diff --git a/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/device_cg.rs b/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/device_cg.rs
index 10d1665..e307745 100644
--- a/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/device_cg.rs
+++ b/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/device_cg.rs
@@ -243,9 +243,9 @@ impl DeviceCg {
         self.active_host = fine.active.clone();
         self.key = OperatorKey::of(problem, params);
         // The V-cycle's finest level follows the operator (its coarser
-        // levels stay).
-        let levels = export_hierarchy(problem, params);
-        self.vcycle.refresh_fine(&levels[0]);
+        // levels stay): the fine level alone, no hierarchy build.
+        let fine_level = super::export::export_fine(problem);
+        self.vcycle.refresh_fine(&fine_level);
     }
 
     pub fn n_cells(&self) -> usize {
diff --git a/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/export.rs b/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/export.rs
index f6b6f67..a978091 100644
--- a/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/export.rs
+++ b/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/export.rs
@@ -2,7 +2,7 @@
 //! lists (cells, colours, the neighbour arrays, the parent map, the CSR
 //! children) and the seven coefficient arrays.
 
-use super::{Hierarchy, Problem};
+use super::{Hierarchy, Level, Problem};
 use crate::solvers::incompressible::poisson::MultigridParameters;
 
 /// One exported level. `top`/`bot`: the neighbour above/below each cell
@@ -91,6 +91,40 @@ pub fn export_hierarchy(problem: &Problem, params: &MultigridParameters) -> Vec<
         .collect()
 }
 
+/// The finest level alone (its cells, colours, neighbours, the geometric
+/// parent map and coefficients; no children lists — those belong to the
+/// coarse level's restriction and stay with the kept hierarchy): what a
+/// per-step operator refresh needs, without building the hierarchy.
+pub fn export_fine(problem: &Problem) -> LevelExport {
+    let lv = Level::<f32>::new(problem.clone());
+    let (_, coarse_of) = lv.coarsen();
+    let to_u32 = |v: &[usize]| {
+        v.iter()
+            .map(|&i| if i == usize::MAX { u32::MAX } else { i as u32 })
+            .collect::<Vec<u32>>()
+    };
+    LevelExport {
+        nx: lv.problem.nx,
+        ny: lv.problem.ny,
+        nz: lv.problem.nz,
+        cells: to_u32(&lv.cells),
+        red: to_u32(&lv.red),
+        black: to_u32(&lv.black),
+        top: to_u32(&lv.top),
+        bot: to_u32(&lv.bot),
+        coarse_of: to_u32(&coarse_of),
+        children_ptr: Vec::new(),
+        children_idx: Vec::new(),
+        ae: lv.ae,
+        aw: lv.aw,
+        an: lv.an,
+        as_: lv.as_,
+        at: lv.at,
+        ab: lv.ab,
+        ap: lv.ap,
+    }
+}
+
 /// `z = M⁻¹ r` by the host f32 V-cycle: the reference a device V-cycle is measured against.
 pub fn vcycle_f32_reference(
     problem: &Problem,
diff --git a/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/hierarchy.rs b/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/hierarchy.rs
index 814085b..726b39c 100644
--- a/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/hierarchy.rs
+++ b/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/hierarchy.rs
@@ -206,7 +206,7 @@ impl<T: MgScalar> Level<T> {
     }
 
     /// Galerkin coarsening by 2 in every direction (the 2D rule with k).
-    fn coarsen(&self) -> (Problem, Vec<usize>) {
+    pub(crate) fn coarsen(&self) -> (Problem, Vec<usize>) {
         let p = &self.problem;
         let (nx, ny, nz) = (p.nx, p.ny, p.nz);
         let nxc = (nx / 2).max(1);