Gradient Physics: An Ontological-First Derivative Science - Journal Article III (a) - Continuous Substrate Dynamics and the Thermodynamic Basis of Cognitive Registration: Empirical Instantiation of the Triadic Kernel in Three Independent Neural Datasets

This paper presents the first empirical instantiation of the Triadic Kernel E = 0. 8, C = 0. 7, F = 0. 6 in cognitive neuroscience. From the Kinetostatic Margin Φ = 0. 002 and the derived structural constants φ = 0. 04, Nₛat = 25, and εₛnap = 1/30, four empirical consequences are derived and tested against three independent publicly available raw neural datasets. H1: during habituated visual change detection, the neural manifold displacement per chronon exceeds the structural pixel floor φ at every measured step (mean ΔS = 1. 53, t = 274, p ≈ 0, N = 144, 993 chronon steps). H2: macroscopic behavioral switches are preceded by a mean of 24. 17 micro-displacement steps, against a zero-parameter Kernel prediction of Nₛat = 25 (deviation 3. 3%). H3: pre-stimulus alpha power (8–12 Hz) at parietal electrodes predicts P300 amplitude across 40 subjects and 1, 205 epochs (r = 0. 072, p = 0. 013), consistent with the registration snap interpretation of the P300 as thermodynamic exhaust. H4: even in the complete absence of any task or stimulus, the resting-state neural manifold maintains continuous displacement far exceeding φ, with a detrended fluctuation analysis scaling exponent α = 0. 573 confirming long-range temporal correlations. All four hypotheses are confirmed on their preregistered criteria with zero fitted parameters. The Null Regime—the claim that the neural substrate achieves structural stasis during habituated behavior—is not achievable by the physical substrate at any measurable temporal resolution. The P300 is not a signature of conscious rule-editing; it is the electromagnetic registration of a thermodynamic snap.