diff --git a/experiments/KRYLOV_WINDOW_HYPOTHESIS_2026-09-16.md b/experiments/KRYLOV_WINDOW_HYPOTHESIS_2026-09-16.md
new file mode 100644
index 0000000..e82bcdb
--- /dev/null
+++ b/experiments/KRYLOV_WINDOW_HYPOTHESIS_2026-09-16.md
@@ -0,0 +1,39 @@
+# Larger Krylov window
+
+This branch changes only the sandbox example's existing FGMRES restart setting
+from 40 to 160. It adds no public API and does not change the general backend
+default. The warm-start safeguard is a separate hypothesis and branch.
+
+## Matched evidence
+
+The common diagnostic executable at commit `9bd4af6` ran n=1, K=2/pi, M=1,
+J=0.05, with no central-density constraint, on the unchanged `sandbox.smesh`.
+Both runs used nonlinear rtol=1e-8, atol=0, linear tolerance=0.03, and at most
+200 linear iterations. Only the restart window differed.
+
+| Result | Restart 40 | Restart 160 |
+| --- | ---: | ---: |
+| Accepted full Newton steps | 5 | 7 |
+| Final normalized residual | 6.03609e-9 | 3.38036e-11 |
+| Strict convergence | No: sixth linear solve fails | Yes |
+| Total linear iterations, including failed attempt | 370 | 292 |
+| Largest final virial error among four definitions, q=14/18 | 3.73183e-7 | 3.73466e-7 |
+
+The first four steps coincide exactly. The larger window first changes the
+fifth linear solve. This is live nonlinear evidence, supplemented by the earlier
+frozen-system comparisons. Single wall-time samples (291 versus 272 seconds,
+including physical diagnostics) do not establish a general speedup.
+
+## Limits and validation
+
+The larger window requires more Krylov storage. It is a useful example setting,
+not a universal default: n=1.5 without the central constraint still stalls with
+this window, and eventually fails a linear gate. The n=3 frozen control also
+needs a stronger numerical treatment. This change does not establish a fraction
+of critical rotation and does not alter the convergence or virial tolerances.
+
+Removing the n=1 example's central-density constraint is independently supported
+on `research/central-constraint-20260916`; combine the two changes for the intended
+example. Compilation and a nonrotating run of the combined example are pending.
+Raw results and exact build/mesh/executable provenance are retained in the
+workspace's `diagnostics/numerical_campaign_2026-09-16/controls` directory.
diff --git a/sandbox.cpp b/sandbox.cpp
index 437ec51..7844273 100644
--- a/sandbox.cpp
+++ b/sandbox.cpp
@@ -122,7 +122,7 @@ int main(
         );
 
         auto preconditioner = preconditioning::makePreconditioner();
-        auto linearSolver   = solver::linear::FGMRES({.restartLength = 40, .printLevel = 1});
+        auto linearSolver   = solver::linear::FGMRES({.restartLength = 160, .printLevel = 1});
         const auto contextStart = std::chrono::steady_clock::now();
         // This density initializes the seed; the n=1 equilibrium is free to change it.
         auto context             = solver::makeContext(