From 5298d88ed0ce98830bd900553de6a2912ff0fb95 Mon Sep 17 00:00:00 2001 From: Emily Boudreaux Date: Thu, 17 Sep 2026 18:03:56 -0400 Subject: [PATCH] Document higher-index nonlinear limits after Schur refinement --- .../PRECONDITIONER_IMPROVEMENT_2026-09-18.md | 40 +++++++++++++++++-- 1 file changed, 36 insertions(+), 4 deletions(-) diff --git a/experiments/PRECONDITIONER_IMPROVEMENT_2026-09-18.md b/experiments/PRECONDITIONER_IMPROVEMENT_2026-09-18.md index 15cc925..0f3bf36 100644 --- a/experiments/PRECONDITIONER_IMPROVEMENT_2026-09-18.md +++ b/experiments/PRECONDITIONER_IMPROVEMENT_2026-09-18.md @@ -215,7 +215,39 @@ maximum endpoint coefficient difference is 2.679e-11; the radius difference is admissibility and local EOS metrics. This preserves the existing physical regression, rather than adding independent ESTER validation. -The two hard nonlinear cases and the targeted rotating coupling follow-up are -still running or pending. Production defaults remain unchanged: the stronger -inverse is an optional typed policy, and the coarse candidate remains an -experiment. +## Higher-index nonlinear follow-through + +The n = 1.5, J = 0 curvature case uses the same initial physical state, layout, +mesh, normalization, and stopping settings as the historical independent +preconditioner run. Gravity refinement completes all twelve permitted Newton +steps, with all twelve independently checked linear defects below 0.03. The +historical run stopped after six accepted steps because its next linear solve +failed. The new run therefore removes that immediate linear obstruction. + +It does not establish nonlinear convergence. The final residual is +1.3966991e-5 against a target of 2.7365922e-12, only 6.13% below the historical +endpoint. After the first full step, accepted step lengths are mostly 1/16 or +1/32; the final two are 1/64 and 1/512. All nineteen rejected trials fail the +residual-decrease test. All 31 auxiliary gravity solves pass. This evidence +points to the remaining nonlinear step obstruction, rather than another +failed outer or auxiliary gravity solve. + +The run spends 415.038 s in outer linear solves and 590.003 s in preparation, +including 178.937 s in auxiliary gravity solves. Summed Newton time is +1075.368 s and complete diagnostic-run wall time is 1138.002 s. These are +costs of an unconverged trajectory, not a nonlinear speedup. + +The enthalpy-pressure energy and force virials pass 1e-5, with quadrature-18 +errors 4.06909e-6 and 2.57118e-6. Density-pressure virials remain undefined: +the sampled density minimum is -8.14767e-4, with 9600 negative samples and +negative mass fraction 2.89597e-5. Negative density also occurred in the +historical case. Sampled enthalpy stays positive, but this curvature-only run +does not provide a global polynomial positivity certificate. Thus the virial +numbers alone do not make this an acceptable physical model. The independent +audit records these failures separately from successful linear solves and +artifact verification. + +The hard rotating nonlinear case and the targeted rotating coupling +follow-up are still running or pending. Production defaults remain unchanged: +the stronger inverse is an optional typed policy, and the coarse candidate +remains an experiment.