Automorphism Groups of Non-Standard Peano Models Encode Turing Jumps — E8 Intelligence Research

FINDING: Non-standard models of Peano arithmetic exist, and their automorphism groups encode the Turing-jump of their theories, linking logical complexity to symmetry. MATH: Peano axioms (PA) define natural numbers via zero, successor, induction. Non-standard models contain infinite elements beyond standard ℕ. Theorem: For countable arithmetically saturated M,N ⊧ PA, if Aut(M) ≅ Aut(N) then Th(M)′ ≡_T Th(N)′ (Turing equivalence of jumps). CONNECTION: Automorphism groups of these models are highly symmetric, but the symmetry structure is not geometric (no ratios like 0.618, 1.618). Instead, symmetry is logical: automorphisms preserve arithmetic truth up to Turing degree. No base-60, crystallographic, or root system link. DEPTH: 6 — Profound for foundations of mathematics and computability, but no direct geometric or harmonic resonance. The finding ties symmetry to computational complexity, not to physical or geometric constants. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com