Regular Simplex Hierarchical Gravity Part I: Geometric Derivation of the Gravitational Constant and Resolution of the Cosmological Constant Problem

We derive the gravitational constant G and the cosmological constant from first principles, requiring zero adjustable parameters, by analyzing the geometric frustration inherent in 600-cell tessellation of four-dimensional space. When five regular tetrahedra meet at a shared edge, they fail to close by a deficit angle 7. 36^, generating intrinsic curvature without requiring external embedding dimensions. Combining Israel junction conditions with Regge calculus, we obtain G = 6. 60 10^-11 m³/ (kgs²), achieving 1. 1\% agreement with the observed value—a precision unprecedented for parameter-free derivations. We introduce the concept of informational Pauli repulsion—the inevitable information collision during dimensional reduction from infinite to three dimensions—which serves as the physical driver of cosmic expansion and will be detailed in Part II as the origin of dark energy. The 122-order-of-magnitude discrepancy between quantum field theory's vacuum energy prediction (10^113 J/m³) and observation (10^-9 J/m³) is resolved to within a factor of two via holographic screening: a global information overlap factor ₆₋₎₁₀₋ 10^122 suppresses the bare frustration energy. This geometric framework establishes the foundation for Part II's derivation of the Light-Speed Resource Allocation Principle (LRAP) and the reinterpretation of black hole singularities as computational arrest zones, culminating in Part III's proof that six-fold hierarchical jamming transitions are arithmetically necessary to maintain thermodynamic stability.