E8 kinetic-metric perturbation

Date: 26 October 2026

Status: one positive metric direction promoted; open tube not certified

Evidence: metric ledger Certificate: metric verifier

The perturbation lane now reaches both halves of the Hamiltonian. Replace the charging metric by the positive congruence

while retaining equal locking amplitudes \(u_i=0.5\). Positivity follows exactly because \(D\) is invertible and positive; the verifier also constructs the Cholesky pivots. The original E8 energy shells remain the truncation basis, so poorer basis adaptation is exposed as boundary weight rather than hidden by changing the cutoff geometry.

Complete-shell gaps at cutoffs 6, 8 and 10 are 0.2213227430, 0.2197890871 and 0.2196545313. Their successive changes are 0.693% and 0.0612%, with a final shift of +0.631% from the symmetric reference. The first three low states have residuals below \(2.7\times10^{-11}\), low-four boundary weight remains below \(8.5\times10^{-6}\), and the first transition stays odd, cosine-dark and sine-bright.

Together with the two channel-amplitude directions this gives a finite sampled stencil in potential and kinetic sectors. It does not prove an open tube: mixed corners, continuity between samples, rigorous gap bounds and intercell stability remain open. The next economical test combines one amplitude offset with this metric before adding a spatial cell index.