K_rs
plain-language theorem explainer
K_rs defines the K-gate ratio as π divided by four times the natural logarithm of phi for the RS-native unit system. Researchers expressing coherence energies or phi-ladder scalings in tick and voxel units would cite this constant. The definition is a direct one-line alias to the gate ratio computation.
Claim. The K-gate ratio constant is defined by $K = π / (4 ln φ)$, where φ is the golden ratio.
background
The module sets up an RS-native measurement system with tick (τ₀) as one discrete ledger posting interval and voxel (ℓ₀) as the causal spatial step light traverses in one tick. Derived quanta are the coherence quantum with E_coh = φ^{-5} and the action quantum ħ = E_coh · τ₀, enforcing c = 1 and fixing all dimensionless ratios by φ alone on the φ-ladder for scaling masses, energies, times, and lengths.
proof idea
One-line wrapper that applies the K_gate_ratio definition computing Real.pi / (4 * Real.log phi).
why it matters
This supplies the K-gate ratio for coherence scaling E_coh = φ^{-5} in native units, supporting the module goal of expressing physics without SI reference. It connects to the φ-ladder and the structure of minimal RS units with tau0, ell0, c satisfying c * tau0 = ell0. No downstream uses are recorded yet.
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