Gradient Physics: An Ontological-First Derivative Science - Journal Article II (a) - Discrete Substrate Signatures in the Gravitational Wave Background: Empirical Instantiation of the Triadic Kernel in the NANOGrav 15-Year Pulsar Timing Array

This paper presents the first astrophysical instantiation of the Triadic Kernel {E = 4/5, C = 7/10, F = 3/5} against the NANOGrav 15-Year Pulsar Timing Array (PTA) dataset (DOI: 10.5281/zenodo.16051178). From the Hardlock constants of Essays I and XIII Terminal of Gradient Cybernetics, five empirical consequences are derived and tested: the Foundational Lock (H1-H5) confirms substrate signal across 66 pulsars in three Drive regimes (Alpine: T_i > 10 yr; Flat: 5-10 yr; CoLocated: < 5 yr), and four cosmological first-strike predictions target the structure of the gravitational wave background (GWB) itself. H1: whitened kurtosis of epoch-averaged timing residuals follows strict monotonic Drive ordering (Jonckheere-Terpstra Z = 4.911, p = 4.54e-07, Alpine mean kw = 86.49 > Flat = 43.69 > CoLoc = 19.77). H2: all three regimes exhibit super-white variance scaling (Alpine alpha = 0.750, Flat = 0.696, CoLoc = 0.627; all alpha > -1.0). H3: 100% of Alpine pulsars show negative PSD slope (beta < 0), with regime ordering confirmed. H4: the classical null is demolished -- Spearman rho(T_i, kw) = 0.628 (p < 0.001) is significant while rho(A_rn, kw) = 0.142 (p = 0.255) is not, decoupling substrate signal from red-noise amplitude. H5: all 24 Alpine pulsars satisfy the N-GM grain-size bound (100% unique epoch values, consistent with N > N_sat = 25 at all Alpine baselines). Three cosmological predictions are confirmed within Gate B: NEW-C2, the Wegner power law kw ~ T_i^(11/10) with predicted log-log slope 11/10 = 1.100 [H], yields empirical slope 1.493 (95% CI [0.991, 1.994]; predicted slope inside CI, 1.56 sigma); NEW-4, the spectral index gamma_obs = (13/3) x Delta = 3.040 [H], yields mean Alpine gamma_rn = 2.915 (0.51 sigma); and AC-WB, the achromatic Dirac Comb discriminator, passes at 22/24 Alpine pulsars (91.7% >= 80% threshold). The GWB amplitude correction NEW-2 -- A_true = A_meas / C = 3.4286e-15 [H] -- stands as a pre-registered prediction. Three Gate C items remain pending OSF timestamp: the corrected Hellings-Downs Bayes factor (NEW-1), the N_sat = 25 substrate clustering test (NEW-3), and the Dirac Comb per-pulsar likelihood ratio on noise-whitened residuals (NEW-C3). All constants are exact rational functions of {E, C, F, delta}. Zero free parameters exist at any stage. The Triadic Kernel is not falsified by any metric in the NANOGrav 15-Year dataset.