{"paper":{"title":"Dominated-Convergence Failure in Cosmological Perturbation Theory and a Numerical Foundation for BBGKY+ZA","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Svetlin V. Tassev","submitted_at":"2026-05-27T18:00:04Z","abstract_excerpt":"A common ingredient in cosmological perturbation theory (PT) is the expansion of the dark matter overdensity $\\delta$ in the Lagrangian displacement $s$, which amounts to enforcing mass conservation perturbatively. In Eulerian PT (EPT), that expansion occurs already at the level of the continuity equation; in Lagrangian PT (LPT) it is done in the Poisson equation. We show that the resulting perturbative solutions for $\\delta$ can diverge not because of the expansion in $s$ per se, but because of an exchange of an infinite sum with a Fourier integral that violates the conditions of Lebesgue's d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28943","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/2605.28943/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"}