{"as_of":"2026-08-13T22:19:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0fc04756d1381959b43747afa974481e34963610a388b592d070fae9b9eb01c5","coverage":[{"denominator":13,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":13,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T20:00:25.505818Z","state":"measured"},{"denominator":13,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":13,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2501.09697/citation-record","integrity":"/paper/2501.09697/integrity","json":"/paper/2501.09697/citation-record.json","paper":"/paper/2501.09697"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:00:25.671860Z","title":null,"venue":null,"work_id":"97e4386b-f63c-4c1d-a9d2-856494b2c1c9","year":2007},"citing_paper":{"arxiv_id":"2501.09697","last_updated":"2025-01-26T03:20:51Z","snapshot_observed_at":"2026-08-11T15:44:36.975719Z","submitted_at":"2025-01-16T17:48:25Z","title":"Squarefree discriminants of polynomials with prime coefficients","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:25.457073Z"},"links":{"citing_paper":"/paper/2501.09697"},"observation_digest":"sha256:d404594246fb33b8acba72a44d2a47e24f684040eafb0f9454c5b673770884d4","observation_id":"c60e10bf-c217-4cb0-a6b2-334bbd448c53","resolution":{"observed_at":"2026-08-10T20:00:25.675585Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-10T20:00:25.661150Z","title":"Bhargava and A","venue":null,"work_id":"097d9266-1cef-4f37-aac3-4d45fcb20ce7","year":2015},"citing_paper":{"arxiv_id":"2501.09697","last_updated":"2025-01-26T03:20:51Z","snapshot_observed_at":"2026-08-11T15:44:36.975719Z","submitted_at":"2025-01-16T17:48:25Z","title":"Squarefree discriminants of polynomials with prime coefficients","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:25.461265Z"},"links":{"citing_paper":"/paper/2501.09697"},"observation_digest":"sha256:df72b21944817426ec0f046eabbb87aae8cf8ce13f090aa6b8273d94e1eff663","observation_id":"e6a70547-9857-43e8-9f9e-9cc2040d4413","resolution":{"observed_at":"2026-08-10T20:00:25.664835Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-10T20:00:25.649621Z","title":"Bhargava and A","venue":null,"work_id":"772962da-896d-4ec9-af6a-d9302bd4118b","year":2015},"citing_paper":{"arxiv_id":"2501.09697","last_updated":"2025-01-26T03:20:51Z","snapshot_observed_at":"2026-08-11T15:44:36.975719Z","submitted_at":"2025-01-16T17:48:25Z","title":"Squarefree discriminants of polynomials with prime coefficients","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:25.465291Z"},"links":{"citing_paper":"/paper/2501.09697"},"observation_digest":"sha256:c04ab36d9c00a189b81fdc1aab2aeb404d4106aa07ec3fc5a2c34aa7ae86c918","observation_id":"426d819a-d11f-4f14-9a6c-cf19b6c79858","resolution":{"observed_at":"2026-08-10T20:00:25.653500Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1312.7333","last_updated":"2013-12-27T20:40:05Z","snapshot_observed_at":"2026-07-06T03:32:02.808381Z","submitted_at":"2013-12-27T20:40:05Z","title":"The average number of elements in the 4-Selmer groups of elliptic curves is 7","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1312.7333","snapshot_observed_at":"2026-08-10T20:00:25.469482Z","title":"Bhargava and A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2501.09697","last_updated":"2025-01-26T03:20:51Z","snapshot_observed_at":"2026-08-11T15:44:36.975719Z","submitted_at":"2025-01-16T17:48:25Z","title":"Squarefree discriminants of polynomials with prime coefficients","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:25.469482Z"},"links":{"cited_paper":"/paper/1312.7333","citing_paper":"/paper/2501.09697"},"observation_digest":"sha256:796d7d253ef0fa82e7561fb3744d2acbec678151c20d9314953e9dcf3a0e73a5","observation_id":"0d777d03-98f5-4ba1-9301-292f2664ce98","resolution":{"observed_at":"2026-08-10T20:00:25.469482Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1312.7859","last_updated":"2013-12-30T20:43:23Z","snapshot_observed_at":"2026-08-09T22:10:34.463762Z","submitted_at":"2013-12-30T20:43:23Z","title":"The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1312.7859","snapshot_observed_at":"2026-08-10T20:00:25.473614Z","title":"Bhargava and A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2501.09697","last_updated":"2025-01-26T03:20:51Z","snapshot_observed_at":"2026-08-11T15:44:36.975719Z","submitted_at":"2025-01-16T17:48:25Z","title":"Squarefree discriminants of polynomials with prime coefficients","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:25.473614Z"},"links":{"cited_paper":"/paper/1312.7859","citing_paper":"/paper/2501.09697"},"observation_digest":"sha256:a932dcacef5088632d013f24c3524dce0a97ab7eeb77f59027dc050bdbad99a5","observation_id":"55fa7e0e-c349-4e6d-9851-030aba04c58f","resolution":{"observed_at":"2026-08-10T20:00:25.473614Z","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":"2026-08-10T20:00:25.638803Z","title":"Bhargava, A","venue":null,"work_id":"fb866666-0cae-412c-a531-f7be5c4376ba","year":2022},"citing_paper":{"arxiv_id":"2501.09697","last_updated":"2025-01-26T03:20:51Z","snapshot_observed_at":"2026-08-11T15:44:36.975719Z","submitted_at":"2025-01-16T17:48:25Z","title":"Squarefree discriminants of polynomials with prime coefficients","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:25.477719Z"},"links":{"citing_paper":"/paper/2501.09697"},"observation_digest":"sha256:68095a62987a54e1301e462eb2c99fddd847fd256951e65dd6a2ca5204cf2907","observation_id":"5d680639-2709-46fe-873f-b17accdcd2b0","resolution":{"observed_at":"2026-08-10T20:00:25.642375Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2207.05592","last_updated":"2022-07-12T15:12:27Z","snapshot_observed_at":"2026-08-13T15:05:38.148827Z","submitted_at":"2022-07-12T15:12:27Z","title":"Squarefree values of polynomial discriminants II","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2207.05592","snapshot_observed_at":"2026-08-10T20:00:25.481613Z","title":"Bhargava, A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2501.09697","last_updated":"2025-01-26T03:20:51Z","snapshot_observed_at":"2026-08-11T15:44:36.975719Z","submitted_at":"2025-01-16T17:48:25Z","title":"Squarefree discriminants of polynomials with prime coefficients","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:25.481613Z"},"links":{"cited_paper":"/paper/2207.05592","citing_paper":"/paper/2501.09697"},"observation_digest":"sha256:3cb9fc41fa37c0ef7c840ae2d8a1ccb0bbbf5b2d1023cdb4ed5a4f699d435104","observation_id":"500978e9-78f2-48bd-909a-45fa580c86bd","resolution":{"observed_at":"2026-08-10T20:00:25.481613Z","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":"2026-08-10T20:00:25.626224Z","title":null,"venue":null,"work_id":"68222eff-7800-47f4-96dc-9878689cd041","year":2011},"citing_paper":{"arxiv_id":"2501.09697","last_updated":"2025-01-26T03:20:51Z","snapshot_observed_at":"2026-08-11T15:44:36.975719Z","submitted_at":"2025-01-16T17:48:25Z","title":"Squarefree discriminants of polynomials with prime coefficients","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:25.485712Z"},"links":{"citing_paper":"/paper/2501.09697"},"observation_digest":"sha256:34cc3cb58a8e6c80cfc141e422390192e0b1bb3be6a8855e6ec867f94c05992a","observation_id":"ebdb9054-052c-4434-92c5-9b4a340c7df5","resolution":{"observed_at":"2026-08-10T20:00:25.630394Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-10T20:00:25.615227Z","title":"Lapkova and S","venue":null,"work_id":"5a1d2ce6-f085-4c80-8686-9543337a4c9a","year":2019},"citing_paper":{"arxiv_id":"2501.09697","last_updated":"2025-01-26T03:20:51Z","snapshot_observed_at":"2026-08-11T15:44:36.975719Z","submitted_at":"2025-01-16T17:48:25Z","title":"Squarefree discriminants of polynomials with prime coefficients","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:25.489252Z"},"links":{"citing_paper":"/paper/2501.09697"},"observation_digest":"sha256:4ed2ddb066f42ac4468c4b75fb4113bfc38f04d4941084763f6362689629d692","observation_id":"ab742301-3147-4265-a150-2da5a6c6510e","resolution":{"observed_at":"2026-08-10T20:00:25.618908Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2306.05961","last_updated":"2025-06-12T15:24:17Z","snapshot_observed_at":"2026-08-13T11:20:15.259634Z","submitted_at":"2023-06-09T15:27:51Z","title":"The density of ADE families of curves having squarefree discriminant","version":3},"cited_work":{"arxiv_id":"2306.05961","doi":null,"metadata_source":"pith","pith_arxiv_id":"2306.05961","snapshot_observed_at":"2026-08-10T20:00:25.536357Z","title":"The density of ADE families of curves having squarefree discriminant","venue":"math.NT","work_id":"7aea5e5d-2dbc-44a6-8e7d-c87d09d7c748","year":2023},"citing_paper":{"arxiv_id":"2501.09697","last_updated":"2025-01-26T03:20:51Z","snapshot_observed_at":"2026-08-11T15:44:36.975719Z","submitted_at":"2025-01-16T17:48:25Z","title":"Squarefree discriminants of polynomials with prime coefficients","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:25.493254Z"},"links":{"cited_paper":"/paper/2306.05961","citing_paper":"/paper/2501.09697"},"observation_digest":"sha256:67aba2a847fe1546106723c65eb1562adcf715835b0be03bdf76920631544512","observation_id":"82c28e79-b156-4260-881e-ee5719a06769","resolution":{"observed_at":"2026-08-10T20:00:25.542374Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-10T20:00:25.603631Z","title":null,"venue":null,"work_id":"1fcb734d-5e02-4a89-a5a7-9bed13025ef0","year":null},"citing_paper":{"arxiv_id":"2501.09697","last_updated":"2025-01-26T03:20:51Z","snapshot_observed_at":"2026-08-11T15:44:36.975719Z","submitted_at":"2025-01-16T17:48:25Z","title":"Squarefree discriminants of polynomials with prime coefficients","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:25.497393Z"},"links":{"citing_paper":"/paper/2501.09697"},"observation_digest":"sha256:c6e7de23354334a02d2b7df82353e5ed1fb154e640a31c724bcb25a31fb67352","observation_id":"041bb8d6-f873-4661-b8f1-e110d09f9e2b","resolution":{"observed_at":"2026-08-10T20:00:25.607480Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-10T20:00:25.592022Z","title":null,"venue":null,"work_id":"4691b0da-840a-44dd-9c90-59d1ccfd9277","year":2023},"citing_paper":{"arxiv_id":"2501.09697","last_updated":"2025-01-26T03:20:51Z","snapshot_observed_at":"2026-08-11T15:44:36.975719Z","submitted_at":"2025-01-16T17:48:25Z","title":"Squarefree discriminants of polynomials with prime coefficients","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:25.501432Z"},"links":{"citing_paper":"/paper/2501.09697"},"observation_digest":"sha256:1c70bc7c706ecd5e497020d42e4cbd534a54daf490842953fb7198b95a052c78","observation_id":"5a81fab2-4adf-4efe-851f-075ad27b6570","resolution":{"observed_at":"2026-08-10T20:00:25.595859Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-10T20:00:25.580341Z","title":"Yamamura, Some analogue of Hilbert’s irreducibilit y theorem and the distribution of algebraic num- ber ﬁelds","venue":null,"work_id":"6a481799-494c-42c8-a73c-4f424ab65afe","year":1991},"citing_paper":{"arxiv_id":"2501.09697","last_updated":"2025-01-26T03:20:51Z","snapshot_observed_at":"2026-08-11T15:44:36.975719Z","submitted_at":"2025-01-16T17:48:25Z","title":"Squarefree discriminants of polynomials with prime coefficients","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:25.505818Z"},"links":{"citing_paper":"/paper/2501.09697"},"observation_digest":"sha256:a180f24b3d5f048ede781363eb39f961f8e1c761df471f59d80707cbf6c2929c","observation_id":"fa7ed1c2-7b56-4e61-afe0-8370491b0b39","resolution":{"observed_at":"2026-08-10T20:00:25.584444Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.09697","last_updated":"2025-01-26T03:20:51Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-11T15:44:36.975719Z","submitted_at":"2025-01-16T17:48:25Z","title":"Squarefree discriminants of polynomials with prime coefficients"},"reference_resolution":{"displayed":13,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":1,"verified_fuzzy":5},"total_outbound_references":13},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2501.09697."}