions and arithmetic (Durham, 1989).London Mathematical Society Lecture Note Series, 153:235–256","venue":null,"work_id":"d67efad8-437c-4acd-b563-3d41aa71d16c","year":1989},"citing_paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-19T13:06:11.119310Z"},"links":{"citing_paper":"/paper/2505.22470"},"observation_digest":"sha256:eaed4ffa0a8231d1698fe651a0d10eb1dee9343c42ea91bbdd349068a85a209b","observation_id":"ad4bfff8-ef64-4f97-9b6f-9c96574775c5","resolution":{"observed_at":"2026-05-19T13:07:18.399290Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2509.24937","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"[KMR14] Zev Klagsbrun, Barry Mazur, and Karl Rubin","venue":null,"work_id":"984adf50-50b3-4fe7-9ec9-8c1b8f7d3701","year":null},"citing_paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-19T13:06:11.119310Z"},"links":{"citing_paper":"/paper/2505.22470"},"observation_digest":"sha256:4b38a07082e71d887e6d8eb90633915d31b16989b9c6f72768c6f2ef4fcd0878","observation_id":"7287ed5d-d2cd-454f-a3bb-8f4df89a4a65","resolution":{"observed_at":"2026-05-19T13:07:18.135722Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2412.01768","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-01T11:45:46.831408Z","title":"[KP25] Peter Koymans and Carlo Pagano","venue":null,"work_id":"2879dcc3-36fb-4139-8e5f-458327080762","year":2024},"citing_paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-19T13:06:11.119310Z"},"links":{"citing_paper":"/paper/2505.22470"},"observation_digest":"sha256:54fc8f1fd833fc7c738517d8234f454aeaa23ef4d6b10839b2f086008aa3cb66","observation_id":"05e31e8e-235d-45b9-9625-e0546f41cc92","resolution":{"observed_at":"2026-05-19T13:07:18.187995Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.16910","last_updated":"2025-05-22T17:10:05Z","snapshot_observed_at":"2026-07-06T21:28:43.610849Z","submitted_at":"2025-05-22T17:10:05Z","title":"Elliptic curves of rank one over number fields","version":1},"cited_work":{"arxiv_id":"2505.16910","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.16910","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"[KR89] Ernst Kani and Michael Rosen","venue":null,"work_id":"573be393-04f2-41e7-8cbd-d323a4a0231a","year":null},"citing_paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-19T13:06:11.119310Z"},"links":{"cited_paper":"/paper/2505.16910","citing_paper":"/paper/2505.22470"},"observation_digest":"sha256:a6040aa7c0f43df8c40d100dd834ee164526b86f37647549891c8f49ef2aee36","observation_id":"3c9ded7e-0ff3-488c-8e43-b422b50235ac","resolution":{"observed_at":"2026-05-19T13:07:18.173913Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.09311","last_updated":"2024-05-15T13:11:13Z","snapshot_observed_at":"2026-07-06T18:14:41.996656Z","submitted_at":"2024-05-15T13:11:13Z","title":"Sums of rational cubes and the $3$-Selmer group","version":1},"cited_work":{"arxiv_id":"2405.09311","doi":"10.48550/arxiv.2405.09311","metadata_source":"arxiv_reference","pith_arxiv_id":"2405.09311","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"[Mil86a] James Milne","venue":"arXiv (Cornell University)","work_id":"56844028-d0bd-4529-b685-acec7cbcec93","year":null},"citing_paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-19T13:06:11.119310Z"},"links":{"cited_paper":"/paper/2405.09311","citing_paper":"/paper/2505.22470"},"observation_digest":"sha256:4953b1f82d99e091cea517d6b024014b52aa488a160ac6d602fdc0e688499af3","observation_id":"5c4939a9-f7be-49a7-b9e6-5fc0546e0d08","resolution":{"observed_at":"2026-05-19T13:07:18.148122Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2407.16459","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Hasse principle for intersections of two quadrics via Kummer surfaces","venue":null,"work_id":"1d64c1ec-acc2-4a5e-a5c7-b0d307b76c5c","year":null},"citing_paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-19T13:06:11.119310Z"},"links":{"citing_paper":"/paper/2505.22470"},"observation_digest":"sha256:0f5a1b40b00fc00c189db461de044fafd344e201d94751a285609c1ff1432ad8","observation_id":"5bf6a0bd-441f-4ef7-af9e-f42d0762ee87","resolution":{"observed_at":"2026-05-19T13:07:18.177757Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.17605","last_updated":"2025-08-20T19:54:39Z","snapshot_observed_at":"2026-08-03T18:07:35.440455Z","submitted_at":"2025-06-21T05:56:57Z","title":"Infinitely many elliptic curves over $\\mathbb{Q}(i)$ with rank 2 and $j$-invariant 1728","version":2},"cited_work":{"arxiv_id":"2506.17605","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.17605","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"[Sch95] Edward F","venue":null,"work_id":"3108e02b-218d-4327-9c66-d764310d8c5b","year":null},"citing_paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-19T13:06:11.119310Z"},"links":{"cited_paper":"/paper/2506.17605","citing_paper":"/paper/2505.22470"},"observation_digest":"sha256:f67f202fdfd59e87242bf3f4a74d4183e52d209cf22493249332ce727cae18ea","observation_id":"e0c7c525-c9e6-4cb7-b21a-b36b9df02cba","resolution":{"observed_at":"2026-05-19T13:07:18.165437Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2207.05674","last_updated":"2023-02-08T07:02:19Z","snapshot_observed_at":"2026-07-06T13:30:28.485107Z","submitted_at":"2022-07-12T17:00:16Z","title":"The distribution of $\\ell^\\infty$-Selmer groups in degree $\\ell$ twist families I","version":2},"cited_work":{"arxiv_id":"2207.05674","doi":"10.48550/arxiv.2207.05674","metadata_source":"arxiv_reference","pith_arxiv_id":"2207.05674","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"[Smi22b] Alexander Smith","venue":"arXiv (Cornell University)","work_id":"f8820c5e-72ce-4017-b6f3-31d657a60287","year":null},"citing_paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-19T13:06:11.119310Z"},"links":{"cited_paper":"/paper/2207.05674","citing_paper":"/paper/2505.22470"},"observation_digest":"sha256:e1ec7c61b4d56b9725d4cd374a1dd4ec45736e820368e2d31cbda766e65790aa","observation_id":"41122515-e88e-4fbf-a4dd-c5ab9c21362d","resolution":{"observed_at":"2026-05-19T13:07:18.123826Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2207.05143","last_updated":"2023-02-08T07:00:22Z","snapshot_observed_at":"2026-07-06T13:30:06.275093Z","submitted_at":"2022-07-11T19:14:24Z","title":"The distribution of $\\ell^{\\infty}$-Selmer groups in degree $\\ell$ twist families II","version":2},"cited_work":{"arxiv_id":"2207.05143","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2207.05143","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"[Smi25] Alexander Smith","venue":null,"work_id":"60f2d24b-79ae-40fd-a5b6-b876000b79f8","year":null},"citing_paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-19T13:06:11.119310Z"},"links":{"cited_paper":"/paper/2207.05143","citing_paper":"/paper/2505.22470"},"observation_digest":"sha256:cd160af339e1241cc877d2f74752e358661fa8f15340f5280f0784c0a5b5361b","observation_id":"589e518c-1884-4c57-88e8-24f530ba3c1b","resolution":{"observed_at":"2026-05-19T13:07:18.154871Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.17619","last_updated":"2025-03-22T02:30:45Z","snapshot_observed_at":"2026-07-06T20:57:02.587855Z","submitted_at":"2025-03-22T02:30:45Z","title":"The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture","version":1},"cited_work":{"arxiv_id":"2503.17619","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2503.17619","snapshot_observed_at":"2026-07-02T15:37:06.647164Z","title":"[SS03] Edward Schaefer and Michael Stoll","venue":null,"work_id":"a210766f-0a91-47c6-8382-da19de76ea81","year":2025},"citing_paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-19T13:06:11.119310Z"},"links":{"cited_paper":"/paper/2503.17619","citing_paper":"/paper/2505.22470"},"observation_digest":"sha256:f0a3d49af605f6975941ec7a58089018b9791711042db287450eff0396f2b000","observation_id":"3b29240c-651e-46f9-8cf9-234a92612b09","resolution":{"observed_at":"2026-05-19T13:07:18.182734Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.16960","last_updated":"2025-05-22T17:43:35Z","snapshot_observed_at":"2026-07-06T21:28:43.610849Z","submitted_at":"2025-05-22T17:43:35Z","title":"Rank one elliptic curves and rank stability","version":1},"cited_work":{"arxiv_id":"2505.16960","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.16960","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"[Zyw25c] David Zywina","venue":null,"work_id":"56fef3b4-6b23-4efe-bb7f-cb77c55c93e7","year":2025},"citing_paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-19T13:06:11.119310Z"},"links":{"cited_paper":"/paper/2505.16960","citing_paper":"/paper/2505.22470"},"observation_digest":"sha256:d50edd1e2cddc2fc7eadb99f72d0c080cf3fbbd52ad409170c0ae85fa6eed918","observation_id":"9a33b257-0306-4323-990c-f84243e3d79d","resolution":{"observed_at":"2026-05-19T13:07:18.129530Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.01957","last_updated":"2025-02-04T03:06:01Z","snapshot_observed_at":"2026-08-05T02:08:27.053258Z","submitted_at":"2025-02-04T03:06:01Z","title":"There are infinitely many elliptic curves over the rationals of rank 2","version":1},"cited_work":{"arxiv_id":"2502.01957","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.01957","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany Email address:stevangajovic@gmail.com, swpark2008@gmail.com","venue":null,"work_id":"3ed847b6-cbca-49ce-8da2-5f9e5919da9a","year":null},"citing_paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two","version":4},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-19T13:06:11.119310Z"},"links":{"cited_paper":"/paper/2502.01957","citing_paper":"/paper/2505.22470"},"observation_digest":"sha256:12e9227e9ebc0fb22f4d6cdb668605eb941daaa55de8289bcb8dc5002f582734","observation_id":"13f364ad-c0cc-4edb-b8a4-e494d0782b03","resolution":{"observed_at":"2026-05-19T13:07:18.160140Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.22470","last_updated":"2026-04-21T17:08:51Z","latest_version":4,"primary_category":"math.NT","snapshot_observed_at":"2026-07-06T21:32:13.791617Z","submitted_at":"2025-05-28T15:22:40Z","title":"Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two"},"reference_resolution":{"displayed":15,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":13,"verified_fuzzy":2},"total_outbound_references":15},"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":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"thesis":"As of 6 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 1 inbound Pith citation observation for arXiv:2505.22470."}