{"paper":{"title":"Exact Lagrangian Realization and Robust Strain Sensing in Incompressible Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hao Huang","submitted_at":"2026-07-29T13:26:40Z","abstract_excerpt":"We prove that the full group \\(\\SL(3,\\R)\\) occurs as the set of one-particle deformation gradients of periodic, unforced, single-shell solutions of both the three-dimensional Euler and Navier--Stokes equations. More precisely, given a particle label \\(p\\in\\T^3\\), a time \\(T>0\\), and \\(F_*\\in\\SL(3,\\R)\\), every sufficiently large odd integer \\(N\\) admits a real-analytic curl eigenfield \\(W_N\\) with \\(\\operatorname{curl}W_N=NW_N\\). With an explicit scalar amplitude, \\(W_N\\) yields a steady Euler solution; with an explicit exponentially decaying amplitude, it yields a Navier--Stokes solution for a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26895","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/2607.26895/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"}