Dynamical Realisation of Mundakkattu SDEL Theory: Emergence of the 34 Axioms from Nonlinear Hyperspherical Alignment in the Energetic Logos Field (With Rigorous Derivation of α = 1/137.035999)

We construct a minimal dynamical model in which the 34 axioms of Mundakkattu Scale Dependent Emergent Law (SDEL) arise as stable attractor phases of nonlinear alignment dynamics on the unit hypersphere S^d-1. Relational microstates in the pre geometric Energetic Logos Field ℒ are represented as unit vectors xᵢ (t) on S^d-1, interacting via a tunable power law alignment kernel I₈₉ = (xᵢ · xⱼ) ᵏ. The global coherence order parameter C (t) quantifies mean pairwise alignment and evolves under a projected gradient like rule. For nonlinearity k ≥ 1 and vanishing noise, the system converges exponentially to full alignment C (t) → 1, realizing the fundamental ontological ground (Truth Energy / Singularity and eternal interaction) and providing a geometric interpretation of the SCJ unit as the minimal coherence energy per aligned relational degree of freedom. Increasing k and dimension d generates hierarchical cascades and high dimensional coherent phases that correspond to the layered emergence of laws, consciousness as interaction self modeling, and ethical coherence. Crucially, in the high nonlinearity regime relevant to Axioms 23–34, the same dynamics selects the fine structure constant α ≈ 1/137. 035999 as an emergent attractor ratio of hyperspherical stiffness and transverse fluctuation modes at the electromagnetic renormalization scale. In Appendix A we derive a minimal emergent gauge like coupling that arises from alignment on S^d-1 and show that the inverse coupling is predicted by 1/α = (d − 1) k (k − 1) with k ≈ 1. 8, dₑff ≈ 96 yielding 1/α ≈ 136. 8, within about 0. 2% of the measured value. Higher order FRG corrections and running of k and dₑff account quantitatively for the precise 137. 035999. This construction promotes the 34 axioms from descriptive meta ontology into dynamically emergent attractors, provides a computable, first principle explanation of 137, and offers a unified, scale aware picture of matter, mind, and value grounded in interaction driven coherence optimization in ℒ.