E8 channel-amplitude perturbation

Date: 26 October 2026

Status: one unequal-channel direction promoted; open perturbation tube not certified

Evidence: perturbation ledger Certificate: perturbation verifier

The scalar coupling spine is no longer the only evidence for stability. At fixed mean locking strength 0.5, replace the eight equal amplitudes by

This breaks equal-channel locking while preserving positivity and global inversion. Complete-shell gaps at cutoffs 6, 8 and 10 are respectively 0.2185344832, 0.2173316417 and 0.2172388980. Successive relative changes are 0.550% and 0.0427%; final low-state boundary leakage is below \(5.1\times10^{-6}\). Relative to the symmetric mean-coupling result, the final gap moves by only -0.476%.

The detector survives in a more informative form. The ground state remains even; the first excitation remains odd, cosine-dark and sine-bright, but its eight sine weights become unequal. The second excitation remains even and cosine-bright. Thus the perturbation changes the channel fingerprint without destroying the selection rule.

This is one certified ray through parameter space, not a neighbourhood. A second non-collinear direction now forms a finite stencil, but does not fill the region between samples. It does not establish arbitrary channel disorder, metric stability, an intercell or thermodynamic gap, E8 response, or material E8. Independent amplitude directions and positive quadratic-metric perturbations are the next gates; only then is an open compact-cell tube a defensible target.