k_rec_com
plain-language theorem explainer
The declaration sets the comoving UV knee wavenumber k_rec,com to the constant 1.4e6. Inflation modelers using Recognition Science would reference this scale when locating the transition where the primordial spectrum softens due to lattice visibility. The entry is a direct numerical definition with no further computation or lemmas.
Claim. The comoving recognition wavenumber is defined by $k_{rec,com} := 1.4×10^6$ (Mpc$^{-1}$), above which the lattice structure becomes visible and the spectrum softens.
background
The Gravity.Inflation module formalizes RS inflationary predictions from the phi cost-functional self-similarity. Core elements are the α-attractor with parameter φ², the spectral index n_s ≈ 1 - 2/N, the tensor-to-scalar ratio r ≈ 12φ²/N², and the modulation frequency Ω₀ = 2π/ln(1/X_opt) with X_opt = φ/π. The module works in RS-native units where c = 1 and the curvature bound at the recognition event satisfies |R| ≤ 1/λ_rec² = 1.
proof idea
Direct definition that assigns the numerical value 1.4e6 to the identifier. No lemmas, tactics, or reductions are applied.
why it matters
The constant supplies the UV cutoff that marks the onset of visible recognition-lattice effects in the inflationary spectrum. It supports the parameter-free tilt and tensor-ratio results derived from the phi self-similarity and the recognition composition law. The entry fills the comoving-knee slot required by the module's inflation predictions without introducing new hypotheses.
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