The Holographic Circlette: Part 20 — Newton's Constant from Holographic Self-Consistency of the 4.8.8 Lattice

Audit note. This paper derives the Planck mass via holographic self-consistency between 4.8.8 node geometry and the Friedmann equation, yielding M_P^2 = 24\pi\alpha^2\Lambda_{\text{QCD}}^3/(H_0\Omega_\Lambda) at 0.07\% numerical agreement with CODATA. The exact algebraic theorems of §§2--4 (silver-ratio area cancellation, Euler-characteristic flatness, holographic trap identity) are immune to formula-freedom audit. However, the gravitationally active vacuum energy E_{\text{vac}}^{\text{grav}} = \tfrac{3}{4}\alpha^2\Lambda derived in §6 is assembled post-hoc from three independently motivated but phenomenologically coupled parameters (S_{\text{vac}} from Part 16, a structural fraction 3/4 from R1--R4 counting, and a radiative-coupling factor \alpha^{-1}) into a screening factor \mathcal{S} = 458.15. The walk-operator self-energy derivation of \mathcal{S} from first principles is currently open. Per t The Planck mass follows from holographic self-consistency: M_P^2 = 24*pi*alpha^2*Lambda_QCD^3 / (H0*Omega_Lambda), yielding M_P=1.2217e19 GeV (0.07% error). The vacuum energy density rho_Lambda=9*alpha^2*Lambda_QCD^3*H0 matches observation exactly, resolving the cosmological constant problem. The 4.8.8 tiling has zero Euler characteristic, making spatial flatness topologically inevitable. v2.0 (2026-06-12): an in-PDF dated status/erratum note has been added reflecting the June 2026 canon audit (DRIFT/ANCHOR ledger); see the paper's status note for the specific corrections, supersessions, or upgrades. 2026-06-20 legacy canon revision: This is a canon-reconciled legacy version. Planck-mass route superseded by proton-primary/selector analysis The paper retains its historical derivation trail but carries a 2026-06-20 canon revision note identifying current status and superseded claims.