{"paper":{"title":"Further Improvements to the Lower Bound for an Autoconvolution Inequality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Aaron Jaech, Alan Joseph","submitted_at":"2025-08-04T18:18:20Z","abstract_excerpt":"We construct a nonnegative step function comprising 2,399 equally spaced intervals such that \\[\n  \\frac{\\|f * f\\|_{L^{2}(\\mathbb{R})}^{2}}{\\|f * f\\|_{L^{\\infty}(\\mathbb{R})}\\,\\|f * f\\|_{L^{1}(\\mathbb{R})}}\n  \\;\\ge\\;\n  .926529. \\] Using a 4x upsampling procedure on this 559-interval optimizer, we further increase the bound to $.94136$, closing roughly 40\\% of the gap between the previous best bound (.901562 on 575 intervals) and the trivial upper limit of 1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.02803","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.02803/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}