Parameter-Free Solution of the Cosmological Constant Problem from the Two-State Intertwiner Boltzmann Mechanism (Paper 37 in the Intertwiner Series)

We show that the cosmological constant problem is resolved by recognizing that the gravitationalvacuum energy is determined by the two-state intertwiner Hilbert space Hint = span{|k=0⟩,|k=1⟩}of the four-valent vertex in loop quantum gravity, rather than by the infinitely many zero-pointmodes of quantum field theory. We prove that the standard Connes–Chamseddine spectral action expansion has zero radius of convergence for the bounce geometry, invalidating the polynomialextraction Λ ∼ f4Λ4cutoff. The Boltzmann probability of the k = 1 intertwiner state, with Euclidean action V4 = 280 derived from three spectral invariants {M0 =12, M2 =240, κ20 =2} of theloop quantum cosmology bounce window function, gives ρΛ/ρP = e−280 ≈ 10−122, matching thePlanck 2018 observed value to 0.8%. The exponential structure automatically protects the hierarchy:electroweak and QCD vacuum shifts enter the exponent as corrections of order 10−67, convertingthe standard 1054 fine-tuning catastrophe into a negligible multiplicative factor. Two independentpredictions emerge from the same three spectral numbers: the scalar power spectrum amplitudeAs ≈2.100×10−9 (matching Planck to 0.03σ) and the testable identity Λ = A14s /Cmod.