{"as_of":"2026-08-21T23:28:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:148cd3bb5d02b4da7fba325e2b2ff419cc5d7f2dcb173690225f2821c2801117","coverage":[{"denominator":28,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":28,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-30T04:40:19.612110Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+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/2606.30567/citation-record","integrity":"/paper/2606.30567/integrity","json":"/paper/2606.30567/citation-record.json","paper":"/paper/2606.30567"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Axler, P","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:cc12e2af1a138dd08dcd5940473f87132c9a62f6e06a8eca542c0bb7e12fabb8","observation_id":"5a788c0b-9d45-4488-b660-3aa10d437338","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":"2108.12283","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T16:44:56.482607Z","title":"Balkanova, D","venue":null,"work_id":"9c4baf73-f62c-45da-89f7-8a685bafd71d","year":2021},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:d93f05565445f731fab8962b9114c62adf7e63bcc970060e9b4bd0ec2131ff97","observation_id":"35172217-c5ec-480d-b2b8-a2d321715dcb","resolution":{"observed_at":"2026-06-30T16:44:56.483826Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-06-30T04:40:19.612110Z","title":"Blomer and F","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:12edccda4750957574f700d4a4fb0d0a2d177078857dbb9d4593620b3854f054","observation_id":"d682662a-ec4c-4325-9874-40fc602ecea1","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":null,"venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:0be7d175f887f3a991fea5be572403531db98e9c74e407a9b3f50efd3912b784","observation_id":"09aea106-9b8f-4808-9861-bbad5f91186a","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Deshouillers, S","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:57d859c7e503772ed5a1ea437c03f1fc35cf74a6806a0997ae8a9b5b2c089e94","observation_id":"15bfe628-0f72-4e84-9ec3-ef675ebbe079","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Erd˝ os, A","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:3330ca4f6ff50f8ff02159697d9042ba4193f1894239cab1eef35972c0709c3e","observation_id":"9cfce271-9f5b-4bed-87fd-23a1cbd132fb","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Friedlander and H","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:7bd880e51f2ce81fa40d1c336988fd555a0ec5a751f926d5d81b1d8431ac1796","observation_id":"766d2182-e355-4c7c-a970-1c8fe2287901","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Green, Roth’s theorem in the primes,Ann","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:080bc7880340ed0913407cec994681940623ee6cd140d866c181d8f9a4b1be55","observation_id":"ba5ddb38-122a-442a-8129-e95022850a80","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Green and T","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:48ab4064668838524d5279c4589aa5c27bd6ba0c15e10363ebc854e1f84a1a63","observation_id":"34e59ea4-a74d-461d-bf4c-497281577b18","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:803a444d1335d77f6c78e56dd16bda7c239820a3d0fa91de36e4d40f8071d0db","observation_id":"22370b3d-3a79-4958-925b-ac717f4eeaa1","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:61884ce0e7d3c1a58b45017717b9cb96931fee1b496f1195634747c0dd266508","observation_id":"f93bc68e-690e-49db-8853-13e5c4230c07","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Hecke, Eine neue Art von Zetafunktionen und ihre Beziehungen zur Verteilung der Primzahlen,Math","venue":null,"work_id":null,"year":1918},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:79e2fbe1895180fe84963785343e0f8fc836a5b06cc212d9216f4e5dd0d04dea","observation_id":"b91356f9-e6b5-454e-bca4-5e7814a4e611","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Iwaniec and E","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:0108e6f71ca9cc045cf21a891ea57f762cf1acb6fa890850c09497282e476dac","observation_id":"418718f7-11ed-4972-a8db-78ff17d1c64b","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Lang,Algebraic Number Theory, Graduate Texts in Mathematics, vol","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:c1f1741d9d20961ce828ef9c05bedb166682e7df1e7865986b56ffcd9aac1d6a","observation_id":"9a0e3b65-2e28-4104-9921-20d10eb8e36f","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Masser and J","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:05465e470bbe9fcbc7f5bac9946c94e46b8a52038756ed2123b9691005fde3a2","observation_id":"8a4d7d48-b0cb-4472-a2b4-49be19f13239","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Matom¨ aki and J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:d8e5f4e87e78f8481e98660cc5a08534ed1f0201d14bcf29a321e866892ab357","observation_id":"62f279d0-7bf3-409c-8102-df58bd7540cc","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Mitsui, Generalized prime number theorem,Japanese J","venue":null,"work_id":null,"year":1956},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:b484b7c9b7de4d2c4d4708c028e24cd785723ac4034921ccbc94c4a4a3e6da72","observation_id":"4a8183f6-2847-434e-934a-dc840da5a404","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:2e59af97cd9371ed3f4b175f6d562a9b4b8822d9be1caeecb61e7572084d266b","observation_id":"3bc98dda-fd4c-46f7-86d7-5d5803c2c2c2","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Neukirch,Algebraic Number Theory, Grundlehren der Mathematischen Wissenschaften, vol","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:008af0da78256d46bafcbf3af3a25c81d1bf395c9bc768de418580dcbbbbeaf7","observation_id":"e6e6c8cc-1da7-45d7-a26d-1a2e6de725c0","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Rademacher, On the Phragm´ en–Lindel¨ of theorem and some applications,Math","venue":null,"work_id":null,"year":1959},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:4d765b1151df33743b1e649e3a70ae176e16030ca2d19db860c2d029adc5680d","observation_id":"32ff1476-e224-451a-9b6d-089dfad43702","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Raghuram, Notes on the arithmetic of HeckeL-functions,Proc","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:b6b330904e5dcdb398288baccc57cbe9fb2e16d16cbac5a4bee35e279dbc83c1","observation_id":"9f52242d-9a24-4191-a511-62f4933ef4fd","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Rosen, A generalization of Mertens’ theorem,J","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:ad33d319c3705ef0f3cf4ea070d30c6557ac6848de30cbeecf8b083bc93de06e","observation_id":"bec0b4fc-787b-4d40-89aa-4897159baeba","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Sawin, Square-root cancellation for sums of factorization functions over squarefree progressions inF q[t],Acta Math.233(2024), no","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:21bde60a16fd7d5f4ac142c81dbdaea454bebb76846c1edf581ab223f326aea2","observation_id":"45c8c76a-a241-424b-b2ea-b0dd2fd4d4d9","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Tao and V","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:0056b0d3ab27e9b12f616478ea4c4faa60c74522dc01beda4dcfabe4e45bb97c","observation_id":"8931fd50-24f5-4091-99a9-9fdf7d6db39c","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Widmer, Counting primitive points of bounded height,Trans","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:a1c289fadb2ec38407258c1571f2f0aa73c815328f30f043082f10f47ff7487a","observation_id":"78f16980-131a-4c15-8a59-e13b79a12e8f","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:40:19.612110Z","title":"Wu, Burgess-like subconvexity for GL 1,Compos","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:61933abd8ba0fbd950072618fa72f24ecc7c32309c54af4ea218e0cb86bb4ff3","observation_id":"11d550ca-4586-42bd-8495-30f194b0ae27","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2510.17612","last_updated":"2025-11-10T16:52:07Z","snapshot_observed_at":"2026-08-18T06:47:27.769803Z","submitted_at":"2025-10-20T14:59:01Z","title":"On a Conjecture of Erd\\H{o}s over Function Fields","version":3},"cited_work":{"arxiv_id":"2510.17612","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2510.17612","snapshot_observed_at":"2026-07-07T03:18:49.839184Z","title":"Xie, On a conjecture of Erd˝ os over function fields, arXiv:2510.17612; to appear inMath","venue":null,"work_id":"ebcfce4d-adb0-4459-b051-7d59138fde72","year":null},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"cited_paper":"/paper/2510.17612","citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:de33fe63d04be6ebbced624f4414a72e328e40f281cd14a3a4dd8536adf757f7","observation_id":"96979fa9-bad2-491d-a0bd-75ac55129030","resolution":{"observed_at":"2026-07-07T03:18:49.839184Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-06-30T04:40:19.612110Z","title":"Zaman, Explicit estimates for the zeros of HeckeL-functions,J","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-06-30T04:40:19.612110Z"},"links":{"citing_paper":"/paper/2606.30567"},"observation_digest":"sha256:6fd9cf84b54c5875c5bd09276ad208d638d9565ba336209618d3b384dfa8b265","observation_id":"0eb350a7-51b9-4d51-a55b-05604d96ff28","resolution":{"observed_at":"2026-06-30T04:40:19.612110Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.30567","last_updated":"2026-06-29T17:09:28Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-19T16:50:49.667711Z","submitted_at":"2026-06-29T17:09:28Z","title":"Products of prime ideals in ray class groups"},"reference_resolution":{"displayed":28,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":26,"verified_exact":2,"verified_fuzzy":0},"total_outbound_references":28},"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2606.30567."}