The missing triangle: Maxwell, Shannon and Boltzmann in adaptive coherence

This working paper proposes the EICI framework as the formal criterion that connects Maxwell (E), Shannon (I), and Boltzmann (F) as joint predictors of adaptive coherence — a connection that Prigogine's dissipative structures and Mandelbrot's fractal geometry each approached but did not explicitly formalize. EICI = Eₙ × Iₙ / Fₙ is presented as a candidate hypothesis, not a proven physical law. The paper explicitly separates three epistemological levels: formal (structural hypothesis), empirical (exploratory cross-scale operationalization), and philosophical (interpretive framing). Planetary biosignature application reserved for future dedicated paper. Supplementary S1 provides formal mathematical development including bifurcation ODE, critical slowing down (τ → ∞), Shannon SNR mapping, Boltzmann entropy export condition, and Sobol sensitivity definitions. Author: C.J. Pérez Pulido, ISHEA Institute, Bologna. Deposited May 2026 as child component of K-Model parent project WST24 (August 2025).