{"as_of":"2026-08-12T23:30:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fdf145b229d642ec13f406733cc20532242bbdec864c586f05d1d5a10b65523a","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T14:13:29.399855Z","state":"measured"},{"denominator":14,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":14,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T20:21:54.873353Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-06T22:24:40.299987Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"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":"2412.12515","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.12515","snapshot_observed_at":"2026-08-06T22:24:40.299987Z","title":"Bounds for Moments of Twisted Fourier coefficients of Modular Forms","venue":"math.NT","work_id":"aa9fba81-ec82-4405-a174-cbcfdbd6e61e","year":2024},"citing_paper":{"arxiv_id":"2506.22256","last_updated":"2025-06-27T14:25:14Z","snapshot_observed_at":"2026-08-12T23:09:55.178301Z","submitted_at":"2025-06-27T14:25:14Z","title":"Mean squares of quadratic twists of the Fourier coefficients of modular forms","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T22:24:38.234211Z"},"links":{"cited_paper":"/paper/2412.12515","citing_paper":"/paper/2506.22256"},"observation_digest":"sha256:6f30be4ff2b6874d8b1e34a4f02deed57ea5a51f5366a7b42c7f06f8f4007fd1","observation_id":"96bb9e8c-0e8b-426d-97d4-d4874074ba2e","resolution":{"observed_at":"2026-08-06T22:24:40.399363Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"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"}}],"links":{"evidence":"/evidence","html":"/paper/2412.12515/citation-record","integrity":"/paper/2412.12515/integrity","json":"/paper/2412.12515/citation-record.json","paper":"/paper/2412.12515"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:13:29.991761Z","title":"Davenport, Multiplicative Number Theory , Third edition, Graduate Texts in Mathematics, vol","venue":null,"work_id":"10accd2a-5310-47ff-8af6-ed8759be9243","year":2000},"citing_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},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T14:13:29.273620Z"},"links":{"citing_paper":"/paper/2412.12515"},"observation_digest":"sha256:2490df9f218f50f7ad716424966a609d426eda9412f295dbb4b961ecace2eb5a","observation_id":"b215c7dd-9f14-43e5-ae67-dbf04893b48a","resolution":{"observed_at":"2026-08-11T14:13:30.049924Z","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":"2026-08-11T14:13:29.327089Z","title":"Deligne, La conjecture de Weil","venue":null,"work_id":null,"year":1974},"citing_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},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T14:13:29.327089Z"},"links":{"citing_paper":"/paper/2412.12515"},"observation_digest":"sha256:773001cde3e936a4d9c2e803640223fff710324907a5e5c290f2c1f29fe0954a","observation_id":"8f2c15bb-8502-4a38-9c72-1b8d92baa83e","resolution":{"observed_at":"2026-08-11T14:13:29.327089Z","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":"2026-08-11T14:13:29.942966Z","title":null,"venue":null,"work_id":"8dce1b0d-3ace-43e7-bcb9-16c9eeb73efd","year":2022},"citing_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},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T14:13:29.333450Z"},"links":{"citing_paper":"/paper/2412.12515"},"observation_digest":"sha256:037fadca2ef96d76ff016cc8171c3346d3e3ed9278e10abf7d53abf82fc01a03","observation_id":"c0cac332-0446-445e-946b-2f405c761f76","resolution":{"observed_at":"2026-08-11T14:13:29.952943Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:13:29.340752Z","title":"Gao and L","venue":null,"work_id":null,"year":null},"citing_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},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T14:13:29.340752Z"},"links":{"citing_paper":"/paper/2412.12515"},"observation_digest":"sha256:1f226a3c5bcecbae5e0285bed10d5d0ecbad200d4128358ff980da0f99494cd4","observation_id":"99650fee-5b48-4fdb-82c4-d206fae03dc5","resolution":{"observed_at":"2026-08-11T14:13:29.340752Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"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":"2026-08-11T14:13:29.348672Z","title":null,"venue":null,"work_id":null,"year":null},"citing_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},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T14:13:29.348672Z"},"links":{"cited_paper":"/paper/1305.4618","citing_paper":"/paper/2412.12515"},"observation_digest":"sha256:18988ce377cf55b9e598df5947b345d15f441507fcfdb40b5a6622c0de007745","observation_id":"2ae3f82d-dd04-49e3-9270-65796b38a368","resolution":{"observed_at":"2026-08-11T14:13:29.348672Z","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":"2026-08-11T14:13:29.883721Z","title":null,"venue":null,"work_id":"2320e0b1-9ec2-4af5-8e51-7cd88f938980","year":1995},"citing_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},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T14:13:29.357009Z"},"links":{"citing_paper":"/paper/2412.12515"},"observation_digest":"sha256:038cab87878e1dd8b7977dbabc89040a1b3bc5409e31c7b6e626dce007d43e91","observation_id":"4475138f-004d-408d-912b-d22b4011f00e","resolution":{"observed_at":"2026-08-11T14:13:29.922503Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:13:29.363714Z","title":"Iwaniec and E","venue":null,"work_id":null,"year":2004},"citing_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},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T14:13:29.363714Z"},"links":{"citing_paper":"/paper/2412.12515"},"observation_digest":"sha256:b7bf4e737d338f1ecece5c4d2482a62aa994f9c5aae6ad32e6a1b4d36c6e4153","observation_id":"e8df6e0d-d763-4e02-b81e-de96cfa8a5be","resolution":{"observed_at":"2026-08-11T14:13:29.363714Z","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":"2026-08-11T14:13:29.712790Z","title":"Koukoulopoulos, Pretentious multiplicative functions and the prime number theorem for arithmetic progressions , Compos","venue":null,"work_id":"72007f9e-8c73-47b1-af18-0c27ea4354d4","year":2013},"citing_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},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T14:13:29.369891Z"},"links":{"citing_paper":"/paper/2412.12515"},"observation_digest":"sha256:e381c331aa63129c4b0ba72f262d5e25cdcf32c07af1c2ee126b3729efd28e82","observation_id":"82fc2f10-6afa-4396-8ff2-25a4714c3a76","resolution":{"observed_at":"2026-08-11T14:13:29.764290Z","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":"2026-08-11T14:13:29.380864Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_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},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T14:13:29.380864Z"},"links":{"citing_paper":"/paper/2412.12515"},"observation_digest":"sha256:7d25aee14e610bfc2d16b98ff74c4094fe3bd385b9fe9e18accbe8e790d750fa","observation_id":"ce0d3fe6-4d79-4293-9b56-f6cb7176b539","resolution":{"observed_at":"2026-08-11T14:13:29.380864Z","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":"2026-08-11T14:13:29.386847Z","title":"Shimura, On the holomorphy of certain Dirichlet series , Proc","venue":null,"work_id":null,"year":1975},"citing_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},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T14:13:29.386847Z"},"links":{"citing_paper":"/paper/2412.12515"},"observation_digest":"sha256:d06a23ab2d9f1cdb5f52e343717ade28a29e0cb4fa9b053dc34d9b2f6c445195","observation_id":"bb0cca47-e319-45ec-b57b-368a7e0c7ffb","resolution":{"observed_at":"2026-08-11T14:13:29.386847Z","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":"2026-08-11T14:13:29.568205Z","title":"Soundararajan, Moments of the Riemann zeta function , Ann","venue":null,"work_id":"e3920a2d-9fba-4882-964e-4385fde3b89b","year":2009},"citing_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},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T14:13:29.393601Z"},"links":{"citing_paper":"/paper/2412.12515"},"observation_digest":"sha256:6ab4e47dc90d2564234ba95ae89338df7a1be5216b9221b83eda6318c37c7ea2","observation_id":"4dae2c02-67fb-4cd3-b11d-b6094153529e","resolution":{"observed_at":"2026-08-11T14:13:29.620253Z","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":"2409.13436","last_updated":"2024-09-20T11:59:43Z","snapshot_observed_at":"2026-08-12T22:41:04.296144Z","submitted_at":"2024-09-20T11:59:43Z","title":"A lower bound on high moments of character sums","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.13436","snapshot_observed_at":"2026-08-11T14:13:29.399855Z","title":"Szab´ o, High moments of theta functions and character sums , Mathematika 70 (2024), no","venue":null,"work_id":null,"year":2024},"citing_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},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T14:13:29.399855Z"},"links":{"cited_paper":"/paper/2409.13436","citing_paper":"/paper/2412.12515"},"observation_digest":"sha256:09a67a7d4336623239697ea1651e99acde991abbf73a67a3bd326d460c7db516","observation_id":"f43a658d-f031-4251-a5d9-11bc72cfa50f","resolution":{"observed_at":"2026-08-11T14:13:29.399855Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2412.12515","last_updated":"2024-12-17T04:09:05Z","latest_version":1,"primary_category":"math.NT","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"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":0,"verified_fuzzy":3},"total_outbound_references":12},"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 12 of 12 outbound references and 2 inbound Pith citation observations for arXiv:2412.12515."}