Consciousness as Criticality: Many-Body Effective Potential Unifies Mind and Sustainability Transitions — E8 Intelligence Research

FINDING: Consciousness arises from a causally complete many-body interaction solution via extended effective potential, linking criticality to sustainability transitions. | MATH: Extended effective potential method; many-body problem solved without perturbation/integrability constraints; critical transition points emerge from multi-component dynamics. | CONNECTION: None explicit; however, criticality in multi-component systems often exhibits universal scaling exponents (e.g., 0.5 mean-field, 0.618-like in some self-organized critical models) — but no direct geometric ratio stated. | DEPTH: 4 (broad claim, mathematically vague in abstract; no explicit constants or ratios). --- FINDING: Claimed theorem: \( P = 6^{m+1} \cdot N - 1 \) is prime for \( 1 < N \le 13, N \ne 8 \), with exclusion \( N \ne i^{m+1} \bmod (6i+1) \), \( i \in \mathbb{Z}^+ \), \( m \) odd positive. | MATH: \( P = 6^{m+1}N - 1 \); modular exclusion condition \( N \not\equiv i^{m+1} \pmod{6i+1} \). Base-6 structure ( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com