Quaternionic Norm Response Theory (QNRT) proposes a discrete, geometricallystructured spacetime based on the Hurwitz quaternion lattice ΓH. Through a singlealgebraic operation—quaternion inversion—the theory generates a Z2 UV—IR scaleduality whose fixed point simultaneously determines the dark-energy scale and theneutrino mass scale.The dynamical field ϕ : ΓH → HC takes values in the complexified quaternionalgebra HC∼= M2(C) and carries the Hermitian norm N(ϕ) = ϕϕu2020, giving thelogarithmic scale field σ = log(N(ϕ)/ℓ2P). Inversion ϕ 7→ ϕ−1 = ϕu2020/N(ϕ) sendsσ 7→ −σ, exchanging ultraviolet and infrared regimes. The norm-response scaling(NRS) theorem shows that this map has a unique fixed point rc =√ℓP R⋆.The fixed-point scale rc = 84 µm (with R⋆ ≈ 4.4×1026 m, N⋆ = R⋆/ℓP ≈ 2.70×1061) defines a reference wavenumber k0 = 1/rc. This is precisely the wavenumberof the self-dual lattice mode (n = nc =√N⋆ in the harmonic expansion over R⋆),an algebraic identity verified to 0.000% numerical error. The corresponding energyE0 = ℏck0 = 2.354 meV and temperature Tc = 27.27 K equal the geometric meanof the Planck and de Sitter temperatures, and coincide with the CMB temperatureat redshift zc ≈ 9 (cosmic reionisation epoch).The self-dual scale gives ρΛ = ℏc/(ℓP R⋆)2 = c4/(GR2⋆) ≈ 6.3 × 10−10 J m−3,within 21% of the Planck 2018 value 5.3×10−10 J m−3. The identity ρΛ = c4/(GR2⋆)shows that ℏ cancels algebraically, so the cosmological constant problem reduces tothe purely classical question of why R⋆/ℓP ≈ 2.7 × 1061. The fermionic counterpartyields Mcc2 =pMP c2 · MHc2 ≈ 2.4 meV, within the active-neutrino mass win-dow. The lattice-derived kinetic coefficient clat = 6 fixes the continuum action; theduality-symmetric potential V (σ) = 2ρΛ cosh σ produces thawing-quintessence darkenergy with w0 ∈ [−0.990, −0.908] and wa ∈ [−0.082, −0.014] for σi ∈ [0.5, 3.0]. Allpredictions are consistent with ΛCDM.The principal limitations are as follows. The value R⋆ ≈ 4.4 × 1026 m is setby self-consistency of the numerical outputs; its epoch-independent determinationis Open Problem OP1 and is not resolved in this paper. The QNRT predictionsw0 ∈ [−0.990, −0.908] are inconsistent with the DESI DR2 (2025) central value w0 ≈−0.75 at 2.7—4.0 σ, while remaining consistent with ΛCDM. The Euclid forecastedprecision σ(w0) ∼ 0.02 will provide a decisive test. The Standard Model gauge embedding and the physical determination of σi are the remaining principal openproblems.