embedded3 PERF-3 P1-4 (steps 1–3 + d): the band-persistent operator — CutGeometry marks re-evaluated corners; Mask::changed_cells (touched by either build, dilated by one); Level::patch re-derives the changed rows with the constructor's formulas on the kept level; the fine export patched likewise with the parent map as a parallel per-cell map; components plane by plane with a small union across planes; Problem::link_map (sparse) replaces the per-cell link lists on the per-step path; RTX_E3_BAND_CHECK=1 compares against full rebuilds (passed on the slab) — slab CSV byte-identical at every step, device moving/cg green; ny 124 rebuild block 2,569 → 2,119 ms per step

Co-Authored-By: Claude Fable 5.1 <[email protected]>

crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/cut.rs

@@ -33,6 +33,10 @@ pub struct CutGeometry {
     /// motion, comes within the band; far corners keep a stale value with
     /// the right sign, which is all their cells use).
     pub bound: Vec<f64>,
+    /// P1-4: the corners re-evaluated by this build (all of them without a
+    /// narrow band) — a cell whose corners are all untouched has unchanged
+    /// apertures, volume and activity.
+    pub touched: Vec<bool>,
 }
 
 impl CutGeometry {
@@ -64,10 +68,12 @@ impl CutGeometry {
         use rayon::prelude::*;
         let mut phi = vec![0.0; n_nodes];
         let mut bound = vec![0.0; n_nodes];
+        let mut touched = vec![true; n_nodes];
         phi.par_iter_mut()
             .zip(bound.par_iter_mut())
+            .zip(touched.par_iter_mut())
             .enumerate()
-            .for_each(|(n, (phi_n, bound_n))| {
+            .for_each(|(n, ((phi_n, bound_n), touched_n))| {
                 let (k, j, i) = (
                     n / ((ny + 1) * (nx + 1)),
                     (n / (nx + 1)) % (ny + 1),
@@ -78,6 +84,7 @@ impl CutGeometry {
                     if b > band {
                         *phi_n = p.phi[n];
                         *bound_n = b;
+                        *touched_n = false;
                         return;
                     }
                 }
@@ -196,9 +203,34 @@ impl CutGeometry {
             d_v,
             d_w,
             bound,
+            touched,
         }
     }
 
+    /// The cells with a touched corner (P1-4).
+    #[must_use]
+    pub fn touched_cells(&self) -> Vec<bool> {
+        use rayon::prelude::*;
+        let g = self.grid;
+        let (nx, ny) = (g.nx, g.ny);
+        (0..g.cells())
+            .into_par_iter()
+            .map(|idx| {
+                let (k, j, i) = g.kji(idx);
+                let mut t = false;
+                for dk in 0..2 {
+                    for dj in 0..2 {
+                        for di in 0..2 {
+                            t |= self.touched[Self::node(g, k + dk, j + dj, i + di)];
+                        }
+                    }
+                }
+                let _ = (nx, ny);
+                t
+            })
+            .collect()
+    }
+
     /// φ at the corner `(k, j, i)` of the corner lattice.
     #[inline]
     #[must_use]