E8 Cartan-kernel shell-10 spectroscopy gate

Date: 26 October 2026

Status: first sub-one-percent increment; shell-12 confirmation required

Parent: operator-completeness gate

Evidence: shell-10 spectroscopy ledger

Certificate: cutoff and parity verifier

First credible plateau signal

The operator-complete (K)-kernel branch has now been solved at kinetic shell 10, containing 794,161 states. Its four lowest projected levels are

The first gap is (0.1020184010). Relative to shell eight it changes by only 0.295%, the first increment below the frozen one-percent threshold. All four level boundary probabilities are below (1.88\times10^{-4}), and the first three residuals are below (2.6\times10^{-11}).

This is the first credible plateau signal, but not yet a promoted gap. The programme requires two successive sub-one-percent increments so that one accidental flat step cannot close the gate. Shell 12 is the confirmation rung.

The detector must respect parity

Global charge inversion is exact. The ground state is even, the first excited state is odd, the second is even and the third is odd. An ordinary cosine drive is even, so its ground-to-first weights are at numerical zero, while it couples visibly to the second excitation. A laboratory using only amplitude/ cosine modulation would therefore miss the true first gap and report the larger even-sector line.

The apparatus must pair even cosine modulation with an odd sine or phase- quadrature drive. The solver now emits both transition tables. The small-shell certificate independently reproduces the rule: cosine is dark and sine is bright for the first odd state.

Promotion rule

Run shell 12 with the same gap, residual, boundary probability, parity and eight-channel drive record. Promote a provisional nonlinear (K)-kernel gap only if the 10-to-12 drift is also below one percent and the visible transition weights stabilize. This would still be a compact-cell result, not the E8 chiral anomaly or thermodynamic coupled-wire gap.