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: Tᵢ > 10 yr; Flat: 5-10 yr; CoLocated: 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 Nₛat = 25 at all Alpine baselines). Three cosmological predictions are confirmed within Gate B: NEW-C2, the Wegner power law kw ~ Tᵢ^ (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 gammaₒbs = (13/3) x Delta = 3. 040 H, yields mean Alpine gammaᵣn = 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 -- Aₜrue = Aₘeas / 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 Nₛat = 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.