Gradient Physics: An Ontological-First Derivative Science - Journal Article V (a) - Discrete Substrate Signatures in the C. elegans Whole-Brain Optogenetic Neural Activity Dataset: Empirical Instantiation of the Triadic Kernel in the Randi et al. (2023) Dandiset 001075 Neural Signal Propagation Atlas (Leifer Lab)

This paper presents the first noetic instantiation of the Triadic Kernel {E=4/5, C=7/10, F=3/5} against the Randi et al. (2023) C. elegans whole-brain single-neuron optogenetic calcium imaging dataset (Dandiset 001075; Leifer Lab, Princeton University). From the Hardlock constants of Essays I and XIII Terminal of Gradient Cybernetics, five empirical consequences are derived and tested against 12,806 neurons across 105 wild-type C. elegans worms (strain AML462) in three Drive regimes. H1: per-neuron kurtosis of the trial chronon sequence Δz(n,w,s) follows the G3-class platykurtic pattern confirmed by JT (J=29,444,051, Z=9.4123, p<10⁻⁸). The median ordering is strictly monotone: Alpine(1.2503)<Flat(1.3956)<CoLocated(1.8018). Mean kurtosis: Alpine(3.0437), Flat(3.0123), CoLocated(4.1064). The Alpine-Flat mean difference (0.031 units) is small relative to Alpine-CoLocated separation (1.066 units, 34×); the JT uses the full rank distribution and is the sole declared inferential test (see Note on kurtosis direction, Section IV). Alpine NON-GAUSSIAN p=0.000. H2: super-white variance scaling on neuron Drive axis (α=−0.634, Z=12.11, p<10⁻⁶, n=12,806, n_scales=10). H3: snap fraction at r=√(14/9)=1.2472 [H]: Alpine 17.47%>Flat 16.00%>CoLocated 15.47%>null 17.08% — zero free parameters. H4: DC likelihood ratio [Λ=0.2984 [H], Δ=0.7016 [H], r=1.2472 [H]]: Alpine 19.3%>Flat 7.34%>CoLocated 4.71% — full order confirmed, zero free parameters. H5: resp_arr global pool frac_unique=0.9952 (230,048/231,167) — continuous. All constants are exact rational functions of {E,C,F,δ}. Zero free parameters exist at any stage. The Triadic Kernel is not falsified.