Reader Distillation: From 24-Cell Occupancy to Sign Concordance and Autocorrelation

The parent paper showed that a discriminative occupancy readout of the 24-cell reader carries temporal-organizationinformation unavailable to marginal moments, and localized that information to a sign-concordance layer. External reviewasked the obvious next question: if the winning direction is sign concordance, why keep the 24-dimensional machine? Weanswer by distillation. We compare, under one frozen protocol, the occupancy discriminative projection, a single scalarsign-concordance statistic C = P[sgn(x_t)=sgn(xₜ₋ₜₐᵤ)], its 150-dimensional ordinal-pattern relative (permutationentropy), and ordinary lag-1 autocorrelation. On clean Gaussian regime changes the chain collapses all the way:occupancy reduces to C, and C reduces to lag-1 autocorrelation, which wins; indeed for Gaussian processes C equalsone-half plus arcsin(rho) over pi, an identity we verify to machine precision. The occupancy surplus over C is not a stablecomponent: after regressing C out, the residual detection power is a finite-sample artifact (near-coin-flip across seeds). Soon clean data the 24-cell reader is fully dispensable. But distillation is conditional on what is allowed to change. When weperturb the value geometry the reader discarded -- adding outliers, or applying a monotone nonlinear value transform --lag-1 autocorrelation degrades sharply while the rank/sign readers (occupancy and C) stay intact, because they areinvariant to those value-domain changes by construction. The simplest reader is not the most robust one; which reader isminimal depends on the group of nuisance transformations one permits. The 24-cell machine functioned here as astructure-discovery instrument that surfaced C; C's own value over raw autocorrelation was not extra clean-data powerbut robustness to the tested value-domain contaminations. ※ The license for codes is AGPL3.0-or-later