Pre-Registration: Predicting Node of Ranvier Spacing from the Geometric Threshold ln(3) — A Stochastic Geometric Dynamics (SGD) Framework Application
Description
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.
Notes
If validated, this prediction will establish ln(3) as a Geometric Constitution—a fundamental constraint that transcends the boundary between physics, engineering, and biology. While the previously reported seven systems (including vehicular traffic, battery thermal runaway, and soft-ground consolidation) are governed by different PDEs, a successful prediction for myelinated nerve fibres—governed by the cable equation—would solidify the geometry-first principle of Stochastic Geometric Dynamics (SGD).
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Related works
- Is supplement to
- Preprint: arXiv:2603.15521 (arXiv)