{"as_of":"2026-08-12T16:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1469a5ae2c205f91cd52c63638cc5ede74fd24eedba4e39bc6fbd38db18d93ac","coverage":[{"denominator":29,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":29,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T20:21:54.958029Z","state":"measured"},{"denominator":29,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":29,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2608.05961/citation-record","integrity":"/paper/2608.05961/integrity","json":"/paper/2608.05961/citation-record.json","paper":"/paper/2608.05961"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T20:21:55.639146Z","title":null,"venue":null,"work_id":"6d1526d0-cb87-4b2b-8513-00c8da75d32f","year":2020},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.816122Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:eceee472fd5e1fe6133d558beeaf1c1bef9c6697353f0c0443e2ced1da507185","observation_id":"3904d798-12ff-4860-af2f-3a02a385c2e4","resolution":{"observed_at":"2026-08-07T20:21:55.644070Z","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":"1401.0418","last_updated":"2014-01-02T11:23:43Z","snapshot_observed_at":"2026-08-11T06:23:21.379811Z","submitted_at":"2014-01-02T11:23:43Z","title":"Mean Value Theorems for L-functions over Prime Polynomials for the Rational Function Field","version":1},"cited_work":{"arxiv_id":"1401.0418","doi":null,"metadata_source":"pith","pith_arxiv_id":"1401.0418","snapshot_observed_at":"2026-08-07T20:21:55.161013Z","title":"Mean Value Theorems for L-functions over Prime Polynomials for the Rational Function Field","venue":"math.NT","work_id":"8eb15e97-ed2a-495d-920a-2faca74201f7","year":2014},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.821928Z"},"links":{"cited_paper":"/paper/1401.0418","citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:fc7806d2d5e48a88637997a7fee65c15cda54d004d2b90dadacbaf660c5a2fc5","observation_id":"3d3eb35d-8dab-4bab-b5cb-a6e3e1b76c63","resolution":{"observed_at":"2026-08-07T20:21:55.166478Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T20:21:55.623304Z","title":null,"venue":null,"work_id":"8712f664-93d2-4ed8-a5b8-f51bf41e86a8","year":1999},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.827563Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:5a95feec486d83a675d7feb8310bdcd158a911fb74bd2afc6c91ec5bbd1df529","observation_id":"10c70102-fec7-4053-b411-7ec69478b9d0","resolution":{"observed_at":"2026-08-07T20:21:55.628505Z","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":"1809.09992","last_updated":"2018-09-26T13:39:20Z","snapshot_observed_at":"2026-07-06T07:04:27.019428Z","submitted_at":"2018-09-26T13:39:20Z","title":"Dirichlet $L$-functions of quadratic characters of prime conductor at the central point","version":1},"cited_work":{"arxiv_id":"1809.09992","doi":null,"metadata_source":"pith","pith_arxiv_id":"1809.09992","snapshot_observed_at":"2026-08-07T20:21:55.137064Z","title":"Dirichlet $L$-functions of quadratic characters of prime conductor at the central point","venue":"math.NT","work_id":"618b248d-6146-486f-9f14-5bc5b252017e","year":2018},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.832871Z"},"links":{"cited_paper":"/paper/1809.09992","citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:352649192403df3594be606d0771a28397cc6200f3aa8c531fac039f12e94147","observation_id":"1292d27a-8a9d-470a-84bc-72919a542adc","resolution":{"observed_at":"2026-08-07T20:21:55.143267Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T20:21:55.607030Z","title":null,"venue":null,"work_id":"935e4842-489b-475c-b458-7d19fadf4ec8","year":2018},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.838606Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:99bf46e8af1ecec2b25f3cfe1bbb6631f59fdf4759ba0dab309ec063f07eddc9","observation_id":"7b29d4eb-7a9e-45ef-8515-239d46197b6f","resolution":{"observed_at":"2026-08-07T20:21:55.611992Z","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":"2026-08-07T20:21:55.590813Z","title":null,"venue":null,"work_id":"7f19d712-a214-447f-877d-b0550beb626e","year":1974},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.843734Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:860d2b37f036ab4a1fddd319e3bc49f352b87d0a8d5a8018f9ff37ad9fd9a16c","observation_id":"8b1cde1d-832c-4f01-8161-7fb16e67463b","resolution":{"observed_at":"2026-08-07T20:21:55.595829Z","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":"2026-08-07T20:21:55.574211Z","title":null,"venue":null,"work_id":"33fc4546-8a40-4494-acb7-4f7a07010a0f","year":2022},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.848887Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:a46db6831dbe8496fdd43cfa9a3996bcee724e3f919cb77e3d9ab1f43bb092c6","observation_id":"b2c955c1-eb1e-47f9-871e-188bdd5b5e37","resolution":{"observed_at":"2026-08-07T20:21:55.579364Z","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":"2026-08-07T20:21:55.468663Z","title":"Gao and L","venue":null,"work_id":"0715ecc1-f075-469c-94b4-e475f0518a70","year":2021},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.853714Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:8193a228b92330b1a0a7f947324334c27adc3d5bee59a9cb30e366ec4c6b3942","observation_id":"2d151684-e17e-4d9c-9a4f-273159d9123c","resolution":{"observed_at":"2026-08-07T20:21:55.473966Z","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":"2026-08-07T20:21:55.450756Z","title":"Gao and L","venue":null,"work_id":"4e73d432-f050-4677-9701-b2c894443488","year":2023},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.858989Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:869cf98e06e203edddc624e5c108720eb15529d1b4ee44b641dbfd40bfd523a1","observation_id":"b9b05673-3711-4c29-98fd-5334565413d7","resolution":{"observed_at":"2026-08-07T20:21:55.456496Z","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":"2026-08-07T20:21:55.432820Z","title":"Gao and L","venue":null,"work_id":"9903c120-76eb-42c5-925a-b180a2a1eff2","year":2025},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.863649Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:62ddf7846a94f7c0a49dafde2770f1e5d9e0e6c5423e71d0916c57b05cb1e801","observation_id":"3e8452bd-ac14-41b6-af97-4c70a215d41f","resolution":{"observed_at":"2026-08-07T20:21:55.438414Z","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":"2026-08-07T20:21:55.415620Z","title":"Gao and L","venue":null,"work_id":"3b9c8cf2-2991-4129-8574-de4485967081","year":2025},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.868519Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:b51837bc5cd4958f5c0b84ea3d9f8746fb6840463f46655dd175e1575f6e82e4","observation_id":"7637a266-055b-4d93-923f-b37514481e33","resolution":{"observed_at":"2026-08-07T20:21:55.420808Z","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":{"arxiv_id":"2412.12515","last_updated":"2024-12-17T04:09:05Z","snapshot_observed_at":"2026-08-11T20:04:59.815536Z","submitted_at":"2024-12-17T04:09:05Z","title":"Bounds for Moments of Twisted Fourier coefficients of Modular Forms","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.12515","snapshot_observed_at":"2026-08-07T20:21:54.873353Z","title":"Gao and L","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.873353Z"},"links":{"cited_paper":"/paper/2412.12515","citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:43c33bf9451564af78c7f415c1021ecef91fa0fae2d7843ce61d269e10386a24","observation_id":"5372e55c-c7aa-4d5f-b588-a61103e1cd20","resolution":{"observed_at":"2026-08-07T20:21:54.873353Z","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":"2026-08-07T20:21:55.399182Z","title":"Gao and Y","venue":null,"work_id":"07327c6b-e1d2-4d6f-8eba-d22847b67d8f","year":2026},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.878877Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:b85e241f1f5c53d4a2a97248e071e8416dda430c780d9cf7969c2e63945948d5","observation_id":"7fe4ea8b-99e4-4413-b97c-2f5bbe28799d","resolution":{"observed_at":"2026-08-07T20:21:55.404145Z","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":"2509.20085","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T20:21:55.094154Z","title":"Gao and Y","venue":null,"work_id":"252c6198-6a0b-4241-a085-ed916fa86341","year":null},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.883808Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:c4d2502ba590d0d7141de99c8529c1e561d336e42df21d3eb95f93a07a33bc95","observation_id":"05d88315-3c96-4e40-87a4-f2cd45dfdde2","resolution":{"observed_at":"2026-08-07T20:21:55.103203Z","resolver_source":"raw_fallback","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T20:21:55.382454Z","title":"Goldfeld and X","venue":null,"work_id":"fb520c6a-bdd3-46c0-9581-ca997752022f","year":2018},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.888792Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:1ce124cae99d598480cdd429faecea3c8bd8af0b7f303bdf11933c4ffa0974e0","observation_id":"9899f295-aa68-4301-bddd-6efd72e25360","resolution":{"observed_at":"2026-08-07T20:21:55.388049Z","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":"2026-08-07T20:21:55.365883Z","title":"Goldfeld and C","venue":null,"work_id":"8e61fd68-9838-4188-a548-dd39e725ed66","year":1979},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.893653Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:660cd81ca2cda885beda70297294633af1cc986e8fea4b6ee34a2bbc95a48de9","observation_id":"65d79443-382b-4591-9f05-fd354b926a93","resolution":{"observed_at":"2026-08-07T20:21:55.371132Z","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":{"arxiv_id":"1305.4618","last_updated":"2013-05-20T19:41:52Z","snapshot_observed_at":"2026-07-06T03:13:48.645449Z","submitted_at":"2013-05-20T19:41:52Z","title":"Sharp conditional bounds for moments of the Riemann zeta function","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1305.4618","snapshot_observed_at":"2026-08-07T20:21:54.898473Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.898473Z"},"links":{"cited_paper":"/paper/1305.4618","citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:75757641ffefbc9926da689786b13a74f6f95050f60ddebc3433c0aa78ab13c4","observation_id":"807499fd-03f3-4ded-88dc-88fe3a709f1e","resolution":{"observed_at":"2026-08-07T20:21:54.898473Z","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":"2026-08-07T20:21:54.903873Z","title":null,"venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.903873Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:6c3aa8c98ce47c1e49d461ece0ff3e19e01285fa64198eb4b13a5b5f9cfe1792","observation_id":"58671933-f0ca-44bd-9f86-24be6d95a1de","resolution":{"observed_at":"2026-08-07T20:21:54.903873Z","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":"2026-08-07T20:21:55.337084Z","title":"Iwaniec and E","venue":null,"work_id":"e6db9ab4-094d-4a64-8798-c9958fa0940c","year":2004},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.908775Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:95e7ea618b84e28e3c79c7c5bc0638f928f3443009bd9757b44c559eee6b77e9","observation_id":"8a7ff98e-3482-4579-a649-83bd38a04571","resolution":{"observed_at":"2026-08-07T20:21:55.342009Z","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":"2026-08-07T20:21:55.321140Z","title":null,"venue":null,"work_id":"8ec95f4c-abf5-49ee-889e-b529ac4e79ac","year":1981},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.913639Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:179fd50b23a2f0cc1728b15d55c4e4f2f89b1bb0af2318d2918a54bde5a601ae","observation_id":"f6a0b8f7-653e-4184-9054-f09701c37264","resolution":{"observed_at":"2026-08-07T20:21:55.325995Z","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":"2026-08-07T20:21:55.304665Z","title":null,"venue":null,"work_id":"1af505b0-2f6c-42f2-887d-a6129cdd6d7b","year":2012},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.918736Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:b8d35b023a0d957a2d3d6c5d4b06fd07495bd1e6db4f00b3053313ac9cdf1c93","observation_id":"5eafd008-e32c-4673-8858-5012dbc16010","resolution":{"observed_at":"2026-08-07T20:21:55.310124Z","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":"2026-08-07T20:21:55.288217Z","title":null,"venue":null,"work_id":"3e74082a-f9f1-4b4f-9e22-758089165af7","year":2000},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.923474Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:f9f042d69e52ad5d0cb8c1956851f4c6c36ba7ab832f7b23afdac733328d15de","observation_id":"0bc467fe-6e33-4bce-91ca-c37e6abdde05","resolution":{"observed_at":"2026-08-07T20:21:55.293025Z","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":"2026-08-07T20:21:55.272200Z","title":"Koukoulopoulos","venue":null,"work_id":"c2bf1b78-0981-43f7-9f91-1a2a1c493e44","year":2013},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.928156Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:0532bb6e559c0265347893d347aa52404968fde105f66d9a8a017052bdc54814","observation_id":"9f6458c7-cc9f-462d-9cb0-9ea1c14b6cc5","resolution":{"observed_at":"2026-08-07T20:21:55.277190Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T20:21:54.932939Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.932939Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:6579500c24200df91497fd528c5a0944acda1bc302247a67e2c821da08ecd55c","observation_id":"71024932-6d71-4348-a95b-ae1b8a18d2fc","resolution":{"observed_at":"2026-08-07T20:21:54.932939Z","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":"2026-08-07T20:21:55.244952Z","title":"Munsch and Y","venue":null,"work_id":"a6955e91-89a8-4749-a49b-a65db99a2757","year":2026},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.937975Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:971494f48dc9fd052a85d691900474adcc26d4017bb1e57aad0d2636b1e38ca6","observation_id":"bc3de5a2-4854-48a8-a7dc-d36d23324001","resolution":{"observed_at":"2026-08-07T20:21:55.249773Z","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":"2026-08-07T20:21:55.226930Z","title":null,"venue":null,"work_id":"270a70f6-79dc-47e3-9606-106c655ca5d3","year":1975},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.942881Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:835f135005699bafaee8c8a68cb4a0c242999342d4a4790f205c97ae257d8696","observation_id":"cd57318c-9cef-45ea-bc16-3b207e251253","resolution":{"observed_at":"2026-08-07T20:21:55.232581Z","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":"2026-08-07T20:21:55.210532Z","title":"Soundararajan","venue":null,"work_id":"a4a074b9-1228-46ad-b4e0-ada6c4925d96","year":2009},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.947737Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:91b37a89204f705325c07992c88839a67c76cfbfd425cd93d451fbca460e7537","observation_id":"605ece8d-aa44-4fee-916f-8c8e24abd63d","resolution":{"observed_at":"2026-08-07T20:21:55.215647Z","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":"2026-08-07T20:21:55.194458Z","title":null,"venue":null,"work_id":"b6b36b27-1739-4ec7-8c6a-b1d25d02f9f8","year":2024},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.952864Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:16e4fd87a9b63895b015c75621f2bec7e68f1311933856044dffc61c124962d9","observation_id":"7b4796d8-0afa-4e1d-9384-2cdd84f5c8aa","resolution":{"observed_at":"2026-08-07T20:21:55.199356Z","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":"2026-08-07T20:21:55.178115Z","title":null,"venue":null,"work_id":"6d2d2090-5ac4-4397-9f91-566c6d0b03da","year":2026},"citing_paper":{"arxiv_id":"2608.05961","last_updated":"2026-08-06T12:36:13Z","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T20:21:54.958029Z"},"links":{"citing_paper":"/paper/2608.05961"},"observation_digest":"sha256:cb5386db54da4844c6163fdaf3abbcdafe5ec2efca2ee378b4329c9f35080f8e","observation_id":"e4411b7e-c1f7-42c1-aaad-b6d97b4c8c1d","resolution":{"observed_at":"2026-08-07T20:21:55.183200Z","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":"2608.05961","last_updated":"2026-08-06T12:36:13Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-12T15:02:10.801539Z","submitted_at":"2026-08-06T12:36:13Z","title":"Bounds for moments of twisted quadratic characters of prime modulus"},"reference_resolution":{"displayed":29,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":3,"verified_fuzzy":11},"total_outbound_references":29},"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 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2608.05961."}