Regular Simplex Hierarchical Gravity Part I: A Dimensional Reduction Theory of Gravity

We present Regular Simplex Hierarchical Gravity (RSHG), an informational cosmology that derives the gravitational constant GG G from first principles with zero free parameters. The theory originates from a single observation: quantum entanglement and the Pauli exclusion principle, which appear mutually contradictory, are in fact two physical expressions of the same mathematical fact — the impossibility of filling three-dimensional space with regular tetrahedra. We term this identification Axiom Zero. The algebraic foundation is supplied by Niven's theorem (1956): since arccos⁡(1/3)/π\arccos(1/3)/\pi arccos(1/3)/π is irrational, the packing deficit δ=2π−5arccos⁡(1/3)≈7.36°\delta = 2\pi - 5\arccos(1/3) \approx 7.36° δ=2π−5arccos(1/3)≈7.36° cannot be annihilated by any computational process, whether the underlying space is continuous or discrete. This ineliminable frustration forces an escape to four dimensions, where the unique regular closure preserving the local topology of three-dimensional frustration is the 600-cell (H4H_4 H4 symmetry, order 14,400). The projection of this four-dimensional elastic structure onto the observable three-dimensional brane — isomorphic to frictionless jamming as established by O'Hern et al. (2003) — manifests the geometric tension as force chains, which we identify with gravity. From arccos⁡(1/3)\arccos(1/3) arccos(1/3) and the spatial dimension n=3n = 3 n=3 alone, combining depth-weighted vertex counting, exact projection isotropy (⟨sin⁡2θ⟩=3/4\langle\sin^2\theta\rangle = 3/4 ⟨sin2θ⟩=3/4 under H4H_4 H4 symmetry), uniform redundancy (cluster coefficient 5/115/11 5/11), and a stress inertia rate η=3α/2T\eta = 3\alpha/2T η=3α/2T uniquely fixed by dimensional constraints, we derive the effective vertex count Ωlocal≈100.000069\Omega_{local} \approx 100.000069 Ωlocal≈100.000069. Substituting into the Israel junction condition framework yields G=6.60×10−11 m3/(kg⋅s2)G = 6.60 \times 10^{-11}\ \mathrm{m^3/(kg \cdot s^2)} G=6.60×10−11 m3/(kg⋅s2), in 1.1% agreement with the CODATA 2018 value, with zero adjustable parameters. Holographic screening by the factor Ωglobal∼10122\Omega_{global} \sim 10^{122} Ωglobal∼10122 resolves the cosmological constant problem to within a factor of 3.3. The H4H_4 H4 symmetry of the 600-cell predicts systematic deviations ΔCℓ/Cℓ≈0.05\Delta C_\ell/C_\ell \approx 0.05 ΔCℓ/Cℓ≈0.05–0.100.10 0.10 at multipoles ℓ=120n\ell = 120n ℓ=120n in the CMB angular power spectrum, consistent with an anomaly near ℓ≈120\ell \approx 120 ℓ≈120 independently reported in Planck and WMAP data.