{"as_of":"2026-08-07T17:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:09f32c6fc157a6dfaf79209deaf0cbcaa2ed57c4e658ebee2779f69b1c95dff3","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T19:31:46.368142Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T07:13:05.155348Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-03T01:17:30.674714Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"cited_work":{"arxiv_id":"2507.06115","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.06115","snapshot_observed_at":"2026-07-03T01:17:30.674714Z","title":"Optimal Young’s convolu- tions inequality and its reverse form on the hypercube.arXiv preprint arXiv:2507.06115, 2025","venue":null,"work_id":"0a124647-afcd-485d-b4de-0699420a6f0e","year":2025},"citing_paper":{"arxiv_id":"2606.08958","last_updated":"2026-06-08T03:00:40Z","snapshot_observed_at":"2026-07-06T23:48:21.633158Z","submitted_at":"2026-06-08T03:00:40Z","title":"A spectral correlation inequality for increasing Boolean functions","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-27T16:43:04.921041Z"},"links":{"cited_paper":"/paper/2507.06115","citing_paper":"/paper/2606.08958"},"observation_digest":"sha256:d72c60abcb07940981e7c22a76634c95aa48a988fe5fb575cd26139778947925","observation_id":"0884e1a3-b3cd-47f8-8852-bb4c30eb8ace","resolution":{"observed_at":"2026-07-03T01:17:30.676627Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"cited_work":{"arxiv_id":"2507.06115","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.06115","snapshot_observed_at":"2026-07-03T01:17:30.674714Z","title":"Optimal Young’s convolu- tions inequality and its reverse form on the hypercube.arXiv preprint arXiv:2507.06115, 2025","venue":null,"work_id":"0a124647-afcd-485d-b4de-0699420a6f0e","year":2025},"citing_paper":{"arxiv_id":"2606.32024","last_updated":"2026-06-30T17:52:59Z","snapshot_observed_at":"2026-07-07T00:05:41.920778Z","submitted_at":"2026-06-30T17:52:59Z","title":"The sharp diagonal spectral correlation inequality on the discrete cube","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-01T04:17:25.416483Z"},"links":{"cited_paper":"/paper/2507.06115","citing_paper":"/paper/2606.32024"},"observation_digest":"sha256:bf4bafeba1ebe8ffe24e5b1cbd3de1bb63f86f1f886cfa2c11863f3e1b04a582","observation_id":"ce666652-1f55-4a4a-8413-db56bb887e0d","resolution":{"observed_at":"2026-07-01T11:35:43.237911Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.06115","snapshot_observed_at":"2026-08-01T07:13:05.155348Z","title":"Beltran, P","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.21589","last_updated":"2026-07-23T17:58:16Z","snapshot_observed_at":"2026-08-07T01:34:17.548589Z","submitted_at":"2026-07-23T17:58:16Z","title":"The Frankl--Tokushige product conjectures for $r$-cross-intersecting families","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T07:13:05.155348Z"},"links":{"cited_paper":"/paper/2507.06115","citing_paper":"/paper/2607.21589"},"observation_digest":"sha256:add45bad722e591e755ccb7a888a5dee47ba2d7bb318b3ae1572fe0d794931a3","observation_id":"9b5fddbd-9256-4e4b-aefb-37a9dd84eee2","resolution":{"observed_at":"2026-08-01T07:13:05.155348Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2507.06115/citation-record","integrity":"/paper/2507.06115/integrity","json":"/paper/2507.06115/citation-record.json","paper":"/paper/2507.06115"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2404.04486","last_updated":"2024-04-15T15:25:18Z","snapshot_observed_at":"2026-07-06T17:56:23.317089Z","submitted_at":"2024-04-06T03:40:13Z","title":"Discrete Brunn-Minkowski Inequality for subsets of the cube","version":2},"cited_work":{"arxiv_id":"2404.04486","doi":null,"metadata_source":"pith","pith_arxiv_id":"2404.04486","snapshot_observed_at":"2026-08-06T19:31:46.498752Z","title":"Discrete Brunn-Minkowski Inequality for subsets of the cube","venue":"math.CO","work_id":"83f9e32f-a29a-440d-92ee-b31038303771","year":2024},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.263795Z"},"links":{"cited_paper":"/paper/2404.04486","citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:eda9f1fc2e545f2d28ea4a4143c92d3cd2fb14c1920ebfc87ccc70fda0662db6","observation_id":"a58e331b-970f-4d7c-b646-085ff4969a61","resolution":{"observed_at":"2026-08-06T19:31:46.503628Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.12579","last_updated":"2024-10-14T17:16:28Z","snapshot_observed_at":"2026-08-07T13:45:16.298661Z","submitted_at":"2024-09-19T09:00:20Z","title":"Sharp estimates for Gowers norms on discrete cubes","version":2},"cited_work":{"arxiv_id":"2409.12579","doi":null,"metadata_source":"pith","pith_arxiv_id":"2409.12579","snapshot_observed_at":"2026-08-06T19:31:46.473317Z","title":"Sharp estimates for Gowers norms on discrete cubes","venue":"math.CO","work_id":"1b105473-b19b-484f-97e2-c08c12a4ccd5","year":2024},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.269648Z"},"links":{"cited_paper":"/paper/2409.12579","citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:2fbf23d7844583caa5424a49a40628dfc5735f49d94490acf58320b808dd8611","observation_id":"484dc26e-bbd4-4880-9bc8-394d0fb5cd76","resolution":{"observed_at":"2026-08-06T19:31:46.479466Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.817647Z","title":"Explicit constructions of RIP matrices and related problems","venue":null,"work_id":"36c21005-b005-4fec-ac68-8dbec8cc9efc","year":2011},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.274826Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:5a5eacd587ba36cadee2cc02ac3844e967061ec8745cfe30856263ef04f280b4","observation_id":"bd166f4f-f63b-42f5-8ef0-2693c01caa6c","resolution":{"observed_at":"2026-08-06T19:31:46.822984Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.01359","last_updated":"2025-07-02T04:50:11Z","snapshot_observed_at":"2026-08-06T20:51:09.612430Z","submitted_at":"2025-07-02T04:50:11Z","title":"Inequalities in Fourier analysis on binary cubes","version":1},"cited_work":{"arxiv_id":"2507.01359","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.01359","snapshot_observed_at":"2026-08-06T19:31:46.449516Z","title":"Inequalities in Fourier analysis on binary cubes","venue":"math.CA","work_id":"1993f847-b548-4eb0-9ad1-bc263d4d92e4","year":2025},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.279752Z"},"links":{"cited_paper":"/paper/2507.01359","citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:c7fc8423b2b0b32bb6e5601c173ba08b5e1b884f1696ec70724299ff632bb85e","observation_id":"932a9aac-e6bc-4876-a7b8-c8f9bef0dc17","resolution":{"observed_at":"2026-08-06T19:31:46.455281Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.798535Z","title":"Additive energies on discrete cubes","venue":null,"work_id":"a3ef8bd3-c3f0-4d2a-a9fe-95a390ee784e","year":2023},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.284866Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:084b30d5a65110d5481785945cdeb3932eebb173e946efd9b1b84c1902cbd4d6","observation_id":"675f3302-1994-47e4-b0eb-b7b6e545a14a","resolution":{"observed_at":"2026-08-06T19:31:46.803997Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.781883Z","title":"Hajela and P","venue":null,"work_id":"a7fb1e85-462c-4b38-800f-712aeaa119d2","year":1985},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.289548Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:edacc634c95ba500acf2e4480191a993a870ea30d1462ad3ee907539dea9339c","observation_id":"27a0c509-41d0-4f0c-8471-5baecc7548e6","resolution":{"observed_at":"2026-08-06T19:31:46.786814Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.764053Z","title":"A bound on partitioning clusters","venue":null,"work_id":"5cffb0ef-3a05-41cb-9fe4-8ebe31447428","year":2017},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.294862Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:ad2b64d9b690d8b3d66d86380d06d5c2f00ec49b2bae1b3bf908f3f63cf6a3dd","observation_id":"9bfa05b6-5590-4dcb-8620-7c498439ab76","resolution":{"observed_at":"2026-08-06T19:31:46.769478Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.747037Z","title":"Leindler","venue":null,"work_id":"05ba2dc9-49f8-463b-aa79-0dcd6531c6f9","year":1971},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.299383Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:b8a138243613ba81ae3bdd6c9f411992f172b02c6962baeff04fcc2e3f7f4b8d","observation_id":"d9691a60-0097-4699-99d8-4b7aeac400ec","resolution":{"observed_at":"2026-08-06T19:31:46.752136Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.729623Z","title":"Shkredov","venue":null,"work_id":"84878792-f0ce-4421-86d8-45f67a848f5e","year":2013},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.304012Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:a787d6c0b4d16fd6e86b92727bad70951288aea2cc7f26aaa43df88e5f3ea8b2","observation_id":"2971ce90-f33d-4230-8b2b-b056c8f180a5","resolution":{"observed_at":"2026-08-06T19:31:46.734663Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.709921Z","title":"Energies and structure of additive sets","venue":null,"work_id":"34e1e785-7044-4f3c-ac79-743fd305fb6b","year":2014},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.308944Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:31197b0794d6aed6e411c882beebff84a2392ba8134f6379d5ef5ad70199c10c","observation_id":"495c1408-b199-4521-bb47-8559e66d8030","resolution":{"observed_at":"2026-08-06T19:31:46.714970Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.690912Z","title":null,"venue":null,"work_id":"0a4a497d-b311-46ce-93d6-ae5c51a72ded","year":1977},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.313403Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:7aad7974b06357d80b7f50bdf06bf1c1594e6a1fb4ce03f9625699198b29dce6","observation_id":"e4fa8083-ec56-493c-ae39-9a81c2b1497e","resolution":{"observed_at":"2026-08-06T19:31:46.697682Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.665710Z","title":"Bourgain, S","venue":null,"work_id":"7b90cc4d-486e-43a7-ac83-205ee5f0db0f","year":2011},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.318243Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:7b45aeeddc021e8100520e40256143f872238bb064f4c28791c2d41e26a7eefa","observation_id":"56ad6965-e613-44c9-ab67-f4af049682fb","resolution":{"observed_at":"2026-08-06T19:31:46.671290Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.647310Z","title":"de Dios, R","venue":null,"work_id":"4fc689ec-fca4-44c5-add7-16558190fa62","year":null},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.322745Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:05a0ff7dad91075463e3f4517dc315711a9641e4fa0f741eb95ddca8b50a1122","observation_id":"0a1615af-38d7-4efc-8f0e-909bffc54dc7","resolution":{"observed_at":"2026-08-06T19:31:46.652795Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.629708Z","title":"Fish, Ben Lund, and A","venue":null,"work_id":"1814bbf7-3d24-4ca6-bc3f-108f0a0ee6ae","year":2019},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.327248Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:ca09a8c669fcf23865f630196b0c3adbe3a70911cafb23966c1e472c5f8de6cd","observation_id":"0d3c1ff1-a89b-4957-ab3a-62ce6aa0d89e","resolution":{"observed_at":"2026-08-06T19:31:46.633967Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.613464Z","title":"Gyarmati, M","venue":null,"work_id":"ad972b24-57d4-4f23-ab7a-e6457cdaa090","year":null},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.331630Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:92fbc6276ca964780eb152fa792839aa7b8af33e63e80168117c8c7593696912","observation_id":"2f5696d8-27b6-461d-8e95-9d5603c49f34","resolution":{"observed_at":"2026-08-06T19:31:46.618570Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.596470Z","title":"Green, D","venue":null,"work_id":"c4aed0cb-3a08-4207-9546-d2fbe0ca785e","year":null},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.336027Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:9181bd74efbaea3d212daec7a5f35d6b27207fc4bae2a1d664c8aaf38bbe39ac","observation_id":"664f63bb-7185-4ad2-9131-8ad5005a1773","resolution":{"observed_at":"2026-08-06T19:31:46.601844Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.579951Z","title":null,"venue":null,"work_id":"cade985d-1dbd-4cf3-8b0d-f3a5995dc00d","year":2006},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.341217Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:36c36bf023a8f6c767e19661cbce126ebe68691dda4afd11ec962bd08d8169e8","observation_id":"ce437220-8057-430d-8366-1b7ba1f85aa9","resolution":{"observed_at":"2026-08-06T19:31:46.584614Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.564205Z","title":"Hanson and G","venue":null,"work_id":"91820177-8df0-448a-a907-925d31031d3e","year":2021},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.346065Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:2bc50a9c3128ff9df42940719631f73b76d4459be595732183a9f0de99f67de4","observation_id":"3c712501-bbdd-4038-8436-0e2a866ae0be","resolution":{"observed_at":"2026-08-06T19:31:46.568754Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.548412Z","title":"Ivanisvili, Convolution estimates and the number of disjoint partitions, The Electronic Journal of Combinatorics, Volume 24, Issue 2 (2017), Paper P2.43","venue":null,"work_id":"ff0942bf-f4de-4a0e-8c91-3d29b849412a","year":2017},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.350482Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:2c66eec0f7ae7d69beb4a273cd571a3c452bd44fb2bdfa503974dc6fb664350f","observation_id":"d9cbea1d-2730-48a7-a48b-a7343063bbe6","resolution":{"observed_at":"2026-08-06T19:31:46.553182Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2206.01591","last_updated":"2023-06-05T21:40:17Z","snapshot_observed_at":"2026-08-05T16:38:36.860870Z","submitted_at":"2022-06-03T14:21:21Z","title":"On binomial sums, additive energies, and lazy random walks","version":5},"cited_work":{"arxiv_id":"2206.01591","doi":null,"metadata_source":"pith","pith_arxiv_id":"2206.01591","snapshot_observed_at":"2026-08-06T19:31:46.425100Z","title":"On binomial sums, additive energies, and lazy random walks","venue":"math.CA","work_id":"bec2ccfa-ccab-42d0-bbb8-52afde1503ee","year":2022},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.354760Z"},"links":{"cited_paper":"/paper/2206.01591","citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:cb135e5c3bc3f7bf4642eabc8a4624902b28440734d7a74a2fca319039b681d0","observation_id":"35d40614-5fd1-48be-b5f1-e8bc250144f4","resolution":{"observed_at":"2026-08-06T19:31:46.431443Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.533074Z","title":"Kane and T","venue":null,"work_id":"426ee022-9ab5-45e7-b4d0-403973cf53bd","year":2017},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.359486Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:8d461f5d9c65c5513d9b39c6a1f59a53b7759983812e0bc279ec4f299e376ce0","observation_id":"27c2f468-0fcf-4ced-92c9-993d5a0f2aed","resolution":{"observed_at":"2026-08-06T19:31:46.537984Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00493-021-4547-0","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:46.399900Z","title":"Matolcsi, I","venue":null,"work_id":"a4dd2d31-cd08-43b0-8539-77fea704fc01","year":2022},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.363775Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:9b3b34e0478d148cf593a37e8a24fbd6943f860c6208eed36ba6d09133387db9","observation_id":"063f5ad5-c962-4e7f-87b1-d21bc206fb6f","resolution":{"observed_at":"2026-08-06T19:31:46.406050Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:31:46.515697Z","title":null,"venue":null,"work_id":"8d7956b3-70e0-40bf-b2fa-6ce4bfb93f95","year":2006},"citing_paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-06T19:31:46.368142Z"},"links":{"citing_paper":"/paper/2507.06115"},"observation_digest":"sha256:469a6584d5bdebf991679611beea50c15dc6e6c1657c06ced1f7aa71fa536ced","observation_id":"6f5a5950-8000-497b-9555-311295133225","resolution":{"observed_at":"2026-08-06T19:31:46.521507Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.06115","last_updated":"2025-07-08T15:58:18Z","latest_version":1,"primary_category":"math.CA","snapshot_observed_at":"2026-08-06T19:08:22.043305Z","submitted_at":"2025-07-08T15:58:18Z","title":"Optimal Young's convolutions inequality and its reverse form on the hypercube"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":5,"verified_fuzzy":15},"total_outbound_references":23},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 3 inbound Pith citation observations for arXiv:2507.06115."}