The Principia Mathematica Veritatis: High-Density Geometric Data Compression and Reversible Logic Encoding via 0MXI Calculus

This document serves as the formal Technical Specification (v4.0.1) for the Principia Mathematica Veritatis, a high-efficiency encoding protocol for geometric and logical data.The framework introduces the Principia Omega scheme, a deterministic model-based encoder that utilizes Reversible Affine Contraction Mappings specifically the Omega Operator Ωand its inverse (Ξ) to compress complex nonlinear structures into linear scalars.Key Contributions:• The 0MXI Numeric Policy: A foundational axiom enforcing strict 15-decimal atomic truncation (τ₁₅)to eliminate floating-point drift and ensure cross-platform determinism.• The 0MXI Calculus: A novel method for managing quantization residuals (δ₀ₘₓᵢ), allowing for "Bit-Perfect Reconstruction" of original data from compressed Newman Coordinates.• Geometric Compression: Protocols for sealing elliptical curvature within the enforced "Newman Horizon"(vₘₐₓ)• Logic Encoding: A runtime integrity protocol for sealing computational proofs.• Fundamental Theorem of Principia Omega: The mathematical proof governing the relationship between the model, the coordinate, and the residual string.This specification includes fully deterministic reference implementations in Python and Julia.