Record audited nonlinear controls and interior diagnostics

experiments/COUPLED_CONVERGENCE_STUDY_2026-09-19.md

@@ -42,20 +42,26 @@ 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
+## Completed nonlinear controls
 
-The following scalar observations precede the final retained-artifact audit.
+The retained-artifact audit passes all five screen cases: provenance, complete
-All three cases exhaust twelve updates and every reported full linear solve
+output hashes, block accounting, reported full linear gates and independently
-passes its requested relative true-residual gate.
+recomputed virial accounting. Every case exhausts twelve updates; none meets
+its nonlinear stopping threshold. The audit checks the production linear
+reports, not a fresh FEM application of every live Newton Jacobian.
 
 | 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 |
+| n=1, J=.1, eta=.03 | 5.83293e-3 | 310.43 | 226 | 3.23282e-4 / 3.36216e-4 |
+| n=1.5, J=.1, eta=.03 | 7.22567e-5 | 550.70 | 717 | 5.10711e-5 / 5.20697e-5 |
 
-Initial norms are 3.81795e-4 and 3.09931e-3 respectively; actual stopping
+The nonrotating initial norms are 3.81795e-4 and 3.09931e-3 respectively;
-thresholds are 3.81795e-12 and 3.09931e-11. q14/q18 differences in all six
+actual stopping thresholds are 3.81795e-12 and 3.09931e-11. The rotating
+initial norms are .0857344 and .139488, with thresholds 8.57344e-10 and
+1.39488e-9. q14/q18 differences in all six nonrotating h-pressure
 virial errors are below 8e-14 absolute. This quadrature agreement does not
 establish a physical equilibrium or pointwise accuracy.
 
@@ -89,6 +95,50 @@ 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.
 
+The rotating n=1 case ends at alpha=1/65536, with 26 pressure-preparation
+rejections and no metric rejections. The n=1.5 case has seven of each and
+ends at alpha=1/64. Its first eight updates reach 7.60346e-5; four further
+updates give only a 4.97% reduction. These are distinct obstructions, not
+evidence that every difficult model is failing its linear solve.
+
+### Interior checks and residual location
+
+The n=2 endpoint has positive sampled density (minimum 2.93907e-4), and
+its density-pressure energy/force virials also pass: 2.49026e-6/5.70105e-7.
+It supplies a stalled control independent of a sampled negative-density
+obstruction. This is not a pointwise positivity certificate.
+
+| Case | EOS density RMS / sampled density scale | Bernoulli RMS / sampled h scale | Hydrostatic-gradient RMS | Minimum sampled map determinant |
+|---|---:|---:|---:|---:|
+| n=2, J=0 | 1.87717e-4 | 2.80766e-4 | .0264341 | .982421 |
+| n=3, eta=.03 | 3.52140e-4 | 2.30017e-3 | .398054 | .999838 |
+| n=3, eta=.003 | 3.69501e-4 | 2.65289e-3 | .479759 | .943956 |
+| n=1, J=.1 | 1.26849e-3 | 2.21774e-3 | .104394 | .938419 |
+| n=1.5, J=.1 | 1.69365e-4 | 6.32866e-4 | .0366157 | .955286 |
+
+These q18 volume observations are sampled error measures, not mesh-convergence
+results. Gradient RMS is in the diagnostic's G=M_reference=R_reference=1
+units; it is not a relative percentage. Good virials do not remove these
+interior defects. Density-pressure virials are undefined for the two rotating
+screens because sampled density is negative; their h-pressure virials remain
+defined and are reported without modifying either independent field.
+
+A separate source-derived row map locates the saved normalized Poisson
+residual: 84.437% of its squared norm is stellar at n=2 capture seven,
+99.9768% for n=3 control, 99.9995% for n=3 tight, and over 99% for both
+rotating captures. The n=2 envelope alone contributes 70.602%. The stalled
+norm cannot be explained solely by exterior rows. These are algebraic
+residual-row shares, not pointwise div(g)-4*pi*rho errors. The mapping and
+dependency/provenance caveats are recorded in the evidence directory's
+`poisson_regions/README.md`.
+
+Saved nonrotating surface directions also do not support translation as their
+dominant component: at capture seven, l=1 contributes only .0086253%,
+.0000077557% and .000103632% of squared normalized surface-direction norm for
+n=2, n=3 control and n=3 tight. Degrees zero and four dominate. Physical scale
+recovery and the small COM drift are documented in `translation_check/README.md`;
+this does not prove that the Jacobian has no weak translational response.
+
 ## Adaptive follow-up, specified before execution
 
 The completed n=2 control has energy/force enthalpy virials 3.25e-7/2.25e-6
@@ -157,6 +207,32 @@ formula, but the sparse grid is not a replay of its adaptive line search.
 Remainder scalars are direct FEM observations; saved Jp, RHS and correction
 allow independent verification of the linear defect and merit slope.
 
+## Completed matched gravity-path test
+
+The retained-artifact audit passes both six-update restarts. Both begin at
+F=9.0134584624e-6 and every reported full linear gate passes. Raw Newton ends
+at 8.8762959137e-6 in 449.196 Newton seconds; gravity-path Newton ends at
+8.6749533568e-6 in 887.543 seconds. The latter endpoint is only 2.2683% lower
+at 1.97585 times solver cost. Neither reaches the shared 1e-12 target.
+
+The first gravity-path update accepts alpha=1/16 versus raw's 1/128, giving
+90.1683% of its eventual six-step improvement immediately. Its final alpha
+is 1/2048, eight times smaller than raw's final 1/256. All rejections are
+metric failures, not pressure failures. Preparation time rises 3.72673-fold;
+22 auxiliary gravity solves use 866 iterations. Their final prepared defect
+passes its own threshold, so the stalled full solve must not be described as
+a failed auxiliary gravity correction.
+
+The final gravity-path squared norm remains 85.0361% Poisson, with larger
+hydrostatic (6.4051%) and mass (1.8661%) shares than raw. Its q18 h-pressure
+energy/force virials are 7.29743e-7/1.22487e-6; raw's are
+3.27166e-7/2.25835e-6. Both meet the global milestone while local nonlinear
+progress remains poor. There is no demonstrated durable cure or speedup,
+and no default strategy change is warranted by this pair.
+
+Full control tables, timing scopes and audit hashes are retained in the
+evidence directory's `CONTROL_RESULTS.md` and `CONTROL_RESULTS.json`.
+
 ## Compatibility of the rotating n=3 target
 
 This is a separate physical-model issue, not an explanation of the measured