GRADIENT-3 Pipeline v1

GRADIENT-3: Zenodo Repository Metadata REGISTERED — April 2026 Discrete Substrate Signatures in the Arabidopsis Circadian Transcriptome: A Triadic Derivation and Empirical Non-Falsification Program for Kinetic Substrate Structure in Circadian RNA-seq — Pipeline, Data, and Pre-Registration Archive Registered Record OSF Pre-registration DOI 10.17605/OSF.IO/B4R3W Pipeline v1 DOI 10.5281/zenodo.19648448 Journal Article IV(a) DOI 10.5281/zenodo.19648470 Pipeline SHA-256 8026f8d074e62e3305dc41ce1b863e6a6add493495641d262fb9d859ad0005cb Registration date 19 April 2026 Contributor Pretorius, Eugene Citations Pre-registration: Pretorius, E. (2026, April). Discrete Substrate Signatures in the Arabidopsis Circadian Transcriptome: A Triadic Derivation and Empirical Non-Falsification Program for Kinetic Substrate Structure in Circadian RNA-seq. Open Science Framework. [10.17605/OSF.IO/B4R3W] Pipeline: Pretorius, E. (2026). GRADIENT-3 Pipeline v1 OFFICIAL [Software]. Zenodo. [10.5281/zenodo.19648448] SHA-256: 8026f8d074e62e3305dc41ce1b863e6a6add493495641d262fb9d859ad0005cb Journal Article IV(a): Pretorius, E. (2026). Gradient Physics: An Ontological-First Derivative Science — Journal Article IV(a) — Discrete Substrate Signatures in the Arabidopsis Circadian Transcriptome: Empirical Instantiation of the Triadic Kernel in the SRP222555 RNA-seq Dataset [Preprint]. Zenodo. [10.5281/zenodo.19648470] Title Discrete Substrate Signatures in the Arabidopsis Circadian Transcriptome: A Triadic Derivation and Empirical Non-Falsification Program for Kinetic Substrate Structure in Circadian RNA-seq — Pipeline, Data, and Pre-Registration Archive Description Overview GRADIENT-3 is the third 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 (v1 OFFICIAL), the three-regime Gate B audit results across 20,683 Arabidopsis thaliana genes from the circadian RNA-seq dataset SRP222555 (PRJNA566413; GEO: GSE137732; Xin et al. 2019 Plant Cell), and the complete pre-registration metadata to be registered on OSF. The ontological derivation chain is published in full in Journal Article IV(a): Primordial Axiom of Relationality → Triad → {E=4/5, C=7/10, F=3/5} → TI=42/125 → β=13/40 → Φ=0.002 → Δ=0.7016 → r=√(14/9)=1.2472 → H1–H5 + GC-1–GC-5 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 = 1/10). They are not calibrated to data. The universality class exponent β = 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 β = 13/40 — the unique lattice-consistent value producing a viable non-dissipative Kinetostatic Margin Φ = 0.002. The three Triadic primitives map exactly to the GRADIENT-3 empirical protocol: Systematization E = 4/5: Drive (D). Forcing magnitude |⟨z_LD⟩| of each gene — the mean absolute departure of a gene's LD expression from its zero-gradient CL baseline across the full 16-ZT time course. Genes are assigned to three equal forcing-magnitude tertiles before any test statistic is computed. Constraint C = 7/10: Limit (L). The zero-gradient CL reference. μ_CL(g) and σ_CL(g) — the mean and standard deviation of gene g in continuous-light samples — constitute the biological Constraint condition. They define the Heaviside threshold against which LD forcing residuals are measured. Registration Frequency F = 3/5: Registration (R). Discrete ZT expression events per gene per chronon in the circadian time course. The derived signal z(g,ZT) = [log₂(TPM_LD(g,ZT)+1) − μ_CL(g)] / σ_CL(g) is the primary Registration observable — the circadian forcing residual in units of the zero-gradient noise floor. The Derived Biological Consequences IMPORTANT: This preregistration does not disclose contingent probe parameters. All predictions below are derived from {E=4/5, C=7/10, F=3/5, δ=1/10} by exact rational arithmetic before any expression data was examined. They are necessitated by the Triadic structure, not chosen to fit the data. Where the OSF preregistration format invites disclosure of calibration constants or contingency parameters, this submission distinguishes: (a) Hardlock-derived constants [H] — immutable, zero free parameters; (b) pipeline engineering choices [C] — standard methodological procedures pre-declared before data contact; (c) the derived probe logic — which is not contingent. Derived from the Hardlock constants before the SRP222555 dataset was examined: GC-5 — Wegner Power Law: kw ~ |⟨z_LD⟩|^(11/10). Predicted log-log slope = 11/10 = 1.100 [H] (exact rational, derivable before data contact). κ_exp = 5 × α_Wegner = 5 × 11/50 = 11/10. No framework in circadian biology predicts how gene kurtosis scales with forcing magnitude. GC-3 — N_sat = 25 Substrate Clustering: k-means on the 20,683-gene × 16-ZT z_LD matrix yields elbow at k = N_sat = 25 ± 2. N_sat = 1/φ = 1/(σ×δ) = 25 [H]. Exact rational, zero free parameters. GC-2 — Snap Phase Clustering: Alpine gene snap events (|z_LD(g,ZT)| > r = 1.2472 [H]) cluster at ZT15–ZT21 (dark-phase onset and mid-dark phase in LD 16:8). Phase preference driven by clock output cascade timing. 8 pre-registered ZT phases, Bonferroni correction. GC-4 — DC Likelihood on Harmonic Residuals: Δℓ > 0 on residuals after subtracting best-fit harmonic regression (24h + 12h fixed periods). Harmonic periods are fixed by circadian biology — not free parameters. The DC formula uses Λ, Δ, r [all H], zero free parameters. GC-1 — GO-Term Independent Regime Validation: H1–H5 ordering holds when gene regime is assigned from Gene Ontology annotation (GO:0007623, circadian rhythm) rather than |⟨z_LD⟩|. This provides a fully independent regime axis and confirms structural independence of the probe from the expression signal. Preliminary Biological Confirmation The following results are audit-locked Gate B values (16 April 2026). They are not preliminary; they are the pre-registered test outcomes for the Gate B hypotheses. Gate C items remain blinded pending OSF timestamp. H3 Snap Fraction — r = √(14/9) [H] (Gate B confirmed): Predicted threshold r [H] 1.247219 = √(14/9); derived from σ_ratio² = 1 + ε_snap²/Φ = 14/9 CL null rate (empirical) 21.05% (theoretical N(0,1): 21.23%) — calibration CONFIRMED Alpine snap rate 77.55% | excess 3.68× null Flat snap rate 44.14% | excess 2.10× null CoLocated snap rate 18.43% | excess 0.88× null (BELOW null — actively buffered) Gradient order Alpine > Flat > CoLocated CONFIRMED Free parameters ZERO — r [H] derived before data contact H4 DC Likelihood Ratio — Λ, Δ, r [H] (Gate B confirmed): Λ (Lambda) [H] 0.298447 = 1 − TI^β Δ (Delta) [H] 0.701553 = TI^β r [H] 1.247219 = √(14/9) DC exp coefficient [H] 5/28 = (1−1/r²)/2 exact rational Alpine DC-win rate 100.0% (6,894 / 6,894 genes) Flat DC-win rate 99.4% (6,857 / 6,895 genes) CoLocated DC-win rate 20.4% (1,403 / 6,894 genes) — null-consistent Free parameters ZERO — all constants [H] derived before data contact These results confirm that the Dirac Comb substrate structure is present in the forcing residuals of the SRP222555 circadian RNA-seq dataset, that the snap fraction in Alpine genes exceeds the Hardlock-derived threshold r by 3.68× the zero-gradient null rate, and that the Dirac Comb model with fixed Hardlock constants separates the gene regime classes with complete discriminability. None of these predictions were adjusted after data contact. Hypotheses (H1-H5 Foundational Lock + Gate C Biological Predictions) H1: Per-gene kurtosis of z_LD(g) ordered monotonically by Drive regime (CoLocated < Flat < Alpine). Derived from Heaviside threshold on L producing non-Gaussian temporal forcing profiles in strongly forced genes. Test: Jonckheere-Terpstra, α = 0.001, one-tailed. H2: Super-white variance scaling (α > −1.000) on the gene forcing-magnitude axis. Derived from non-zero gene-gene covariance forced by circadian module co-regulation — the biological analog of Registration footprint autocorrelation. H3: Per-observation snap fraction using threshold r = √(14/9) = 1.2472 [H] follows Alpine > Flat > CoLocated, with empirical CL null rate ≈ 21.2% consistent with z_CL ∼ N(0,1). Zero free parameters. H4: Per-gene Dirac Comb log-likelihood ratio: DC-win fraction (sum Δℓ > 0) follows Alpine > Flat > CoLocated. Λ = 0.2984 [H], Δ = 0.7016 [H], r = 1.2472 [H]. Classical Gaussian null demolished for Alpine gene class. H5: The z-field is continuously distributed (n_unique/n_total > 0.99). N-GM grain-size bound: f_lattice > 1 ZT chronon (3h) for all genes. No quantisation at the measurement cadence. GC-5: kw ~ |⟨z_LD⟩|^(11/10). Predicted log-log slope 1.100 [H] inside 95% CI of empirical OLS slope. GC-3: k-means elbow at k = N_sat = 25 ± 2 on the z_LD gene×ZT matrix. N_sat = 25 [H]. GC-2: At least 80% of Alpine snap events cluster at ZT15–ZT21 (dark-phase onset). 8 pre-registered ZT phases, Bonferroni correction. GC-4: Δℓ > 0 on per-gene z_LD residuals after subtraction of best-fit harmonic model (24h + 12h fixed periods). Zero free parameters. GC-1: JT ordering CoLoc < Flat < Alpine holds when gene regime is assigned from GO:0007623 circadian rhythm annotation independently of |⟨z_LD⟩|. Three-Regime Endpoints Alpine (High Drive, top forcing tertile): 6,894 genes. Forcing magnitude |⟨z_LD⟩| ≥ 1.5352. N observatio