{"as_of":"2026-08-20T15:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f1da7ee6739652be9455acc5e3d3be880c691dcaa6e5d2ded784a7f0f5810c11","coverage":[{"denominator":41,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":41,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T20:27:41.803978Z","state":"measured"},{"denominator":42,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":42,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T16:57:35.958790Z","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":"2026-08-15T16:57:36.003791Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"cited_work":{"arxiv_id":"2505.13256","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.13256","snapshot_observed_at":"2026-08-15T16:57:36.003791Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","venue":"math.NT","work_id":"f8306e7a-f4cd-4c97-9836-6ec05701db8d","year":2025},"citing_paper":{"arxiv_id":"2508.20576","last_updated":"2025-08-28T09:13:54Z","snapshot_observed_at":"2026-08-19T22:39:15.415155Z","submitted_at":"2025-08-28T09:13:54Z","title":"Weyl bound for trilinear periods via conformal bootstrap","version":1},"reference_index":115,"source":"pdf_text","source_observed_at":"2026-08-15T16:57:35.958790Z"},"links":{"cited_paper":"/paper/2505.13256","citing_paper":"/paper/2508.20576"},"observation_digest":"sha256:d5a96a5400fd2fff0b20ef7817314846a6d8ba869d029e5d151e1f61c02a787c","observation_id":"33d14068-47c7-423b-8f15-2cbdbafdb478","resolution":{"observed_at":"2026-08-15T16:57:36.010484Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.13256/citation-record","integrity":"/paper/2505.13256/integrity","json":"/paper/2505.13256/citation-record.json","paper":"/paper/2505.13256"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T20:27:42.794995Z","title":"A proof of K irillov's conjecture","venue":null,"work_id":"5761ea27-b41d-4ffa-9279-9cda8929c841","year":2003},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.507398Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:a7c6d32fcb32fab4737a5d81da7323407aa7a644e009e42e5659c463f0e22800","observation_id":"b2422505-0ef1-452f-8cfe-20150af22056","resolution":{"observed_at":"2026-08-15T20:27:42.803013Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:41.514484Z","title":"On the R amanujan conjecture over number fields","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.514484Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:1f71d42a64d84a4024633ca0bb2608c837f81db70e90bd299ff7c5efacb373b2","observation_id":"2441c1e6-4355-41a7-87ed-150c0fb57a3f","resolution":{"observed_at":"2026-08-15T20:27:41.514484Z","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":"2026-08-15T20:27:41.521120Z","title":"Bernstein","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.521120Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:1a46a193a18967079069e5954b56fc8de82f71a9610ccd1009dae6f8536a5b8c","observation_id":"325e6e3b-cd58-4439-ad23-58e4b0af0b14","resolution":{"observed_at":"2026-08-15T20:27:41.521120Z","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":"2026-08-15T20:27:42.729189Z","title":"Twisted L -functions over number fields and H ilbert's eleventh problem","venue":null,"work_id":"d19a5a0f-8f8a-45fa-ad50-2c2701bc6c65","year":2010},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.528858Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:beb0667b801553d7735d533f7195c68489c84f7e59d53bd62aeeba8015888322","observation_id":"34908b84-534c-4f82-8a38-76314da98071","resolution":{"observed_at":"2026-08-15T20:27:42.736399Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.698957Z","title":"Subconvexity implies effective quantum unique ergodicity for H ecke- M aa \\ cusp forms on SL_2( Z) SL_2( R)","venue":null,"work_id":"4969553d-88da-442b-8f9b-ec2871808ef9","year":2024},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.541707Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:182e2435b8feeaaa4a1c312db01178d3bd5d3e768ca0a595adc955794c0a0df1","observation_id":"17bbf0b1-57f4-443b-8394-2d462db29337","resolution":{"observed_at":"2026-08-15T20:27:42.707441Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.673505Z","title":null,"venue":null,"work_id":"120df5da-771a-4b98-9637-dd03fe8a528b","year":2023},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.547966Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:b62b7cedff23ee43440aecf73c28817881e3e87b9fca87ba3a56ff8137e0bb67","observation_id":"eb794bdb-8342-4510-b01b-5ce856a7f0d8","resolution":{"observed_at":"2026-08-15T20:27:42.680775Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.648972Z","title":"Arithmetic and equidistribution of measures on the sphere","venue":null,"work_id":"087a9e78-1b78-484d-bf8c-4d7e1b06c63c","year":2003},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.556388Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:8f490f05cf9279570ab92468a8f7d1fa4ef2dfe1a8840fc62b9f1c4ef65393d7","observation_id":"8f5ae5ef-13f0-4b08-91c1-5e7b1753ac04","resolution":{"observed_at":"2026-08-15T20:27:42.656785Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.623838Z","title":"Automorphic Forms and Representations , volume 55 of Cambridge Studies in Advanced Mathematics","venue":null,"work_id":"d89e2d74-c660-4cb9-b21d-e1e054c579e3","year":1997},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.562215Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:bcb4d36e8d342cdeff4a0cf16d76c74ddbe79bd01b8749618dc5a4ae8c71b77f","observation_id":"79e9d1ba-f6ba-45fe-9730-cc3be3bb9b47","resolution":{"observed_at":"2026-08-15T20:27:42.632979Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.592817Z","title":"On Deligne's conjecture for certain automorphic L -functions for GL (3) GL (2) and GL (4)","venue":null,"work_id":"dfa1fffc-330b-4999-94a8-78a8e9fd9fb3","year":2019},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.569217Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:6eabde5809071579800b2306b48daec27b2325a84cf29df8955022a402245bee","observation_id":"370fa92a-fd7d-44b9-b668-6a2075b5add9","resolution":{"observed_at":"2026-08-15T20:27:42.598691Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.570310Z","title":"Special value formula for the twisted triple product L -function and an application to the restricted L^2 -norm problem","venue":null,"work_id":"cac8ad7f-1566-4e39-b28b-e9c061054d4b","year":2021},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.574595Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:f1065d42d426812e9cd7ac5ed541d1a0450e6f67eac41ed9eb872d7824387668","observation_id":"a04dfb63-a40a-4f96-8a69-e866ae1f5f89","resolution":{"observed_at":"2026-08-15T20:27:42.577100Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.550272Z","title":"Cowling, U","venue":null,"work_id":"4209fa6a-94ed-4952-8667-dc99464d0262","year":1988},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.580431Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:203d9741403c78ba3775833400d1e730f09fd9e7e543e8a016c6100b0ab62147","observation_id":"548aa745-06e7-44f2-b766-5a0d27ac61ee","resolution":{"observed_at":"2026-08-15T20:27:42.556978Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.527718Z","title":null,"venue":null,"work_id":"10e352ca-460c-4ef2-b1f5-86026d7b4fd5","year":2001},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.593109Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:337734d175b9e34120ca3b1fd26e007a5be2c75ddf3ef141b674f6692b389443","observation_id":"52f5e9ce-c386-45da-b989-2c751a841b95","resolution":{"observed_at":"2026-08-15T20:27:42.535481Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2112.01427","last_updated":"2021-12-02T17:18:59Z","snapshot_observed_at":"2026-08-20T05:32:57.683440Z","submitted_at":"2021-12-02T17:18:59Z","title":"Dissipation of correlations of holomorphic cusp forms","version":1},"cited_work":{"arxiv_id":"2112.01427","doi":null,"metadata_source":"pith","pith_arxiv_id":"2112.01427","snapshot_observed_at":"2026-08-15T20:27:41.893076Z","title":"Dissipation of correlations of holomorphic cusp forms","venue":"math.NT","work_id":"d8c6dfa9-bc55-49e6-a531-8fb431142479","year":2021},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.600672Z"},"links":{"cited_paper":"/paper/2112.01427","citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:97eedca5aadbf1492c0429c5e557970f36d118b7a8cacf77b27b55a3d3aabec5","observation_id":"70fb015d-9610-45a2-bb28-62ccec855be3","resolution":{"observed_at":"2026-08-15T20:27:41.901876Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.501717Z","title":null,"venue":null,"work_id":"527eca0c-1627-4776-a48a-6f338be118bc","year":1991},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.610147Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:154985521ea1b3184d58d4675b4cf7145df0e12ab4d71ca26e8c6e9f17a5c506","observation_id":"50e0d023-910f-4583-bce8-94f1f466ae01","resolution":{"observed_at":"2026-08-15T20:27:42.508598Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:41.620300Z","title":"Coefficients of M aass forms and the S iegel zero","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.620300Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:4e4faa8bd2930f4e236c476a49b4a0f6e94f911fa6a583ad6a81431deb191e8c","observation_id":"ddd71b6a-0993-4634-88b1-ebc97beecc9d","resolution":{"observed_at":"2026-08-15T20:27:41.620300Z","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":"2026-08-15T20:27:42.458813Z","title":"Some analytic aspects of automorphic forms on gl(2) of minimal type","venue":null,"work_id":"f4c3c787-3a60-410f-98ae-a390b9bce3fe","year":2019},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.627846Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:ba503793ecec6a9bd9eff5e86480269d03d858026e6f29b8a329634261db065e","observation_id":"762e2c88-1bd1-4173-b031-6dceee075c95","resolution":{"observed_at":"2026-08-15T20:27:42.465718Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:41.636123Z","title":"Mass equidistribution for H ecke eigenforms","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.636123Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:438fea8cb2699de1b6a8aacc92dda749c28831cd91a468d5cc894d48726ad4fd","observation_id":"22c9da66-8e6b-4a6b-a166-5dd46f13f40f","resolution":{"observed_at":"2026-08-15T20:27:41.636123Z","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":"2026-08-15T20:27:42.420185Z","title":"Hida families and p -adic triple product L -functions","venue":null,"work_id":"9ef8ba4b-d687-4284-aa80-be8f16d1ec32","year":2021},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.645847Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:01e9989eb12a1e57988e060c1128b14016f97b90b71e00e4108630f6c893bee8","observation_id":"d60df57e-759d-4914-996a-7213b166e65b","resolution":{"observed_at":"2026-08-15T20:27:42.427379Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:41.652737Z","title":"Triple product formula and mass equidistribution on modular curves of level N","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.652737Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:16445d809711c38bca6bf6db878f23a58c50c2eb6e6a8df29a652cefb627c917","observation_id":"bb1944c7-95c1-4865-b8fb-015cfc411e55","resolution":{"observed_at":"2026-08-15T20:27:41.652737Z","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":"2026-08-15T20:27:41.658772Z","title":"Trilinear forms and the central values of triple product L -functions","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.658772Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:efa13dfc33ed1c351d7229de3ac5d8bfe24cfb8aa1996efc83f2faa4ed3706f2","observation_id":"33e4e073-8d1e-4bd9-9edc-a8d63863db3c","resolution":{"observed_at":"2026-08-15T20:27:41.658772Z","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":"2026-08-15T20:27:41.669445Z","title":"Analytic number theory , volume 53 of American Mathematical Society Colloquium Publications","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.669445Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:0cdc153af3567ff99ceacc5a56f69c588aa6d7bf217cb8697e30dd103a1c8903","observation_id":"8094e63b-4d2c-4ebb-baed-aef049777695","resolution":{"observed_at":"2026-08-15T20:27:41.669445Z","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":"2026-08-15T20:27:42.348153Z","title":"Small eigenvalues of L aplacian for _0(N)","venue":null,"work_id":"5365923b-8fbf-45ca-ab18-75ddd3141959","year":1990},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.674744Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:af54bcad58046833efd4a469f83bd0f106acc98cc2eb3d06b307550511f7f8f0","observation_id":"b432a7f0-3843-4c77-9f03-d330e517b180","resolution":{"observed_at":"2026-08-15T20:27:42.356026Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.322812Z","title":"Automorphic forms on GL (2)","venue":null,"work_id":"d409655f-df73-4dc9-864f-d485c0b73bb6","year":1972},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.679967Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:115499b13d2181eb3b069fe30b58e62abe81ca30c4eec96d43776358ab3cecda","observation_id":"4f616973-cb30-47b4-986b-2183a0d019fc","resolution":{"observed_at":"2026-08-15T20:27:42.328993Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.302713Z","title":"Quantum unique ergodicity for E isenstein series on PSL _2( Z ) PSL _2( R )","venue":null,"work_id":"53b8ebba-f2a4-4aff-8215-2e91eb664961","year":1994},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.686212Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:a4d1676344e08917f62d262cd2e581c9fb813d0c6c9c1a4cf5df70ba525b2cb4","observation_id":"2b009be8-d648-477b-9a68-6a40a6d62504","resolution":{"observed_at":"2026-08-15T20:27:42.308377Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:41.695382Z","title":"Invariant measures and arithmetic quantum unique ergodicity","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.695382Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:59cbf5fb255ef1c36aaf08a41b9a63f02152471de82fd8b0e6075cc16e5ad252","observation_id":"d7c90488-72af-49e2-a881-75bdb617c0ca","resolution":{"observed_at":"2026-08-15T20:27:41.695382Z","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":"2026-08-15T20:27:42.267669Z","title":"Quantum ergodicity of eigenfunctions on PSL _2( Z) H^2","venue":null,"work_id":"eaef30cf-8e7d-47cc-968d-cf3f5abff297","year":1995},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.700942Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:76055982c7353210bc603650914d8f1d3f03bfe0c42ef4d699b42f5b5910f8e5","observation_id":"70eef0bf-971e-430b-b523-f5b5cde70433","resolution":{"observed_at":"2026-08-15T20:27:42.273460Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.229811Z","title":"Triple product L -functions and quantum chaos on SL(2, C )","venue":null,"work_id":"6db386f3-8f7a-4aee-819f-13be65e5188c","year":2014},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.708669Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:7a10b999f5313ec155d896051b558be22c324aacb48717be14924a1ca9739268","observation_id":"e19bbc99-bdba-4106-82f1-452c493a3a8a","resolution":{"observed_at":"2026-08-15T20:27:42.242503Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.205479Z","title":"The subconvexity problem for GL _2","venue":null,"work_id":"73d888b6-7559-4869-9d9f-4fc9a3bd6506","year":2010},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.716648Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:82ee458417001bf210ae7624d5ed7d230836417f06db8acda28f6a051c180b7c","observation_id":"0aaf4d96-da79-45b9-be11-134f48d62110","resolution":{"observed_at":"2026-08-15T20:27:42.211367Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:41.722341Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.722341Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:757a711c5559a3116705c8abdbbe9d83f23862f767a97aa5cdc8375e901917ba","observation_id":"4db16bbd-ae2a-4232-b780-76cb6fb1d451","resolution":{"observed_at":"2026-08-15T20:27:41.722341Z","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":"2026-08-15T20:27:42.171278Z","title":null,"venue":null,"work_id":"b911a0a5-9b82-4ce6-be24-59f176533a2a","year":2012},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.731673Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:e26d97d355a706f2ff182c0417a8b6da514168cfb754f776913ef4c8b6a39f7d","observation_id":"20cc7be8-1ddb-4954-8590-7edad5672957","resolution":{"observed_at":"2026-08-15T20:27:42.176959Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.146153Z","title":null,"venue":null,"work_id":"92e58492-eb92-415d-92fc-44cf5d36ea0a","year":2018},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.739262Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:c3dba82a651f010f5e816a0084abd9f96e3b1b87b3b3eb4215026e9c9575a474","observation_id":"2b25766f-4149-46b7-986e-ecafbd68d7f1","resolution":{"observed_at":"2026-08-15T20:27:42.155210Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.117440Z","title":null,"venue":null,"work_id":"0f8ece38-7ce7-4525-bc5f-fd2edd55dec4","year":2019},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.745563Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:2e661caff4ab73ff5e93fa769d8b37d0cc9eab16c30ed8cd73fc591e53423a9a","observation_id":"d46ff972-ccfa-4447-8948-6e55b4de77ce","resolution":{"observed_at":"2026-08-15T20:27:42.126975Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.090598Z","title":"Nelson, Ameya Pitale, and Abhishek Saha","venue":null,"work_id":"9336a5fc-3027-4e21-bee6-642bc203f3b9","year":2014},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.751281Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:dd5cab2a11bb1bd62b6dad6a2a9ad225b194abbda841f98c120694a04abda7dd","observation_id":"29ee7f2d-c6ec-4a3f-aaf2-21f53ef534a5","resolution":{"observed_at":"2026-08-15T20:27:42.098172Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.064494Z","title":"Laplace- B eltrami operator on a R iemann surface and equidistribution of measures","venue":null,"work_id":"606b711e-b05e-4c75-8490-64c39f029308","year":2001},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.756466Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:87390ab69f6910aff6dff107a69d39103ef1b6e230beb9f28ddda52774d74f82","observation_id":"1569b824-f3ec-4e57-917c-c314bf11975a","resolution":{"observed_at":"2026-08-15T20:27:42.071619Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:42.032913Z","title":"Estimates for R ankin- S elberg L -functions and quantum unique ergodicity","venue":null,"work_id":"993d6a88-805e-4beb-920a-19425a7b3902","year":2001},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.763630Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:eff93b9b7da82f552fdde74b3fe3946469076a043bad72b93f446803005e7331","observation_id":"80ba8a1c-bbc9-4817-8305-ac0bec60c1e2","resolution":{"observed_at":"2026-08-15T20:27:42.044082Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:41.770985Z","title":"Fourier transforms of intertwining operators and P lancherel measures for GL (n)","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.770985Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:e04076112d933228df7e2e761862a7ec35e129b716808806e66036c5d1a4de27","observation_id":"7cef817f-a80e-45ff-9e33-37bfde9630c2","resolution":{"observed_at":"2026-08-15T20:27:41.770985Z","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":"2026-08-15T20:27:41.987881Z","title":"Quantum unique ergodicity for SL _2( Z ) H","venue":null,"work_id":"12aab9c9-8d1c-4301-ac7c-309de5d7d9bf","year":2010},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.777769Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:f928eb8ba0c69ce77b79870365f2769bbe97ad428e030b771b01c3bd20ace36f","observation_id":"8545deba-ee0a-43ae-8c3d-ed34a1dc9d07","resolution":{"observed_at":"2026-08-15T20:27:41.993659Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:41.959217Z","title":"Sarnak and P","venue":null,"work_id":"aacbd997-dc67-4b19-8f0a-ac80118f2172","year":2019},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.784669Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:2e52030b647db4589896cd53a83cb742a0527ef495bd81001fc4e3173b468680","observation_id":"68ff0901-798c-46c4-85c5-9cc27568fef9","resolution":{"observed_at":"2026-08-15T20:27:41.965407Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:27:41.790734Z","title":"Sparse equidistribution problems, period bounds and subconvexity","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.790734Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:af4424af34a1c7f3621c60564f9439944f0261d248af73a307d33446cac80209","observation_id":"c879c446-10f2-4733-978c-ac1dc2ea64c6","resolution":{"observed_at":"2026-08-15T20:27:41.790734Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0810.0425","last_updated":"2008-10-22T06:29:01Z","snapshot_observed_at":"2026-08-19T22:37:40.653893Z","submitted_at":"2008-10-02T14:36:17Z","title":"Rankin Triple Products and Quantum Chaos","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0810.0425","snapshot_observed_at":"2026-08-15T20:27:41.797092Z","title":"Rankin triple products and quantum chaos","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.797092Z"},"links":{"cited_paper":"/paper/0810.0425","citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:73b2f030594dca12dff75cbce61c92340da47fa31997ea37f151f354ee02352a","observation_id":"6dd661e5-28b9-47a4-a238-51cc8912547e","resolution":{"observed_at":"2026-08-15T20:27:41.797092Z","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":"2026-08-15T20:27:41.803978Z","title":"Woodbury","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$","version":2},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-15T20:27:41.803978Z"},"links":{"citing_paper":"/paper/2505.13256"},"observation_digest":"sha256:81efeb1a6d43639f50749515011815e6b0fee8db16f4e32dcaf46ca2647048be","observation_id":"5cc976c2-7bb2-4126-b2d3-8f99f00abe7c","resolution":{"observed_at":"2026-08-15T20:27:41.803978Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2505.13256","last_updated":"2025-09-12T01:14:11Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-20T09:56:24.887576Z","submitted_at":"2025-05-19T15:39:31Z","title":"Soft bounds for local triple products and the subconvexity-QUE implication for $\\mathrm{GL}_2$"},"reference_resolution":{"displayed":41,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":19,"verified_exact":1,"verified_fuzzy":21},"total_outbound_references":41},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 1 inbound Pith citation observation for arXiv:2505.13256."}