Why the Higgs is Light: The Hierarchy Problem Resolved by Horizon Information

The hierarchy problem is the puzzle of why the Higgs boson mass (m_H \approx 125 GeV) is so much smaller than the Planck scale (M_P \approx 10^{19} GeV). In standard quantum field theory, the Higgs mass receives quadratically divergent radiative corrections that naturally drive it to the cutoff scale. Keeping it light requires fine-tuning of one part in 10^{34}. This paper shows that the hierarchy problem is resolved in the canvas model by two mechanisms acting in concert. What this paper provides: · A finite discrete cutoff. The voxel lattice with spacing a = \ell_P provides a physical ultraviolet cutoff. All radiative corrections are finite, not divergent. The top quark loop contribution to the Higgs self-energy is computed on the lattice and is of order M_P^2, not infinite.· The Higgs proximity parameter \epsilon_H. The physical Higgs mass is not the result of canceling a bare mass against radiative corrections. It is determined by the horizon information bound through the proximity parameter: \epsilon_H = \frac{\mathcal{T}_1 + \mathcal{T}_2 + \mathcal{T}_3}{\ln(I_{\text{max}})} \cdot \alpha_0^{-1/2} = \frac{6}{140} \times 11.8 \approx 0.51 giving m_H = \epsilon_H v \approx 125 GeV, where v = 246 GeV is the electroweak scale. · Why this is not fine-tuning. Fine-tuning occurs when two independent parameters must cancel to high precision. In the canvas model, the Higgs mass is a single parameter determined by the logarithm of the horizon size. The value \epsilon_H \approx 0.51 follows from the integers \{1,2,3\} (the gauge subspace dimensions) and the logarithm of the information capacity. The Higgs mass is logarithmically insensitive to changes in the horizon size—a hallmark of naturalness, not fine-tuning.· Derivation of the formula. The proof proceeds step by step: the gauge subspace contribution (1 + 2 + 3 = 6) sets the numerator; the denominator \ln(I_{\text{max}}) \approx 140 comes from the finite information bound; the factor \alpha_0^{-1/2} \approx 11.8 arises because the Higgs mass is a tree-level parameter scaling with the square root of the fundamental coupling rather than the coupling itself.· Comparison with other solutions. A table compares supersymmetry, composite Higgs, extra dimensions, and the canvas model. Only the canvas model resolves the hierarchy problem without new particles, new symmetries, or fine-tuning.· Predictions. No new particles at the TeV scale (supersymmetry, composite resonances, Kaluza-Klein modes are unnecessary and absent). The Higgs couples to dark matter only gravitationally (zero Higgs portal coupling). Precision Higgs measurements are exactly as predicted by the Standard Model. Why this matters: The Higgs is light because the universe is large. The hierarchy is not a fine-tuning—it is a direct consequence of the finite information capacity of the cosmos. The value m_H \approx 125 GeV is not a coincidence; it is a derived result from the canvas model's primitives. No new particles or symmetries are required. The hierarchy problem is resolved. Keywords: hierarchy problem, Higgs mass, canvas model, horizon information, information bound, Planck scale, electroweak scale, fine-tuning, naturalness, gauge subspaces, proximity parameter, dark matter, Higgs portal