Preprocessing-Scale Dependence and Cross-Cohort Inconsistency of Local Covariance Spectral Entropy in Fibromyalgia Whole Blood (Reanalysis of GSE221921 and GSE67311)

A methodological characterization of local covariance spectral (von Neumann) entropy — a label-free structural descriptor of a sample's molecular state — showing how its group-difference behavior on transcriptomic data depends on the preprocessing scale and on the cohort. Two public fibromyalgia whole-blood cohorts serve as the test case (GSE221921, GSE67311). On native linear FPKM the descriptor separates the disease groups in one direction, but that direction appears in only one of six preprocessings, is driven by a few extreme-magnitude probes, and is not preserved under standard log-transformation of the same matrix (Cohen's d +0.67 to -0.85 on GSE221921); the same recipe gives the opposite sign on the second cohort (d = -0.42), so the disease-group direction is not robust in these data. Two transferable methodological points follow: covariance-spectral-entropy descriptors on linear-scale expression data are not scale-invariant and require scale-invariant preprocessing before any direction is interpreted; and top-variance feature selection must be performed before, not after, per-gene z-scoring, which is otherwise degenerate. Under scale-invariant preprocessing both cohorts give a consistent (unconfirmed) direction. Every reported effect size and p-value is produced by a canonical Rust runner and parity-matched to a retained reference implementation (tolerance 1e-9); analysis code and SHA-256 data manifests are openly deposited. No diagnostic, severity, prognostic, or treatment claim is made or supported.