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MeanField/experiments/COUPLED_CONVERGENCE_STUDY_2026-09-19.md

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# Coupled harmonic-surface convergence study
The user has deferred positivity enforcement. This study keeps density an
independent Q2 field and retains the simultaneous all-m degree-four harmonic
surface/interior system. The primary milestones are useful convergence at
higher index and angular momentum, and both enthalpy-pressure virials below
1e-5. Negative-density measurements remain diagnostic, not acceptance repairs.
Base revision: `ef76e0c`. Work is isolated on
`research/coupled-convergence-study-20260919`, with separate
`research/linear-coupling-study-20260919` and
`research/model-slices-20260919` branches for independent implementations.
The original programming checkout is unchanged.
First screen: n=2,J=0; n=3,J=0 at forcing tolerances 0.03 and 0.003;
n=1,J=0.1; n=1.5,J=0.1. All use the same Q2 density, Q3 enthalpy and
displacement, RT2/Q2 gravity, Q4 geometry, reference mesh, normalization,
default inverse, 12-update budget, restart 160, and 300-iteration linear
budget. Only n=3 includes the existing central phase condition. This tests
whether a tenfold more accurate direction changes the n=3 trajectory, but
it is not a same-state preconditioner comparison. Capture updates 0,3,7
for subsequent controlled probes. No input J is identified with a calibrated
fraction of critical rotation.
Follow-up decisions depend on this screen and source review: frozen-state
preconditioner/forcing comparisons; small coupled surface/border corrections;
accepted-state continuation with checked field/coordinate transfer. Linear
claims require independently applied full-J residuals; nonlinear claims use
common stopping thresholds plus physical diagnostics, not residual alone.
Report scalar-border forcing separately from the unbordered equations.
The slice feature will evaluate physical geometry and independent fields,
show the material surface at true scale, retain signed density, and separate
outside-domain points from valid interior samples. It must not silently turn a
reference-coordinate cut into a physical planar cut.
Builds and expensive numerical cases run serially. The existing campaign
runner records exact source, binary, mesh, arguments, saved states and output
hashes. Initial evidence directory:
`../../diagnostics/coupled_convergence_2026-09-19/screen_v1`.
Results and any adaptive extensions will be recorded below before finalizing
the study. Defaults and the physics-facing API are unchanged.