Record matched preconditioner controls and candidate rationale

experiments/PRECONDITIONER_IMPROVEMENT_2026-09-18.md

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+# Preconditioner improvement: matched frozen Newton systems
+
+This experiment changes preconditioning only. The complete Newton Jacobian,
+normalization, physical residual, mesh, and linear acceptance gate are held fixed.
+The date in branch and artifact names is an experiment identifier; provenance
+files contain the actual UTC execution times.
+
+## Reproduction and scope
+
+Integration branch: `research/preconditioner-benchmarks-20260918`, based on
+`10adf7e`. Hypotheses are retained separately on
+`research/gravity-consistent-schur-20260918`,
+`research/preconditioner-cached-cross-actions-20260918`, and
+`research/coupled-shape-coarse-20260918`.
+
+The experiment workspace is
+`/Users/tboudreaux/.codex/.chatgpt-projects/g-p-6a6b3f2194ec8191bebcd59075897f1d`.
+Evidence is under `diagnostics/preconditioner_improvement_2026-09-18` there.
+Each campaign retains its clean source commit, build configuration, copied
+executable and hash, mesh hash, exact commands, input/output hashes, and logs.
+Runs are serial, without overlapping builds or FEM jobs during timing.
+
+Frozen comparisons start FGMRES from zero on the same saved state and right-hand
+side. Each role constructs a fresh inverse, including its own specification
+border responses. The restart length is 160, the initial cap is 200 iterations,
+and the required relative full-J true defect is 0.03. The independently applied
+full Jacobian decides acceptance; the Krylov recurrence flag alone does not.
+All accepted/trial state buffers, normalization factors, preparation generation,
+and a deterministic full-J probe must remain unchanged.
+
+Costs include inverse construction, normalized binding, Krylov setup, Krylov
+solve, and full-J verification. Extra diagnostic applications and artifact I/O
+are recorded separately. A speedup to convergence is reported only if both
+methods meet the same true gate. Less work spent on a failed solve is not a
+time-to-convergence improvement. A frozen linear pass is not nonlinear or
+physical convergence.
+
+## Existing two-way coupling: negative controls
+
+`screen_v1` uses source `018fc1c`, before the cached cross-action optimization.
+
+| Saved state | Inverse | Iterations | Full-J relative defect | Complete verified cost (s) |
+|---|---|---:|---:|---:|
+| n=1.5, J=0 plateau | independent | 200 | 0.0590170471860 | 87.9302 |
+| same | stellar LDU | 200 | 0.0600668598825 | 599.5473 |
+| n=1, J=0.1 plateau | independent | 200 | 0.0826534298794 | 86.9409 |
+| same | stellar LDU | 200 | 0.0720550396371 | 594.2053 |
+
+All four miss the 0.03 gate. Stellar LDU spends 6.82–6.83 times the total cost;
+it slightly worsens the n=1.5 result and reduces the rotating defect by 12.82%.
+Mean inverse application costs rise from approximately 0.19 s to 2.7 s, while
+full-J actions remain approximately 0.23 s. The uncached gravity-to-material
+force column explains the application-cost anomaly.
+
+Poisson contributes 95.53% of the squared n=1.5 baseline defect and 98.28% with
+stellar LDU. For the rotating state those fractions are 85.00% and 98.10%; LDU
+reduces the gradient-row norm by 94.16% but the Poisson norm by only 6.35%.
+These are global normalized block diagnostics, not proof of an exclusively
+exterior error. No exterior weighting is changed.
+
+The independent artifact audit passes 65 provenance checks and 93 checks per
+case. Both saved states and the normalization data exactly match their producer
+artifacts. The two independent baselines reproduce the earlier failed solves.
+
+## Candidate mechanisms
+
+1. **Prepared cross action.** Reuse the complete prepared gravity force with
+   zero density and displacement directions to apply its gravity-gradient
+   column. This is the same mathematical coupling with cached geometry; it does
+   not strengthen the inverse. See `PRECONDITIONER_CACHED_CROSS_ACTION_2026-09-18.md`.
+2. **Consistent gravity Schur refinement.** Keep the existing AMG action, but
+   apply a fixed number of corrections against `B R B^T`, where `R` is the same
+   mass inverse used in flux recovery. Fixed work preserves linear stationarity
+   for stationary child inverses. Damping does not guarantee contraction; it
+   must earn its additional cost. See `GRAVITY_CONSISTENT_SCHUR_2026-09-18.md`.
+3. **Experimental coupled shape coarse inverse.** Use nine fixed geometric
+   modes, complete their material/gravity responses, and construct a checked
+   low-rank correction to the normalized inverse. Modes do not depend on the
+   Newton right-hand side or previous Krylov results. A rank/overlap guard
+   explicitly falls back to the underlying inverse when the correction cannot
+   be trusted. Coarse setup and storage are counted, and actual FEM subspace
+   identities are independently checked before solving.
+
+Candidate numerical results and execution validation are pending. Defaults
+remain unchanged until measurements support a different choice.