Context-Dependent Expression Persistence: AR(2) Eigenvalue |λ| Is Independent of Intrinsic mRNA Half-Life

Background: The eigenvalue modulus |λ| of a second-order autoregressive (AR(2)) model measures temporal persistence in gene expression. Whether |λ| recapitulates intrinsic mRNA stability (half-life) or captures context-dependent regulatory persistence is critical for biological interpretation. Methods: We computed |λ| for 5,945 mouse genes (GSE11923, 48 timepoints) and compared against experimentally measured mRNA half-lives (Sharova et al. 2009). We validated across four non-circadian datasets spanning three species and performed a three-part bias audit. Results: The correlation between |λ| and mRNA half-life was near zero (ρ = 0.006, p = 0.63, n = 5,945). Verified gene-pair exemplars confirm the dissociation: Nr1d2 (half-life 60 min, |λ| = 0.811) shows 72% higher persistence than Rb1 (half-life 420 min, |λ| = 0.472) despite a 7-fold shorter mRNA lifetime. IFIT1 (half-life 31 min) shows low persistence in liver (|λ| = 0.336) but high persistence under active interferon signalling in immune contexts (|λ| = 0.72), demonstrating that |λ| tracks regulatory drive, not molecular stability. Cross-validation confirmed near-zero correlations across all four datasets. The bias audit confirmed that time-shuffling destroys the signal (p < 0.001) and expression-matched controls show significantly lower |λ|. Conclusions: |λ| measures context-dependent expression persistence arising from regulatory network dynamics, not intrinsic mRNA stability. The near-zero correlation with half-life, validated across species and contexts, establishes |λ| as a novel axis of gene expression variation.