Record control outcomes and specify a matched rotating-state benchmark

experiments/COUPLED_CONVERGENCE_STUDY_2026-09-19.md

@@ -42,6 +42,53 @@ hashes. Initial evidence directory:
 Results and any adaptive extensions will be recorded below before finalizing
 the study. Defaults and the physics-facing API are unchanged.
 
+## Initial completed controls
+
+The following scalar observations precede the final retained-artifact audit.
+All three cases exhaust twelve updates and every reported full linear solve
+passes its requested relative true-residual gate.
+
+| Case | Final normalized residual | Newton seconds | Total Krylov iterations | Energy / force h-pressure virials, q18 |
+|---|---:|---:|---:|---:|
+| n=2, J=0, eta=.03 | 8.85263e-6 | 742.74 | 1009 | 3.25447e-7 / 2.24560e-6 |
+| n=3, J=0, eta=.03 | 8.24392e-4 | 499.89 | 429 | 9.46671e-5 / 6.20929e-5 |
+| n=3, J=0, eta=.003 | 5.50731e-4 | 734.09 | 821 | 2.23846e-4 / 1.98912e-4 |
+
+Initial norms are 3.81795e-4 and 3.09931e-3 respectively; actual stopping
+thresholds are 3.81795e-12 and 3.09931e-11. q14/q18 differences in all six
+virial errors are below 8e-14 absolute. This quadrature agreement does not
+establish a physical equilibrium or pointwise accuracy.
+
+After n=2's second update, ten more updates reduce its residual only 2.112%.
+Its last alpha is 1/256. Every rejection is insufficient residual decrease;
+the final squared norm is 94.770% Poisson and 4.076% gravity-gradient error.
+This is a useful globally balanced intermediate model, but a stalled
+nonlinear solve and not an established discrete residual floor.
+
+For n=3, the tighter tolerance lowers the endpoint residual by 33.20%, but
+requires 46.85% more Newton time and 91.38% more Krylov iterations. It follows
+a different nonlinear trajectory, so these are equal-update-budget outcomes,
+not a matched-state preconditioner comparison. The control's final squared
+norm is 79.927% Poisson, 13.854% gravity gradient, and 6.144% closure. The
+tighter case instead has 71.329% closure and 25.876% Poisson. Its smaller
+residual coexists with worse virials and a smaller final alpha (1/32 versus
+1/4). Linear accuracy alone has not resolved the nonlinear obstruction.
+
+Both n=3 runs continue below their earlier eight-update endpoints; those
+endpoints were not demonstrated floors. Their final unbordered norms exceed
+bordered norms by only .180% and .229%, although the artificial central force
+still needs to be reported and may matter locally.
+
+When the full Jacobian is the derivative of the prepared residual, a direction
+with ||J p + F|| <= eta ||F|| obeys
+
+    F dot J p <= -(1-eta) ||F||^2.
+
+Thus both eta=.03 and .003 give strict infinitesimal descent. Small accepted
+steps despite a passing linear gate motivate measurements of finite-step
+curvature, preparation validity and tangent consistency; a faster inner solve
+alone need not remove that limitation.
+
 ## Adaptive follow-up, specified before execution
 
 The completed n=2 control has energy/force enthalpy virials 3.25e-7/2.25e-6
@@ -70,6 +117,12 @@ Test the combined candidate at n=3 update seven separately. Each benchmark
 also runs a fresh default inverse on the identical RHS and physical Jacobian.
 Setup costs and internal Jacobian applications belong to the comparison.
 
+The rotating n=1,J=.1 control initially takes a full update, then its accepted
+alpha falls below .001 by update six, with pressure-preparation rejections.
+Add a combined inverse benchmark at its update-seven capture and eta=.003,
+including the same raw trial grid. This separates the rotation obstruction
+from n=2's gravity-dominated merit rejection without changing admissibility.
+
 The small Schur block contains all 25 surface parameters and every generated
 scalar. Its field inverse is the unbordered structure inverse; restricting an
 already scalar-bordered inverse could spuriously constrain the field solve.

experiments/convergence_linear_cases_2026-09-19.json

@@ -160,5 +160,38 @@
       "--allow-unconverged-restart",
       "--benchmark-trials"
     ]
+  },
+  {
+    "id": "n1_rotating_late_combined",
+    "arguments": [
+      "--index",
+      "1",
+      "--angular-momentum",
+      "0.1",
+      "--surface-prescription",
+      "harmonics",
+      "--surface-degree",
+      "4",
+      "--restart",
+      "160",
+      "--max-linear",
+      "300",
+      "--rtol",
+      "0",
+      "--atol",
+      "1e-12",
+      "--max-newton",
+      "0",
+      "--linear-tol",
+      ".003",
+      "--preconditioner-probe",
+      "--preconditioner-variant",
+      "gravity-schur-surface-border-schur",
+      "--restart-snapshot",
+      "../../diagnostics/coupled_convergence_2026-09-19/screen_v1/n1_J0p1/capture_7/physical_base.txt",
+      "--allow-unconverged-restart",
+      "--no-central",
+      "--benchmark-trials"
+    ]
   }
 ]