The cosmological constant from the Galois structure of the Bunch-Davies vacuum: a parameter-free derivation of Omega_Lambda = 12 - 8 sqrt(2)

Version 2 (12 June 2026). Derivation of Omega_Lambda = 4/eps^2 = 12 - 8 sqrt(2) = 0.68629 (eps = 1+sqrt 2) with no adjustable parameters; G and the UV cutoff cancel identically. v2 reduces the hypothesis to its final form - modular crystallisation: the finite Gibbons-Hawking entropy of the de Sitter horizon realised algebraically as a discrete flow of weights (type III_{1/eps^2}); the ring Z[sqrt 2], the unit direction, the ladder, the value of lambda, and the contemporaneous (equal-time) anchoring are all now derived (joint Matsubara module of the two KMS flows at the self-dual point; flow-swap unit-selection lemma; J-closure selection theorem; Connes classification). New corollaries: Omega_m = 8 sqrt(2) - 11 = 0.31371 exact (-0.22 sigma Planck); z_eq,Lambda = 0.29816; eps^2 Omega_Lambda = 4; no-relock theorem (z* = 3.163) derives post-crystallisation constancy, forcing w = -1, w_a = 0 exactly. Internal fork retained: geometric branch 0.68399; discriminable at sigma