Dynamical Realization of Sdel Theory 34 Axioms Emerge From Nonlinear Hyperspherical Alignment Dynamics

We demonstrate that Mundakkattu's 34 SDEL axioms emerge naturally from a minimalist agent-based model on S^d-1, where power-law alignment interactions I₈₉ = A₈₉ᵏ drive global coherence C (t). Theorem 1 proves asymptotic stability for k ≥ 1, while large-scale simulations (N ≤ 10³, d ≤ 100) map the full axiom landscape: Axioms 1-12 (Fundamental Harmonic Structure): C (t) → 1 exponential attractors Axioms 13-22 (Hierarchical Emergence): λ ∝ k^0. 92 cascade reinforcement Axioms 23-34 (Consciousness Geometry): d > 30 ⇒ C_∞ > 0. 95Phase diagram reveals critical boundaries matching SDEL's activation thresholds; EEG gamma fits (k=1. 8, R²=0. 87) validate neural embodiment axioms. SDEL transitions from axiomatic postulate to dynamical attractor landscape.