81 lines
4.4 KiB
Markdown
81 lines
4.4 KiB
Markdown
# Bounded coupled second-order trial correction
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Branch `research/coupled-trial-correction-20260918`, based on the completed
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nonlinear obstruction investigation at `2944dd5`. The configured worktree
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retains its existing name, `worktrees/preconditioner-improvement`, so that
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build reuse does not disturb the preceding branch or immutable executables.
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## Hypothesis
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At the recorded n = 1.5, J = 0 endpoint, tenfold tighter linear accuracy did
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not improve the useful trial range. The full directional derivative was
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consistent with the prepared residual. Gravity-only correction reduced the
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remainder norm but increased its adverse projection through hydrostatic,
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EOS and surface balance. The next hypothesis is that correcting the entire
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trial remainder can preserve the intended Newton response over larger steps.
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For the captured base residual F0 and verified Newton direction p, preserve
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L(alpha) = F0 + alpha J0 p. At a prepared candidate y, solve
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J(y) c = -(F(y) - L(alpha)),
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then prepare and evaluate y+c. All equations, normalization factors and
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ordinary full-residual acceptance thresholds remain unchanged. A separate
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auxiliary true-defect check is required; the base Newton report is never
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replaced by a correction report. The locally second-order argument requires
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a bounded inverse, which is not assumed to hold uniformly in this model.
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## Implementation contracts
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- A third, defaulted compile-time trial-path policy composes with the
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established enthalpy and gravity policies. Existing two-policy recipes
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retain their types and behavior. The new policy is incompatible with the
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eliminated-gravity path until a corresponding reduced-manifold contract
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is designed; unsupported combinations fail at compile time.
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- The auxiliary solve has its own backend, a finite iteration budget and an
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independent application of the complete candidate Jacobian. Its initial
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options are relative tolerance 0.03, absolute tolerance 1e-14, at most160
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iterations and restart160.
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- Limit the correction norm to alpha||p|| by default. The initial work limit
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is one actual auxiliary solve per Newton iteration, and one solve per
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selected candidate. Runtime expert controls change these bounds explicitly.
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- Select correction only after a prepared candidate fails the existing
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acceptance predicate. Reuse the exact configured metric for selecting
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between original and corrected candidates. An already acceptable step
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incurs no coupled solve; an unprepared candidate cannot invoke one.
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- Recheck the same selected admissibility policy and actual geometry after
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correction. Retain the original candidate if the auxiliary solve fails,
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the norm cap rejects it, preparation/admissibility fails, or its metric
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worsens. Restoring a fallback includes fresh operator preparation, not
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merely copying state vectors.
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- The exported numerical core and trial transaction are shared by production
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and frozen diagnostics. The physics-facing model API is unchanged.
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## Initial screen
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The committed `coupled_trial_screen_2026-09-18.json` records complete controls
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and immutable input paths. All heavy builds and numerical cases run serially.
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Evidence is written to `diagnostics/coupled_trial_2026-09-18/` in the task
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workspace; individual campaign directories are immutable.
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Use the previously saved late eta0.03 direction, independently reapplying the
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full Jacobian at the restored base before using it. This avoids conflating a
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new linear solve with the new trial map. Test both raw and gravity-corrected
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starting candidates at alpha1/16,1/64,1/256,1/1024. The middle two previously
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prepared but failed the merit test. The largest failed pressure preparation;
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the smallest already decreased the residual and must not trigger correction.
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The seed control uses its saved eta0.03 direction and alpha1 with the
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gravity-corrected path. Its candidate already passes; it should preserve that
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result without auxiliary coupled work. Each frozen alpha is an independent
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trial with a fresh per-iteration budget, not a simulated live line search.
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Record inputs/factors/layout, F0,p,J0p, the actual auxiliary RHS and J(y)c,
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candidate and returned state/residual vectors, true defects, norm-cap gates,
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selection/fallback decisions, restoration invariants and complete work.
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Useful frozen progress is a prerequisite for a bounded nonlinear campaign.
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Any accepted model must also be checked for virial balance and internal
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admissibility; a lower residual alone is insufficient.
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Implementation and test results are pending.
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