Cosmological Constant, Hubble Horizon, and the Parameter Λ_PEW = log_φ(1/α_em) in the PEW Framework

We derive the cosmological constant Λ_cosmo within the Primordial Energy Wave(PEW) framework by unifying three previously separate results: (i) the relationΛ_cosmo ∝ ²_min (ATPEW V4, §6.1); (ii) the dimensionless parameterΛ_PEW ≡ log_φ(1/α_em) = 10.2247 (Article 10); (iii) the harmonic tableλ_n = l_P·(1/α_em)^n (Article 10). The missing link is the identification of the harmonic level of the Hubblehorizon: n_H = log(L_H/l_P)/log(1/α_em) = 28.5137. This yields the central formula:Λ_cosmo = 3·Ω_Λ·l_P⁻²·α_em2n_H with a residual of 0.11% relative to Planck 2018, with no free parameter.Equivalently, Λ_cosmo = 3·Ω_Λ·l_P⁻²·φ−2n_H·Λ_PEW, showing that thecosmological constant is encoded in the arithmetic structure of the primordialfield. This result replaces the cosmological conjecture of Article 10 (§9, 75%agreement, status [D]) with a rigorous derivation at 0.11%, and partiallycloses open problem PO-Λ of Article 1. The complete dynamical derivation(PO-Cosmo) remains the subject of Article 12. Epistemic status: [C] n_H = 28.5137 (numerically validated); [C] centralformula 0.11% agreement; [A] n_H = n_H,φ/Λ_PEW (analytically exact);[D] dynamical derivation from Friedmann-PEW (Article 12). MSC: 83F05 · 83C55 · 81V25 · 11K55 PACS: 98.80.-k · 98.80.Bp · 06.20.Jr