After inspecting the exact worst-prefix scan, before this diagnosis.
The worst prefixes repeat at depths12/13: prefix82 mod2^16 forL256,
and prefix130954 mod2^17 forL512. Investigate an actual arithmetic cause,
rather than merely adding another conditional inequality.

For these four fixed cases only, reconstruct the conditional count by direct
integer Syracuse on every remaining high-bit lift and every source in the
window. Group sources first by a PROVED shared affine endpoint, keeping
the exact odd-step count, division total and surviving phase interval.
Different clocks or phase intervals must not be identified. Compare the
true conditional variance with the independent-source baseline, the exact
within-group copy contribution, and the residual cross-group covariance.

This is a diagnostic of the selected worst prefixes, not an unbiased sample
or an all-depth proof. Equality of the finite indicator vectors alone is
reported separately from the analytic affine-state grouping. One CPU process
120seconds, at most4 cases with at most256 high-bit lifts and512 source terms.
