R8-a harness: RTX_E3FSI_RESTORE_CHECK (re-run the accepted candidate from the snapshot)

Co-Authored-By: Claude Opus 5.5 (1M context) <[email protected]>

crates/specialized/rtx-fsi/tests/fsi2_embedded3.rs

@@ -247,6 +247,7 @@ fn fsi2_on_embedded3() {
     let speed = env_f("RTX_E3FSI_SPEED", 3.0);
     let trace = env_f("RTX_E3FSI_TRACE", 0.0) as usize;
     let csv_path = std::env::var("RTX_E3FSI_CSV").ok();
+    let restore_check = env_f("RTX_E3FSI_RESTORE_CHECK", 0.0) as usize;
     let case = FSI2;
 
     let mesh = flag_mesh(35, 2);
@@ -521,7 +522,28 @@ fn fsi2_on_embedded3() {
         let acceptable = (stall_accept * tol).max(0.1 * increment);
         let outcome = Subiterated::aitken(max_subit, tol)
             .unwrap()
-            .solve(&predicted, pass);
+            .solve(&predicted, &pass);
+        // `RTX_E3FSI_RESTORE_CHECK=N`: on the first N steps, the accepted
+        // candidate re-run from the snapshot (the restore's repeatability).
+        if step < restore_check && outcome.is_ok() {
+            let (cand, tot_a, out_a) = {
+                let l = latest.borrow();
+                let l = l.as_ref().expect("a pass ran");
+                (l.3.clone(), l.4, extract(&l.0))
+            };
+            let out_b = pass(&cand);
+            let tot_b = latest.borrow().as_ref().expect("re-run").4;
+            let dout: f64 = out_a
+                .iter()
+                .zip(&out_b)
+                .map(|(a, b)| (a - b).powi(2))
+                .sum::<f64>()
+                .sqrt();
+            println!(
+                "  RESTORE CHECK step {step}: load a ({:+.9e}, {:+.9e}) b ({:+.9e}, {:+.9e}), |Δ structure output| {dout:.3e}",
+                tot_a[0], tot_a[1], tot_b[0], tot_b[1]
+            );
+        }
         let (iters, dres) = match outcome {
             Ok(c) => (c.iterations, c.residual),
             Err(