What question did this study set out to answer?

The aim is to show how Mundakkattu's 34 SDEL axioms emerge from an agent-based model on hyperspheres.

April 21, 2026Open Access

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

Key Points

The aim is to show how Mundakkattu's 34 SDEL axioms emerge from an agent-based model on hyperspheres.
Utilized a minimalist agent-based model on S^{d-1} for simulations.
Analyzed power-law alignment interactions driving global coherence with varying dimensions.
Performed large-scale simulations up to 1000 agents to map axiom landscapes.
Demonstrated that global coherence approaches 1, revealing exponential attractors.
Found that cascade reinforcement in hierarchical emergence follows λ ∝ k^{0.92}.
Identified critical boundaries in the phase diagram that align with SDEL activation thresholds.

Abstract

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.

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

Key Points

Abstract

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