GRADIENT-2 Pipeline v3

GRADIENT-2: Zenodo Repository Metadata REGISTERED — 22 March 2026 Discrete Substrate Signatures in the Gravitational Wave Background: A Triadic Derivation and Empirical Non-Falsification Program for Kinetic Substrate Structure in Pulsar Timing Arrays -- Pipeline, Data, and Pre-Registration Archive Registered Record OSF Pre-registration DOI-https://doi.org/10.17605/OSF.IO/Z5NDM Pipeline v3 DOI-https://doi.org/10.5281/zenodo.19165903 Journal Article II DOI-https://doi.org/10.5281/zenodo.19165633 Pipeline SHA-256583d267b45ef4da52134b4e0731044606e0f5cdcc330c53a68d9139238d623c3 Registration date22 March 2026 ContributorPretorius, Eugene Citations Pre-registration: Pretorius, E. (2026, March 22). Discrete Substrate Signatures in the Gravitational Wave Background: A Triadic Derivation and Empirical Non-Falsification Program for Kinetic Substrate Structure in Pulsar Timing Arrays. Open Science Framework. https://doi.org/10.17605/OSF.IO/Z5NDM Pipeline: Pretorius, E. (2026). GRADIENT-2 Pipeline v3 (Version 1) [Software]. Zenodo. https://doi.org/10.5281/zenodo.19165903 Journal Article II: Pretorius, E. (2026). 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 Data Set - Pulsar Timing Array [Preprint]. Zenodo. https://doi.org/10.5281/zenodo.19165633 Title Discrete Substrate Signatures in the Gravitational Wave Background: A Triadic Derivation and Empirical Non-Falsification Program for Kinetic Substrate Structure in Pulsar Timing Arrays -- Pipeline, Data, and Pre-Registration Archive Description Overview GRADIENT-2 is the second physical instantiation of Gradient Mechanics, an ontological-first derivative science framework governed by three primitives: Drive (D), Limit (L), and Registration (R). This repository contains the hardlocked computational pipeline (v3 FINAL), the three-regime Gate B audit results across 66 millisecond pulsars from The NANOGrav 15-Year Data Set - Pulsar Timing Array, and the complete pre-registration metadata registered on OSF (22 March 2026). The ontological derivation chain is published in full in Journal Article II (DOI: 10.5281/zenodo.19165633): Primordial Axiom of Relationality -> Triad -> {E=4/5, C=7/10, F=3/5} -> TI=42/125 -> beta=13/40 -> Phi=0.002 -> Delta=0.7016 -> H1-H5 + NEW-C2 + NEW-4 + AC-WB + NEW-2 Every step is derivationally necessitated by the step before it. The corpus precedes the experiment. The experiment tests the corpus. The three primitive values are the unique Diophantine solution to four simultaneous internal constraints on the discrete informational lattice (delta = 1/10). They are not calibrated to data. The universality class exponent beta = 13/40 = 0.325 is derived from the Triad's own structural character (d=3, n=1) under the renormalisation group fixed point, with the off-lattice value 1/3 compelled by the discrete lattice to snap to beta = 13/40 -- the unique lattice-consistent value producing a viable non-dissipative Kinetostatic Margin Phi = 0.002. The three Triadic primitives map exactly to the GRADIENT-2 empirical protocol: Systematization E = 4/5: Drive (D). Observation baseline T_i (years) of each millisecond pulsar. The net accumulated chronon cycles traversed by the timing residual over the full observation span. Constraint C = 7/10: Limit (L). Heaviside threshold condition on accumulated Drive. A Registration snap occurs if and only if accumulated fractional frequency deviation exceeds threshold C = 0.700. Registration Frequency F = 3/5: Registration (R). Discrete epoch-averaged timing residuals in the NANOGrav 15-Year series -- the observable footprint of state updates. Whitened residual z = delta_t / sigma_TOA is the primary Registration observable. The Cosmological Predictions Derived from the Hardlock constants before the NANOGrav dataset was examined: NEW-2 -- Amplitude Correction: A_true = A_measured / C = A_measured x (10/7) = 3.4286e-15 [H]. The discrete substrate registers only fraction Delta = 0.7016 of the true GWB amplitude. Resolves the SMBHB population synthesis tension. Zero free parameters. NEW-4 -- Spectral Index: gamma_obs = (13/3) x Delta = (13/3) x TI^beta = 3.040 [H]. The observed GWB spectral index is attenuated from the classical SMBHB prediction (4.333) by exactly the Order Parameter Delta. Resolves the spectral index deficit. Zero free parameters. NEW-C2 -- Wegner Power Law: kw ~ T_i^(11/10). Predicted log-log slope = 11/10 = 1.100 [H] (exact rational, derivable before data contact). No framework in pulsar timing astronomy predicts this exponent. NEW-C3 -- Dirac Comb Likelihood Ratio: Delta_logL = sum log[Lambda x phi(z) + Delta x phi(z/r)/r] - log[phi(z)], where r = sqrt(14/9) [H]. If Delta_logL > 0, the published H-D Bayes factor is systematically understated. Zero free parameters. Gate C (requires MCMC noise-whitened residuals). Preliminary Cosmological Confirmation The following results are audit-locked Gate B values (22 March 2026). They are not preliminary; they are the pre-registered test outcomes for the Gate B hypotheses. Gate C items remain blinded. NEW-4 Spectral Index (Gate B confirmed): Predicted gamma_obs [H]: 3.040 Measured mean Alpine gamma_rn: 2.915 Discrepancy: 0.512 sigma Classical SMBHB prediction: 4.333 (1.42 sigma farther from measurement) NEW-C2 Wegner Power Law (Gate B confirmed): Predicted slope [H]: 1.100 (= 11/10 exact rational) Empirical slope: 1.4926, SE=0.251, 95% CI [0.991, 1.994] Predicted slope inside CI: YES. Discrepancy = 1.564 sigma. AC-WB Achromatic Discriminator (Gate B confirmed): Criterion: >= 80% Alpine pulsars kw_wb > 0 [C] Result: 22/24 Alpine pulsars (91.7%). PASS. These results confirm that the Dirac Comb substrate structure is present in the achromatic wideband residuals of the NANOGrav 15-Year dataset, that the GWB spectral index is attenuated from the classical prediction by exactly the Order Parameter, and that the kurtosis-baseline relationship follows the exact quantitative exponent predicted from the Hardlock. None of these predictions were adjusted after data contact. Hypotheses (H1-H5 Foundational Lock + Cosmological) H1: Whitened kurtosis ordered monotonically by Drive regime (Alpine > Flat > CoLocated). Derived from Heaviside threshold on L producing Dirac Comb structure. Test: Jonckheere-Terpstra, alpha = 0.001, one-tailed. H2: Super-white variance scaling, alpha > -1.000, in all three Drive regimes. Derived from non-zero autocorrelation forced by Registration footprints. H3: 100% of Alpine pulsars show negative PSD slope (beta < 0), with regime ordering in negative fractions. Derived from 1/f structure imposed by high-Drive Registration density. H4: Drive proxy T_i governs kurtosis (rho(T_i, kw) significant) while classical amplitude proxy A_rn does not (rho(A_rn, kw) not significant). Classical null demolished. H5: All 24 Alpine pulsars show 100% unique epoch values (continuous, CONT). N-GM grain-size bound: f_lattice >> 1/(T_i/N_clean) for all Alpine pulsars. Conditional on Gradient Mechanics instantiation. Alpine only. NEW-C2: kw ~ T_i^(11/10). Predicted log-log slope 1.100 [H] inside 95% CI of empirical OLS slope. NEW-4: gamma_obs = (13/3) x Delta = 3.040 [H]. Mean Alpine gamma_rn within 2 sigma. AC-WB: At least 80% of Alpine pulsars show kw_wb > 0 in PINT-generated wideband residuals. NEW-2 (Standing): A_true = A_measured / C = 3.4286e-15 [H]. Gate C: comparison against MCMC posterior amplitude chains. Three-Regime Endpoints Alpine (High Drive, T_i > 10 yr): 24 pulsars. Observation baseline 10.47 to 15.67 years. Total raw epochs: 5,249. Clean epochs: 4,484. Snap events frozen: 28. Longest baseline: J1744-1134 (15.67 yr). High Drive -- maximum Dirac Comb accumulation. Flat (Low Drive, 5-10 yr): 24 pulsars. Observation baseline 5.45 to 9.09 years. Total raw epochs: 3,030. Clean epochs: 2,017. Snap events: 1. Intermediate Drive. CoLocated (Zero Drive, T_i < 5 yr): 18 pulsars retained (2 excluded: J1630+3734 and J0614-3329 with N_clean < 10). Observation baseline 2.41 to 4.75 years. Total raw epochs: 1,358. Clean epochs: 1,046. Snap events: 4. Zero-Drive control -- Gaussian reference process. Total archive: 68 pulsars. Retained: 66 pulsars. Total raw epochs: 9,637. Clean epochs: 7,547. Frozen snap events: 33 across all three regimes. v3 FINAL Pipeline Three-Regime Gate B Results All pre-registered Gate B tests confirmed or formally deferred with documented contingencies. The Triadic model is not falsified by any metric in the NANOGrav 15-Year dataset. H1: Whitened Kurtosis Drive Ordering Alpine mean kw: 86.49 | Flat mean kw: 43.69 | CoLoc mean kw: 19.77 JT: J=1136, Z=4.911, p=4.54e-07 | Ordering Alpine > Flat > CoLoc: CONFIRMED | Alpine normality p> -1.000 | Verdict: CONFIRMED H3: PSD Slope Sign Alpine 100% beta