Empirical Verification of a Cognitive Uncertainty Principle: Bootstrapped Estimation, Confidence Intervals, and Violation Morphology

This work presents the first empirical verification of a Cognitive Uncertainty Principle (CUP) within the framework of Subjective Physics. The principle posits a fundamental lower bound on the product of two observer-centric uncertainty measures: (i) deviation of the spectral exponent (Δβ ) from the ideal 1/f noise regime, and (ii) divergence (ΔKL ) of leading-digit statistics from Benford’s law. Using a large-scale simulation of synthetic observers based on a hybrid jump-diffusion model, we estimate a robust empirical constant C≈3.94×10−4 such that Δβ×ΔKL≳C holds in 95% of configurations. Violations cluster in high-perceptual-resolution regimes, suggesting a boundary of cognitive stability. The study introduces a reproducible pipeline for bootstrap-based confidence estimation and provides open data and code for full verification. This result supports the view that observer entropy and perceptual resolution are fundamentally coupled, offering a quantitative bridge between information-theoretic cognition and statistical physics.