Specify matched live field-feedback trial for rotating n3 family

experiments/COUPLED_CONVERGENCE_STUDY_2026-09-19.md

@@ -230,6 +230,25 @@ isolated on `research/gravity-coupling-ablation-20260919`; the original n=3
 specification branch is retained. These controls add no new nonlinear runs
 or trial grids.
 
+## Live n=3 field-feedback follow-up, specified before execution
+
+At the completed frozen n=3 control capture, the existing
+`stellar-ldu-gravity-schur` policy reduces 99 to 41 Krylov iterations and
+53.190 to 35.200 setup/solve/check seconds. Both eta=.003 gates pass.
+Its largest sampled acceptable alpha remains 1/4, with F_trial/F_base
+.674223 versus baseline's .702686; its full-step ratio is 2.77979 versus
+7.42157. This is promising frozen evidence, not a live speedup or proof
+that the policy transfers to rotation or removal of the central border.
+
+Before executing the rotating compatible-family control, pair it with the
+same ten-update case using this field-feedback inverse. Only the inverse
+changes: both retain n=3, J=.035, K factor=.99, no central phase, all-m L4,
+the gravity-curvature trial path, ordinary live eta=.03 and target1e-12.
+The forcing tolerance differs from the frozen screen, so this is a practical
+generalization test rather than a replay of its direction. The case is added
+to `n3_compatible_family_cases_2026-09-19.json` on isolated branch
+`research/n3-live-field-feedback-20260919`. No surface-order change is made.
+
 ## Completed matched gravity-path test
 
 The retained-artifact audit passes both six-update restarts. Both begin at

experiments/N3_COMPATIBLE_FAMILY_2026-09-19.md

@@ -36,6 +36,14 @@ eta=.03 and absolute nonlinear target 1e-12. The necessary beta bound is then
 a fraction of critical rotation. J already breaks the nonrotating n=3
 homology, so this case does not add an extra central-density phase condition.
 
+Before execution, the favorable frozen n=3 field-feedback result motivates
+one matched live companion using `stellar-ldu-gravity-schur`. It changes only
+the inverse and retains the original ten-update budget, eta=.03, trial path
+and physical specifications. The pair is versioned on
+`research/n3-live-field-feedback-20260919`; the main convergence report records
+the preceding evidence. No success or speedup is assumed from the frozen
+eta=.003, J=0, phase-constrained benchmark.
+
 The energy inequality's assumptions are not automatically satisfied by the
 discrete independent rho/P(h) fields, approximate gravity, or a central
 artificial forcing. This compatibility argument selects a sensible continuum

experiments/n3_compatible_family_cases_2026-09-19.json

@@ -35,5 +35,42 @@
       "--preconditioner-variant",
       "gravity-schur"
     ]
+  },
+  {
+    "id": "n3_J0p035_K0p99_ldu",
+    "arguments": [
+      "--index",
+      "3",
+      "--angular-momentum",
+      ".035",
+      "--n3-K-factor",
+      ".99",
+      "--no-central",
+      "--surface-prescription",
+      "harmonics",
+      "--surface-degree",
+      "4",
+      "--max-newton",
+      "10",
+      "--restart",
+      "160",
+      "--max-linear",
+      "300",
+      "--linear-tol",
+      ".03",
+      "--rtol",
+      "0",
+      "--atol",
+      "1e-12",
+      "--model-slices",
+      "--slice-subdivisions",
+      "4",
+      "--capture-iterations",
+      "0,3,7",
+      "--strategy",
+      "curvature",
+      "--preconditioner-variant",
+      "stellar-ldu-gravity-schur"
+    ]
   }
 ]