GRADIENT-4 Pipeline v1

GRADIENT-4: Zenodo Repository Metadata GRADIENT-4 v1 OFFICIAL | NeuroOPT — Gradient Noetic Optogenetic Probe | July 2026 REGISTERED — July 2026 Discrete Substrate Signatures in the C. elegans Whole-Brain Optogenetic Neural Activity Dataset: Empirical Instantiation of the Triadic Kernel in the Randi et al. (2023) Dandiset 001075 Neural Signal Propagation Atlas (Leifer Lab) Registered Record NeuroOPT v1 OFFICIAL | July 2026 OSF Pre-registration DOI 10.17605/OSF.IO/PBU8X Pipeline v1 DOI 10.5281/zenodo.21378393 Journal Article V(a) DOI 10.5281/zenodo.21378629 Pipeline SHA-256 9dbd25881d2325a06298ed3d2718c20037f6ebd1cb57fe65b6f27f032f76ab32 Registration date July 2026 Contributor Pretorius, Eugene Citations Pre-registration: Pretorius, E. (2026, July). Empirical Instantiation of the Triadic Kernel in the Randi et al. (2023) Dandiset 001075 Neural Signal Propagation Atlas (Leifer Lab) Open Science Framework. 10.17605/OSF.IO/PBU8X Pipeline: Pretorius, E. (2026). NeuroOPT Pipeline v1 OFFICIAL [Software]. Zenodo. 10.5281/zenodo.21378393 SHA-256: 9dbd25881d2325a06298ed3d2718c20037f6ebd1cb57fe65b6f27f032f76ab32 Journal Article V(a): Pretorius, E. (2026). Empirical Instantiation of the Triadic Kernel in the Randi et al. (2023) Dandiset 001075 Neural Signal Propagation Atlas (Leifer Lab) [Preprint]. Zenodo. 10.5281/zenodo.21378629 Dataset: Randi, F., Sharma, A. K., Dvali, S., & Leifer, A. M. (2023). Neural signal propagation atlas of Caenorhabditis elegans. Nature, 623, 406–414. https://doi.org/10.1038/s41586-023-06683-4 Title Discrete Substrate Signatures in the C. elegans Whole-Brain Optogenetic Neural Activity Dataset: Empirical Instantiation of the Triadic Kernel in the Randi et al. (2023) Dandiset 001075 Neural Signal Propagation Atlas (Leifer Lab) Description Overview GRADIENT-4 is the fourth physical instantiation of Gradient Physics, an ontological-first derivative science framework governed by three primitives: Drive (D), Limit (L), and Registration (R). This repository contains the hardlocked computational pipeline (NeuroOPT v1 OFFICIAL), the three-regime Gate B audit results across 12,806 neurons from 105 C. elegans worms from the whole-brain optogenetic calcium imaging dataset (Randi et al. 2023 Nature; Dandiset 001075; Leifer Lab, Princeton University), and the complete pre-registration metadata to be registered on OSF. The ontological derivation chain is published in full in Journal Article V(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 NeuroOPT empirical protocol: Systematization E = 4/5: Drive (D). Stimulus-triggered response magnitude Drive(n,w) = mean|Δz(n,w,s)| of each neuron — the mean absolute departure of a neuron's calcium response from its zero-gradient null baseline across all valid optogenetic stimulus trials s. Neurons are assigned to three equal Drive-magnitude tertiles per worm before any test statistic is computed. Constraint C = 7/10: Limit (L). The zero-forcing null reference. μ_null(n,w) and σ_null(n,w) — the mean and standard deviation of neuron n in worm w across all non-stimulus (null) frames — constitute the noetic Constraint condition. They define the Heaviside threshold against which stimulus-period forcing residuals are measured. Registration Frequency F = 3/5: Registration (R). Discrete calcium snap events per neuron per stimulus trial in the optogenetic chronon sequence. The derived signal z(n,w,t) = [dFF(n,w,t) − μ_null(n,w)] / σ_null(n,w) is the primary Registration observable — the stimulus-period forcing residual in units of the zero-gradient noise floor. The Derived Noetic 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 NWB calcium imaging 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 Randi et al. (2023) NWB archive was examined: GC-5 — Wegner Power Law: kw ~ Drive^(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 neuroscience predicts how per-neuron kurtosis scales with stimulus-triggered Drive magnitude. GC-3 — N_sat = 25 Substrate Clustering: k-means on the 12,806-neuron × n_frames z_dFF 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 Synchrony: Alpine neurons show synchronised snap events (|z(n,w,t)| > r = 1.2472 [H]) at pre-registered lags [0s to 6s post-stim, 8 lags], Bonferroni correction. Snap synchrony driven by network propagation following single-neuron optogenetic stimulation. GC-4 — DC Likelihood on Stimulus Residuals: Δℓ > 0 on per-neuron z_stim residuals after subtracting mean per-neuron stimulus response. Isolates snap structure from mean Drive signal. DC formula uses Λ, Δ, r [all H], zero free parameters. GC-1 — Named-Neuron NeuroPAL Regime Validation: H1–H5 ordering holds when neuron regime is assigned from NeuroPAL identity classification (sensory/interneuron/motor, confidence ≥ 0.70) rather than Drive-magnitude tertile. Provides a fully independent regime axis and confirms structural independence of the probe from the stimulus-response signal. Preliminary Noetic Confirmation The following results are audit-locked Gate B values (July 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 Null rate (empirical): 17.08% (theoretical N(0,1): 21.23%) — GCaMP photon-count floor confirmed; pipeline uses empirical null Alpine snap rate: 17.47% | excess 1.02× null | n=4,270 neurons Flat snap rate: 16.00% | excess 0.94× null | n=4,266 neurons CoLocated snap rate: 15.47% | excess 0.91× null (BELOW null — actively buffered) | n=4,270 neurons 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: 19.3% (824 / 4,270 neurons) Flat DC-win rate: 7.34% (313 / 4,266 neurons) CoLocated DC-win rate: 4.71% (201 / 4,270 neurons) — 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 stimulus-period forcing residuals of the Randi et al. (2023) C. elegans optogenetic calcium imaging dataset, that the snap fraction in Alpine neurons exceeds the Hardlock-derived threshold r at 1.02× the zero-Drive null rate (with CoLocated below null — actively buffered), and that the Dirac Comb model with fixed Hardlock constants separates the neuron regime classes with monotonic gradient ordering. None of these predictions were adjusted after data contact. Hypotheses (H1–H5 Foundational Lock + Gate C Noetic Predictions) H1: Per-neuron kurtosis of the trial chronon sequence Δz(n,w,s) ordered monotonically by Drive regime (Alpine < Flat < CoLocated, platykurtic direction). G3-class: Alpine neurons respond at every stimulus with large Δz → platykurtic (low kw); CoLocated neurons show rare small excursions → leptokurtic (high kw). Test: Jonckheere-Terpstra, α = 0.001, one-tailed. Median kw is the primary descriptive statistic; JT is the sole inferential test. H2: Super-white variance scaling (α > −1.000) on the neuron Drive-magnitude axis. Derived from non-zero neuron-neuron covariance forced by network connectivity — the noetic analog of Registration footprint autocorrelation. H3: Per-observation snap fraction using threshold r = √(14/9) = 1.2472 [H] in stimulus response windows follows Alpine > Flat > CoLocated, with empirical null rate from z_null frames. Zero free parameters. H4: Per-neuron Dirac Comb log-likelihood ratio: DC-win fraction (Σ Δℓ > 0) follows Alpine > Flat > CoLocated. Λ = 0.2984 [H], Δ = 0.7016 [H], r = 1.2472 [H]. Classical Gaussian null demolished for Alpine neuron class. H5: The resp_arr global pool (trial chronon sequence Δz, Alpine neurons) is continuously distributed (n_unique/n_total > 0.99). CLT rationale: resp_arr = mean(z_post ~10 frames) − mean(z_pre ~10 frames) suppresses per-frame photon-