{"paper":{"title":"A convexity-type invariant for the critical coagulation--fragmentation Hamilton--Jacobi equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Truong-Son P. Van","submitted_at":"2026-07-02T15:11:24Z","abstract_excerpt":"We study the critical coagulation--fragmentation equation with multiplicative coagulation kernel \\(a(s,\\hat s)=s\\hat s\\) and constant fragmentation kernel \\(b(s,\\hat s)=1\\). Under the Bernstein transform, mass-conserving solutions correspond to solutions of a singular Hamilton--Jacobi equation studied by Tran and Van (Comm.Pure Appl.Math.75 (2022), no.6, 1292--1331). Through this correspondence they proved that mass-conserving solutions are unique on the full critical range \\(0<m\\le1\\), but could establish their existence only for \\(0<m<\\tfrac12\\). We identify a one-sided, convexity-type invar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02293","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/2607.02293/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"}