E8 channel-amplitude stability stencil

Date: 26 October 2026

Status: two non-collinear amplitude directions promoted; open ball not certified

Evidence: stencil ledger Certificate: stencil verifier

The first unequal-channel result is not isolated. A second, non-alternating direction

keeps mean locking 0.5 while reaching a 20% channel displacement. It is not collinear with the earlier 10% direction: the cosine between their centered amplitude vectors is -0.218.

For the second direction, complete-shell gaps at cutoffs 6, 8 and 10 are 0.2183476531, 0.2171133353 and 0.2170242135. Successive changes are 0.565% and 0.0410%; the final gap is only 0.574% below the symmetric reference. The first three Ritz residuals are below \(3.7\times10^{-11}\), final low-four boundary weight is below \(5.1\times10^{-6}\), and the first excitation remains odd, cosine-dark and sine-bright.

This promotes a finite two-direction stencil, not a continuous neighbourhood. No interpolation theorem or dense sweep has yet excluded a gap-closing pocket between the sampled points. More importantly, both directions perturb the locking vector while leaving the quadratic kinetic metric fixed. A positive metric perturbation is therefore the next qualitatively independent gate.