diff --git a/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/mod.rs b/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/mod.rs
index 1abb7f6..4d66ad2 100644
--- a/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/mod.rs
+++ b/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/mod.rs
@@ -8,7 +8,7 @@
 pub mod device;
 #[cfg(feature = "cuda")]
 pub mod device_cg;
-mod export;
+pub mod export;
 mod hierarchy;
 mod pcg;
 mod problem;
diff --git a/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/step/projection.rs b/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/step/projection.rs
index 71d653c..0a76ac5 100644
--- a/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/step/projection.rs
+++ b/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/step/projection.rs
@@ -12,7 +12,7 @@ impl Solver {
     /// faces): coefficient `dt · A / δ` across every fluid interior face,
     /// zero across prescribed ones, the outlet's Dirichlet half a cell out
     /// as `extra_diag`; the right-hand side left zero.
-    pub(crate) fn poisson_operator(&self, g: Grid, dt: f64) -> Problem {
+    pub fn poisson_operator(&self, g: Grid, dt: f64) -> Problem {
         let (nx, ny, nz, dx, dy, dz) = (g.nx, g.ny, g.nz, g.dx, g.dy, g.dz);
         let b = self.params.boundaries;
         let outlet = Side::PressureOutlet;
diff --git a/crates/specialized/rtx-cfd/tests/embedded3_flag_geometry.rs b/crates/specialized/rtx-cfd/tests/embedded3_flag_geometry.rs
index b67ca35..87864cd 100644
--- a/crates/specialized/rtx-cfd/tests/embedded3_flag_geometry.rs
+++ b/crates/specialized/rtx-cfd/tests/embedded3_flag_geometry.rs
@@ -197,3 +197,55 @@ fn narrow_band_is_bit_identical_and_fast() {
     );
     assert!(vol_same);
 }
+
+/// The per-step operator cost at ny 62 (host side of the device CG's
+/// rebuild: the problem, the fine level, the components, the hierarchy
+/// export) — S2-2b-ii's target.
+#[test]
+#[ignore = "profile: the operator export at ny 62 (seconds)"]
+fn operator_export_profile_at_ny_62() {
+    use rtx_cfd::solvers::incompressible::embedded3::poisson::export::export_hierarchy;
+    use rtx_cfd::solvers::incompressible::embedded3::{
+        Field, Fluid, Parameters, Solver, WallScheme,
+    };
+    use rtx_cfd::solvers::incompressible::{ConvectionScheme, MultigridParameters};
+    let ny = 62;
+    let h = H / ny as f64;
+    let nx = (2.5 / h).round() as usize;
+    let g = Grid::cubic(nx, ny, ny, h);
+    let cyl = |x: f64, y: f64| ((x - 0.2_f64).powi(2) + (y - 0.2_f64).powi(2)).sqrt() - 0.05;
+    let body = Body::from_sdf(move |x, y, z, _t| cyl(x, y).min(flag_3d(x, y, z, 0.3, h)));
+    let mut solver = Solver::new(
+        Fluid {
+            density: 1000.0,
+            viscosity: 1.0,
+            reference_velocity: 1.0,
+            reference_length: 0.1,
+        },
+        Parameters {
+            wall_scheme: WallScheme::CutCell,
+            convection_scheme: ConvectionScheme::TvdVanAlbada,
+            boundaries: Boundaries {
+                x1: Side::PressureOutlet,
+                ..Boundaries::default()
+            },
+            ..Parameters::default()
+        },
+    );
+    solver.set_body(body);
+    let mut f = Field::new(g);
+    let t0 = std::time::Instant::now();
+    solver.initialize(&mut f);
+    let t_init = t0.elapsed().as_secs_f64();
+    let t1 = std::time::Instant::now();
+    let problem = solver.poisson_operator(g, 1e-3);
+    let t_op = t1.elapsed().as_secs_f64();
+    let t2 = std::time::Instant::now();
+    let levels = export_hierarchy(&problem, &MultigridParameters::default());
+    let t_exp = t2.elapsed().as_secs_f64();
+    println!(
+        "  ny 62 operator: initialize (mask + impose) {t_init:.2} s, poisson_operator {t_op:.2} s, export_hierarchy {t_exp:.2} s ({} levels, {} links)",
+        levels.len(),
+        problem.links.len()
+    );
+}