Paper LXXXV: Q⋆from the Local Universe: Tidal Field Derivation from the Virgo Supercluster, Matter-Domination Invariance, and the Closure of As

The primordial scalar amplitude As = 2.101 × 10−9 is not a fundamental constant of nature. It is a property of the specic cosmic neighbourhood in which Fano- lattice condensation occurred, derivable from the Virgo Supercluster mass via a three- step chain requiring no free parameters. Step 1: the Newtonian tidal eigenvalue today, Tgrav,0 = GMeff/r3 UMa, with Meff= 1.77 × 1015 M⊙(Virgo Supercluster bound core at 17 Mpc). Step 2: matter-domination invariance Tgrav/H2 = const closes the apparent 105 epoch gap, giving Q⋆= Tgrav,0/(ΩmH2 0) = 1.089. Step 3: the G2 kinetic prefactor 1/(4αG2) cancels identically in the equations of motion, so fcoupling = 1. The derivation conrms As = Ziso/Zaniso×(H0/H⋆)4 exactly. We additionally present four independent derivations of the p 6/7 lensing factor, the full Fano projection formula (6.6), and the cobaya prescription for the joint Planck 2018 + KiDS-Legacy 2025 likelihood with √Feff as a zero-parameter model prediction. Prediction P20 is conrmed: the required Meff= 1.77 × 1015 M⊙lies within ∼10% of the observed Virgo Supercluster bound core mass.

Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.