lambda_kin
plain-language theorem explainer
This definition sets the kinematic wavelength in RS-native units to the display value (2π ℓ₀)/(8 ln φ) with ℓ₀ the voxel length. Researchers working on wave phenomena or K-gate ratios in the Recognition framework cite it when staying inside the native gauge. The definition is realized as a direct one-line application of the display function to the standard unit structure U.
Claim. λ_kin := (2π ℓ₀)/(8 ln φ) where ℓ₀ = 1 voxel in the RS-native gauge with c = 1.
background
The RS-native unit system takes tick (τ₀ = 1) and voxel (ℓ₀ = 1) as base standards with c = 1, so all dimensionless ratios are fixed by φ alone. The upstream lambda_kin_display supplies the length-side kinematic wavelength formula (2π · ℓ₀) / (8 · log φ). The gauge U instantiates the RSUnits structure with these base values, satisfying c · τ₀ = ℓ₀ by construction.
proof idea
This is a one-line wrapper that applies the lambda_kin_display function from KDisplayCore directly to the native units U.
why it matters
It supplies the kinematic wavelength needed by the downstream theorem lambda_kin_eq_K_gate_ratio that equates the display value to the K-gate ratio. The definition sits inside the constants layer of the Recognition framework and supports the φ-ladder scaling for lengths. It closes the mapping from display formulas to the native tick/voxel gauge used throughout the eight-tick octave structure.
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