Deterministic Solution to the N-Body Problem Through the Sexagesimal Harmony Algorithm and Maat's Zero-Entropy Metric

This document presents Volume I of an advanced research proposal titled "Deterministic Solution to the N-Body Problem Through the Sexagesimal Harmony Algorithm and Maat's Zero-Entropy Metric". Authored as part of an academic initiative at the Faculty of Sciences, School of Physics of the University of Costa Rica (2026), the work addresses the classical non-integrability of the N-body problem in celestial mechanics—a limitation highlighted by Poincaré's Non-Integrability Theorem due to infinite residual divergence in decimal arithmetic. The proposal introduces a novel mathematical framework combining the Sexagesimal Harmony Algorithm (SHA) and the Maat Zero-Entropy Metric (M_60). By reformulating continuous phase space into the regular sexagesimal field (S_60) via the Sumerian Transformation Operator (O_sumer) and implementing the Co-Sexagesimal Resonance Filter (ψ Maat), the model absorbs nonlinear phase deviations using a Symmetric Compensation Tensor (τ^Maat). This approach neutralizes computational truncation errors and suppresses exponential Lyapunov divergence, establishing stationary equilibrium attractors and perpetual orbital periodicity for asymmetric 3-body systems and scaled macroscopic systems of up to N = 8640 bodies without numerical collapse.