Record measured preconditioner screen and validation limits

experiments/PRECONDITIONER_IMPROVEMENT_2026-09-18.md

@@ -81,5 +81,67 @@ artifacts. The two independent baselines reproduce the earlier failed solves.
    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.
+## First candidate screen
+
+`candidates_v1` uses source `dc8d4b0` and the same n=1.5, J=0 plateau state.
+Every fresh independent control reproduces relative defect 0.059017047186 at
+200 iterations. Complete control costs remain between 87.53 and 88.25 s.
+
+| Candidate | Iterations | Full-J relative defect | Gate | Complete verified cost (s) |
+|---|---:|---:|---|---:|
+| Cached stellar LDU | 200 | 0.0600668598779 | fail | 117.4845 |
+| Consistent gravity Schur, k=1, omega=0.5 | 132 | 0.0292091549685 | pass | 72.3981 |
+| Cached stellar LDU + consistent gravity Schur | 121 | 0.0285619160766 | pass | 84.7104 |
+| Nine-mode coupled shape coarse correction | 200 | 0.0668657989082 | fail | 97.0564 |
+
+The cached LDU is 5.1032 times faster than its old execution path at the same
+iteration cap, while mean inverse application cost drops 8.0425 times. This is
+an execution improvement, not a convergence improvement. Saved inputs and the
+full-J probe agree exactly; the final normalized correction changes by only
+2.7051e-11 relatively. Both LDU solves fail, and the cached version remains
+34.2% more expensive than the independent control on this state.
+
+Gravity refinement is the first candidate to cross the original gate. It lowers
+the Poisson-row defect by 55.4% and the gradient-row defect by 15.0%. The squared
+Poisson share drops from 95.53% to 77.59%; surface and hydrostatic defects grow,
+so the improvement is judged by the verified global norm. Work changes from
+400 to 396 mass-inverse applications, 200 to 264 AMG Schur applications, and
+200 to 132 outer inverse applications. The default has not yet passed the same
+gate, so dividing its failed 88 s attempt by 72.4 s is not a convergence speedup.
+The combined LDU saves another eleven iterations but is 17% slower overall.
+
+The coarse candidate has all nine modes active, minimum overlap lower bound
+0.79465, and no fallback. Its extra construction costs 8.6012 s, including mode
+completion and eighteen setup Jacobian applications; it stores 28,491,680 bytes
+in persistent vectors. The actual FEM subspace check passes. Nevertheless, its
+200-iteration defect worsens by 13.3%. This is a negative numerical result for
+these modes on this state, not evidence about every possible coarse space or
+rapidly rotating model. The prototype remains confined to experiments.
+
+## Validation status
+
+The integrated library and experiment driver compile with the repository's
+Release/ThinLTO configuration. Source dc8d4b0 passes 20 focused serial test cases
+(441,978 assertions), including FEM equivalence, geometry/discretization refresh,
+fixed-work algebra, and coarse inverse tests. Distributed unit and coarse tests
+pass on two ranks (13 cases and 213 assertions per rank).
+
+The broad real-FEM MPI run aborts because the existing METIS partition gives one
+rank no compactified vacuum element, which the mapped mass constructor requires.
+The failing log is retained; this campaign does not claim distributed FEM Schur
+validation. See the gravity refinement note for the exact scope and evidence.
+
+The evidence checker passes 22 lightweight tests. Independent reviews of the
+cached LDU and gravity-only cases validate provenance, state/operator invariants,
+true gates, and child-work accounting. Reviews are stored outside immutable
+campaign directories.
+
+Source fcb7833 adds owning experiment-only Newton recipes through the existing
+ADL preparation interface. They use the same concrete prepared inverses as the
+frozen benchmark and the existing context refresh/border lifecycle. The driver
+supports default, gravity-Schur, and stellar-LDU recipes for ordinary Newton,
+positivity, curvature, and positivity-curvature runs. This adds no public
+physics-facing solver API. The updated driver builds successfully at87569c0.
+
+Equal-accuracy hard-state confirmation and Newton/virial regressions are pending.
+The default production recipe remains unchanged during validation.