The Baryon Acoustic Scale at Rung 198 of the Planck Doubling Ladder: A Prediction for the Hubble Constant

In the tetrahedral-octahedral lattice (TOT) counted from the Planck length, rung N has edge a(N) = lP·2N and octaradius (center-to-vertex radius of its octahedron) R(N) = a(N)/√2. The same reading that places the proton charge radius on rung 66 — rp as the octaradius, raw address log₂(rp/lP) = 65.496 — places the baryon acoustic oscillation (BAO) sound horizon on rung 198: R(198) = 148.79 Mpc against rd = 147.09 ± 0.26 Mpc (Planck 2018), raw address 197.483. 198 = 3 × 66. Since BAO surveys measure only the product h·rd, identifying rd with R(198) fixes the Hubble constant: with DESI DR2, h·rd = 101.54 ± 0.73 Mpc, we obtain H₀ = 68.2 ± 0.5 km s⁻¹ Mpc⁻¹ (68.4 with the bare-to-dressed correction (1 + α/3) used for the proton in this series). The value sits with the early-universe determinations and 4.2σ below the Cepheid-calibrated distance ladder. The weak point is stated explicitly: R(198) exceeds the rd inferred from the CMB within ΛCDM by 1.2 % (0.9 % with the correction), i.e. 5–6σ. We give the look-elsewhere estimate, a negative control test, and two ways to falsify the claim. Book, interactive 3D model of the lattice and the open laboratory: https://theoryof.space