GRADIENT-1 Pipeline v5

GRADIENT-1: Zenodo Repository Metadata REGISTERED — 23 February 2026 Registered Record Item Detail OSF Pre-registration DOI https://doi.org/10.17605/OSF.IO/39SDP Pipeline v5 DOI https://doi.org/10.5281/zenodo.18749096 Journal Article I DOI https://doi.org/10.5281/zenodo.18750277 Pipeline MD5 be1a0ca1bf029be7c86d4d4e09c9e1a7 Pipeline SHA-256 e0f3056ebaa072c01d95005686d0f23dd1524adf5da3c09181f266d5e816c5d1 Registration date 23 February 2026 Contributor Pretorius, Eugene Citations Pre-registration: Pretorius, E. (2026b). Geometric Non-Gaussianity in Optical Clock Networks: A Triadic Derivation and Empirical Confirmation of Discrete Kinetic Substrate Signatures. Open Science Framework. https://doi.org/10.17605/OSF.IO/39SDP Pipeline: Pretorius, E. (2026a). GRADIENT-1 Pipeline v5 (Version 1) [Software]. Zenodo. https://doi.org/10.5281/zenodo.18749096 Journal Article I: Pretorius, E. (2026). Gradient Physics: An Ontological-First Derivative Science — Journal Article I — The Kinetic Discrete Lattice and Its Empirical Signature in Optical Clock Networks [Preprint]. Zenodo. https://doi.org/10.5281/zenodo.18750277 Title Geometric Non-Gaussianity in Optical Clock Networks: A Triadic Derivation and Empirical Confirmation of Discrete Kinetic Substrate Signatures — Pipeline, Data, and Pre-Registration Archive Description Overview GRADIENT-1 is the first 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, the three-baseline v5 audit results, and the complete pre-registration metadata registered on OSF (23 February 2026). The ontological derivation chain is published in full in Journal Article I (DOI: 10.5281/zenodo.18750277): Primordial Axiom of Relationality → Triad → {E=0.8, C=0.7, F=0.6} → TI=0.336 → β=0.325 → Φ=0.002 → H1–H5 + First Law Y₀ 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 (δ = 0.1). They are not calibrated to data. The universality class exponent β = 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 0.3333 compelled by the discrete lattice to snap to β = 13/40 = 0.325 — the unique lattice-consistent value producing a viable non-dissipative Kinetostatic Margin Φ = 0.002. The three Triadic primitives map exactly to the GRADIENT-1 empirical protocol: Triad GRADIENT-1 Physical instantiation Systematization E = 0.8 Drive (D) Geopotential height differential Δh Constraint C = 0.7 Limit (L) Heaviside threshold on cumulative Drive Registration Frequency F = 0.6 Registration (R) Discrete fractional frequency residual events The First Law of Gradient Physics Derived from Φ = 0.002 before the ROCIT 2022 dataset was examined: Y₀ = Φ × gΔh / c² (Φ = 0.002, zero free parameters) Y₀ is the GR-subtracted mean fractional frequency residual predicted for any clock comparison baseline from its geopotential height differential alone. It contains one variable (Δh) and zero free parameters. Preliminary confirmation on the Alpine baseline (out-of-pre-registration — not part of H1–H5): Value Predicted Y₀ (Alpine, Δh=158m) 3.448 × 10⁻¹⁷ Measured Y₀ (ROCIT 2022, 177 hourly windows) 3.195 × 10⁻¹⁷ ± 3.03 × 10⁻¹⁸ Discrepancy 0.83σ (92.7% agreement) This is independent evidence that Φ = 0.002 captures a real physical quantity. It is reported in Journal Article I and is not part of the pre-registered falsification protocol. Hypotheses (H1–H5) # Consequence Derived from Test H1 Excess kurtosis ordered monotonically by geopotential gradient Heaviside threshold on L → Dirac Comb Jonckheere-Terpstra, α = 0.001, one-tailed H2 Super-white variance scaling, α > −1.000 Non-zero autocorrelation from Registration footprints Power-law variance regression, p < 0.05 H3 Geometry-dependent sign separation in Allan deviation short-tau slope Net Registration noise ∝ ∫∇U·dl Negative inter-site; positive co-located H4 Geopotential gradient drives kurtosis, not fiber length Dirac Comb density ∝ Δh not L Bootstrap 3σ lower bound > 1.467× fiber ratio H5 No amplitude quantization at 1-second cadence (Alpine) Sub-second Registration frequency f_lattice > 1 Hz (conditional, Alpine only) Three-Baseline Endpoints Baseline Clock pair Δh Fiber N raw Drive regime Alpine INRIM ITYb1 – PTB Sr3 ≈158m ~1100km 372,793 High Drive Flat PTB Sr3 – SYRTE Sr2 ≈12m ~750km 570,490 Low Drive Co-located PTB In – PTB Sr3 ≈0m intra-lab 455,585 Zero Drive (control) PTB Sr3 is the shared-node anchor across all three regimes. Clock species differ across baselines (Yb at INRIM, Sr at SYRTE, In at PTB), providing species independence. v5 Pipeline Three-Baseline Results All pre-registered tests confirmed. The Triadic model is not falsified by any metric in ROCIT 2022. H1: Per-Segment Excess Kurtosis Baseline Segment n segs k>1 Rate k>3 Rate Full κ Alpine (Δh ≈ 158m) 1000-pt 58 63.79% 15.52% 2.1692 Flat (Δh ≈ 12m) 200-pt¹ 489 9.00% 0.20% 0.5292 Co-located (Δh ≈ 0m) 1000-pt 361 3.05% 0.00% −0.0027 ¹ 200-pt segments used for Flat — maximum achievable given 4,475 telemetry gaps and average block 85 pts. Smaller windows suppress kurtosis detection, biasing against the Triadic prediction. Flat exceeding Co-located is therefore stronger evidence than the raw numbers suggest. H1: Jonckheere-Terpstra Metric Value J statistic 172,725.0 Z statistic 14.836 p-value (one-tailed) < 0.000001 Verdict CONFIRMED ✓ H2: Super-White Variance Scaling Baseline α z p (one-tail) Status Alpine −0.9183 1.74 0.041 CONFIRMED ✓ Flat −0.8150 2.05 0.020 CONFIRMED ✓ Co-located −0.6410 4.63 < 0.0001 CONFIRMED ✓ H3: Allan Deviation Sign Baseline MDEV τ=1s MDEV τ=2s Slope Status Alpine 1.0644×10⁻¹⁵ 8.4189×10⁻¹⁶ −0.338331 PASS ✓ Flat 1.3528×10⁻¹⁵ 9.5923×10⁻¹⁶ −0.496027 PASS ✓ Co-located 9.1120×10⁻¹⁷ 1.2796×10⁻¹⁶ +0.489808 PASS ✓ Note: long-τ MDEV (τ > 100s) is computed from limited contiguous blocks and is descriptive only. The short-τ slope (τ = 1s to 2s) is the pre-registered inferential metric. H4: Fiber Falsification Metric Value Bootstrap mean k-ratio 7.239× Bootstrap SD 1.319 3σ lower bound 3.282× Fiber length ratio (null) 1.467× Verdict FIBER NULL REJECTED ✓ (exceeds by 2.24× margin) Limitation: the linear fiber-length null is the simplest classical alternative. Path-dependent coupling (fiber thermal gradients correlated with topographic altitude) cannot be fully excluded by H4 alone. Gate C provides the causal test. H5: N-GM Grain-Size Bound (Alpine only) Alpine: 208,101 unique values / 208,102 total. MaxBinExcess = 8.7×. Continuous. f_lattice > 1 Hz (conditional under Gradient Mechanics). Flat and Co-located show floating-point quantisation artifacts from ROCIT 2022 archiving precision — H5 is not extended to those baselines. Snap Detection Baseline Snaps Rate Gaussian Rate Excess Ratio Alpine 556 0.2672% 0.0063% 42.2× ✓ Gate C Flat 251 0.0661% 0.0063% 10.4× Co-located 30 0.0067% 0.0063% 1.1× (Gaussian) ✓ The co-located snap ratio of 1.1× is statistically indistinguishable from the Gaussian expectation — confirming the zero-Drive control behaves as a reference process. Summary Test Key result Verdict H1 Dirac Comb Z=14.84, p −1.000 at p> 1.467× CONFIRMED ✓ H5 N-GM Bound f_lattice > 1 Hz (Alpine) ESTABLISHED ✓ Y₀ First Law 0.83σ (92.7%) — out-of-protocol PRELIMINARY ✓ Gate C 556 snaps, 13 lags, Bonferroni — quarantined PROSPECTIVE Gate System Gate Status Content Gate A COMPLETE — pre-dates all data contact Derivation of D, L, R → H1–H5. N-GM grain-size bound derived independently. Gate B COMPLETE — v5 three-baseline run Statistical audit. All metrics locked. Gate C PROSPECTIVE — quarantined Mann-Whitney U, 556 Alpine snaps, 13 pre-registered lags (−300s to +300s, 50s steps), Bonferroni correction, against INRIM and PTB atmospheric pressure logs February–March 2022. Pipeline Scope and Scalar Invariance GRADIENT1_pipeline_v5.py is not an instrument built for optical clock data. It is the detection instrument for the necessary consequences of Drive (D), Limit (L), and Registration (R). The ROCIT 2022 optical clock network is the first physical domain in which these consequences are tested. The mathematical core — the Jonckheere-Terpstra trend test, the Dual Discriminator, the Allan deviation sign criterion, the super-white variance scaling test, the fiber falsification bootstrap — contains no domain-specific assumptions. These functions operate on any ordered time series with an associated Drive magnitude. They were derived from the structure of D, L, R, not fitted to optical clock residuals. Scalar invariance is not a property that needs to be engineered into future versions of this pipeline. It is a property inherited from the derivation. When a new physical instantiation is identified — a new domain, a new scale, a new observational cadence — the same pipeline receives new data. The detection logic is unchanged. The pre-registered falsification conditions are unchanged. SHA-256: e0f3056ebaa072c01d95005686d0f23dd1524adf5da3c09181f266d5e816c5d1 This hash is the hardlock across all instantiations. Any execution of this pipeline on any domain that produces a result does so under the same locked code that produced the ROCIT international optical-clock comparison campaign (March 2022) results.