We propose that 𝐻0 is not a constant but a scale-dependent parameter reflecting the ongoing creation of new cascade levels as the universe expands. In the Fractal Mechanics framework, new quantum nodes (qubits) emerge at rate ̇𝑛 = 𝐻 (𝑡) / ln 𝜑 as the universe grows, contributing to energy density as non-relativistic matter. This leads to the prediction: 𝐻0 (𝑧) = 𝐻0base × √1 + 𝛼/ (1 + 𝑧) ³ with 𝛼 = 0. 197 ± 0. 045. Fitting this single-parameter model to six independent 𝐻0 measurements spanning 𝑧 ≈ 0–1100, we obtain 𝜒²/dof = 0. 73, 𝑝 = 0. 569, and significance 4. 36𝜎 for 𝛼 ≠ 0, reproducing both CMB and local 𝐻0 values simultaneously. The model predicts 𝐻0 (𝑧 = 0. 5) ≈ 69. 6 km/s/Mpc and 𝐻0 (𝑧 = 1. 0) ≈ 68. 5 km/s/Mpc, testable with DESI and Euclid within 2029. Keywords: Hubble constant, Hubble tension, dark energy, cosmic expansion, cosmological parameters
Rémi Leroy (Tue,) studied this question.