{"paper":{"title":"A no-go theorem and its resolution for the discrete compressible barotropic Navier--Stokes equations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.AP","authors_text":"Peter Korn","submitted_at":"2026-05-15T18:56:40Z","abstract_excerpt":"The compressible barotropic Navier--Stokes equations in vector-invariant form preserve the vorticity structure of the system and underlie modern atmospheric and ocean dynamical cores, yet no PDE theory has been developed for the compressible discrete system in this form.\n  On a Delaunay--Voronoi mesh we prove via discrete exterior calculus, that every density-independent mass matrix with integration-by-parts-consistent divergence carries a sharp $\\OO(h^2)$ energy residual of indeterminate sign that no operator choice can eliminate. This no-go theorem covers A-, B-, C-, D-, and quasi-B-grid sta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.16554","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/2605.16554/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-19T19:21:56.893246Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.631486Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"4fcb6771a2a687a7e326608eaf5a4663b4c91464ba9211bb624f7d5aa6349fde"},"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"}