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Pre-Registration: Predicting Node of Ranvier Spacing from the Geometric Threshold ln(3) — A Stochastic Geometric Dynamics (SGD) Framework Application

Authors: Ji, Jian;

Pre-Registration: Predicting Node of Ranvier Spacing from the Geometric Threshold ln(3) — A Stochastic Geometric Dynamics (SGD) Framework Application

Abstract

This document constitutes a formal a priori predictive pre-registration under the framework of Stochastic Geometric Dynamics (SGD). Based on the 1D Poisson bilateral coordination theorem—which identifies λℓ = ln(3) ≈ 1.0986 as the exact geometric threshold for bidirectional functional stability—we predict the morphometric scaling of vertebrate myelinated nerve fibres. Specifically, the ratio of cable space constant to Node of Ranvier spacing should satisfy λ_cable / d_node = ln(3), with a predicted error margin of < 15%. This prediction is deposited prior to any meta-analysis of electrophysiological or histomorphometric literature by the author. Companion manuscript: Ji, J. (2026), PRL submitted (LQ20428). Pre-registration timestamp on Zenodo constitutes the L1 record.

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