MeanField/experiments/COUPLED_TRIAL_CORRECTION_2026-09-18.md

Bounded coupled second-order trial correction

Branch research/coupled-trial-correction-20260918, based on the completed nonlinear obstruction investigation at 2944dd5. The configured worktree retains its existing name, worktrees/preconditioner-improvement, so that build reuse does not disturb the preceding branch or immutable executables.

Hypothesis

At the recorded n = 1.5, J = 0 endpoint, tenfold tighter linear accuracy did not improve the useful trial range. The full directional derivative was consistent with the prepared residual. Gravity-only correction reduced the remainder norm but increased its adverse projection through hydrostatic, EOS and surface balance. The next hypothesis is that correcting the entire trial remainder can preserve the intended Newton response over larger steps.

For the captured base residual F0 and verified Newton direction p, preserve L(alpha) = F0 + alpha J0 p. At a prepared candidate y, solve

J(y) c = -(F(y) - L(alpha)),

then prepare and evaluate y+c. All equations, normalization factors and ordinary full-residual acceptance thresholds remain unchanged. A separate auxiliary true-defect check is required; the base Newton report is never replaced by a correction report. The locally second-order argument requires a bounded inverse, which is not assumed to hold uniformly in this model.

Implementation contracts

• A third, defaulted compile-time trial-path policy composes with the established enthalpy and gravity policies. Existing two-policy recipes retain their types and behavior. The new policy is incompatible with the eliminated-gravity path until a corresponding reduced-manifold contract is designed; unsupported combinations fail at compile time.
• The auxiliary solve has its own backend, a finite iteration budget and an independent application of the complete candidate Jacobian. Its initial options are relative tolerance 0.03, absolute tolerance 1e-14, at most160 iterations and restart160.
• Limit the correction norm to alpha||p|| by default. The initial work limit is one actual auxiliary solve per Newton iteration, and one solve per selected candidate. Runtime expert controls change these bounds explicitly.
• Select correction only after a prepared candidate fails the existing acceptance predicate. Reuse the exact configured metric for selecting between original and corrected candidates. An already acceptable step incurs no coupled solve; an unprepared candidate cannot invoke one.
• Recheck the same selected admissibility policy and actual geometry after correction. Retain the original candidate if the auxiliary solve fails, the norm cap rejects it, preparation/admissibility fails, or its metric worsens. Restoring a fallback includes fresh operator preparation, not merely copying state vectors.
• The exported numerical core and trial transaction are shared by production and frozen diagnostics. The physics-facing model API is unchanged.

Initial screen

The committed coupled_trial_screen_2026-09-18.json records complete controls and immutable input paths. All heavy builds and numerical cases run serially. Evidence is written to diagnostics/coupled_trial_2026-09-18/ in the task workspace; individual campaign directories are immutable.

Use the previously saved late eta0.03 direction, independently reapplying the full Jacobian at the restored base before using it. This avoids conflating a new linear solve with the new trial map. Test both raw and gravity-corrected starting candidates at alpha1/16,1/64,1/256,1/1024. The middle two previously prepared but failed the merit test. The largest failed pressure preparation; the smallest already decreased the residual and must not trigger correction.

The seed control uses its saved eta0.03 direction and alpha1 with the gravity-corrected path. Its candidate already passes; it should preserve that result without auxiliary coupled work. Each frozen alpha is an independent trial with a fresh per-iteration budget, not a simulated live line search.

Record inputs/factors/layout, F0,p,J0p, the actual auxiliary RHS and J(y)c, candidate and returned state/residual vectors, true defects, norm-cap gates, selection/fallback decisions, restoration invariants and complete work. Useful frozen progress is a prerequisite for a bounded nonlinear campaign. Any accepted model must also be checked for virial balance and internal admissibility; a lower residual alone is insufficient.

Implementation and test results are pending.