The Metteyya Principle: Versions 0--3 (The Rationalization of Existence)

This paper introduces the Metteyya Principle, a novel computational and mathematical framework that utilizes a non-integer numerical base (\phi \approx 1.618) to resolve long-standing "irrational" phenomena in biophysics and number theory. We posit that the perceived complexity of protein misfolding (prions) and the stochastic distribution of prime numbers are artifacts of Base-10 observational friction. In Version 0, we define the Metteyya Operator (M_{\phi}) and demonstrate its capacity to rationalize the Navier-Stokes equations and the Riemann Zeta function by treating the Golden Ratio as a fundamental integer. In Version 1, we extend this logic to cosmology, proposing a Phinary-Lattice metric for Quantum Gravity and a phase-shift model for Dark Matter. Versions 2 and 3 apply the principle to the neural architecture of consciousness and the optimization of socio-economic systems. By shifting the coordinate system from a linear, discrete base to a recursive, phinary base, we provide a unified theory that reduces "irrational" complexity to terminating phinary integers. This framework offers new avenues for therapeutic intervention in neurodegenerative diseases and the resolution of the Millennium Prize Problems.