MeanField/experiments/GRAVITY_PREPARED_ROUNDOFF_2026-09-17.md

Gravity prepared-residual arithmetic experiment

This hypothesis branch changes only the arithmetic assessment used after a gravity correction has passed its inner true-residual gate. It does not change that inner tolerance, the full-system lifted Newton gate, nonlinear merit acceptance, physical equations, or virial validation.

For fixed retained state, write the normalized gravity residual as G = A_q q + A_phi phi + b. Its norm can be tiny while the separate terms are large. Estimating arithmetic from ||G|| and the combined correction action therefore misses cancellation and the floating-point addition of corrected gravity coefficients.

Before changing the candidate, the workspace now measures the normalized gradient and potential actions separately, for both the old state and its correction. It infers the fixed source as b = G_old - A_q q - A_phi phi. Selection uses the compiled field block types, and applications reuse the prepared gravity operator. Scratch vectors are allocated with the workspace.

The assessment uses 256 epsilon times the sum of those five contribution norms and the norms of the old, desired, and freshly prepared gravity residuals. This is an explicit arithmetic estimate, not a rigorous forward-error bound: it does not bound cancellation inside each individual field action. The factor does not create an absolute residual floor, so a common scaling of the gravity equations scales the assessment equally.

Two separate requirements remain:

1. The discrepancy between the affine prediction and freshly prepared gravity residual must fit the arithmetic estimate.
2. The prepared residual's distance from its target must not exceed the measured inner true residual plus that estimate.

Diagnostics retain the raw affine discrepancy, raw target defect, arithmetic estimate, and resulting target threshold separately. Nonfinite or negative norm inputs fail the assessment. A failed preparation leaves these measurements unavailable rather than reusing the preceding trial's values. Diagnostics also report whether compact gravity operator and inverse applications were selected.

Three focused tests, appended to tests/solver/gravity_reduction.cpp, cover large cancelling contributions, rejection of defects beyond either gate, nonfinite measurements, and scaling over twenty-four orders of magnitude. The real stellar rejection must still be reproduced and reassessed; passing a synthetic arithmetic test alone establishes neither the hypothesis nor stellar convergence.