E8 local operator dictionary

Date: 26 October 2026

Status: reusable eight-root dictionary certified

Dictionary: machine artifact Compiler: dictionary compiler Certificate: dictionary verifier

The expensive local calculation is now separated from spatial scaling. The versioned dictionary contains the eight cutoff-eight local energies, parities, boundary weights and all signed \(8\times8\) matrices for the eight cosine and eight real sine-proxy channels. It was compiled from 340,321 charge states; all local residuals are below \(10^{-10}\), cosine matrices are symmetric and sine proxies antisymmetric to better than \(9\times10^{-15}\).

The chain solver can load this 23.8 KB artifact instead of reconstructing the local eigensystem. A cached replay exactly reproduces the periodic width-three gap 0.1826163504 and its odd, reflection-even first excitation. This makes the projected model monitorable and tunable: changing width, boundary condition or intercell coupling no longer silently changes the local carrier.

Serialization does not remove truncation. Every downstream result inherits cutoff eight and eight retained roots, and must cite them. Higher-root dictionaries are distinct artifacts rather than in-place upgrades. The next computational gain is using this fixed dictionary for widths beyond five and for coupling/boundary sweeps with exact provenance.