Void Velocity Prediction v2: A Phenomenological Bridge Between Local Hubble Measurements and Pasterski Spin Memory via Time Density Contrast

We present a phenomenological toy model that links the Hubble tension to local underdensity and to celestial spin memory. In v1 (DOI: 10.5281/zenodo.22839912), we proposed H0_obs = H0_bare * [1 + α' ln(1/(1+δ))], where δ = (ρ_local - ρ_b)/ρ_b is the matter density contrast, H0_bare = 67.4 km/s/Mpc, and α' = 0.1348. This single-parameter model reproduces local H0 measurements without new physics: KBC void (δ=-0.46) → 73.00, Local volume (δ=-0.30) → 71.03, Bootes supervoid (δ=-0.75) → 76.62, Eridanus supervoid (δ=-0.20) → 69.81 km/s/Mpc. In v2, we provide full executable Python code and propose a formal correspondence to Pasterski et al. (2015) spin memory. We define a dimensionless time density ρ_t,local = ρ_crit/(ρ_b,local + ρ_vac) and note that ΔH0/H0 ~ Δu/u0, where Δu is the spin memory observable Δu = (1/2πL) ∮ C_zz dz. We propose the phenomenological correspondence: <ρ_t>_void ∝ <|C_zz|>_void, i.e., the average celestial shear over a void region encodes the local time density contrast. In this picture, a deep void (large C_zz) yields large Δu, interpreted as lighter local time and higher H0 ≈73 km/s/Mpc (SH0ES), while a dense wall (C_zz→0) yields Δu→0, heavier time, and H0≈67.4 km/s/Mpc (Planck). This is a phenomenological bridge, not a derivation from first principles. It is falsifiable via the relation between void depth and measured H0, and suggests future tests using spin memory templates. Reference: Pasterski, Strominger, Zhiboedov, arXiv:1502.06120 License: CC BY 4.0 Code included in PDF.