The dimensionless stability threshold g = 33 appears across Wigner crystallization of the electron gas (rₛ^* ≈ 30–40), coherent conformational waves in neuronal microtubules (minimum stable segment 33 × 8 nm = 264 nm), and Fibonacci lock-in in plant phyllotaxis (8–13 primordia). In this work the threshold is derived bottom-up from contact geometry on a 3-manifold. The orthogenetic recurrence w (k+3) = w (k+2) + w (k+1) + w (k) yields the Tribonacci polynomial P (η) = η³ − η² − η − 1 (η ≈ 1. 839) and the topographical weight η^-k. This weight geometrizes both the Hilbert-space inner product ⟨j|k⟩ = η^-k δ₉₊ and the geometric Born rule PG (k) = |cₖ|² η^-k. Microscopically, the curvature plane of the contact distribution ker α is realized by non-Abelian anyons. Ising fusion rules, F-symbols, and hexagon equations furnish the 2D topological memory; Fibonacci anyons supply the universal generative grammar. The companion matrix, Jordan form, and Reeb flow close the loop between microscopic braiding and macroscopic orthogenetic stability. Scales (generational index k) and domains (local contact regions) extend the same structure to universal grammar, measurement omission, type discipline, and mathematical economy. The framework converges with Palmer’s Rational Quantum Mechanics (16 March 2026) and Navrátil’s Geometric Quantum Mechanics (4 April 2026) within a three-week window. All operator algebra is formally verified in Lean 4 via the AXLE engine. Explicit falsifiability conditions are stated for each domain. This is the 13th deposit in the Principia Orthogona series (Monster 13).
Grossi Pablo (Wed,) studied this question.