K_def
plain-language theorem explainer
Recognition Science defines the dimensionless bridge ratio K to normalize constants on the phi ladder. This lemma records that K equals the positive square root of the golden ratio phi. Researchers deriving RS-native values for G or the fine-structure constant would reference the equality when switching between phi-powers and explicit radicals. The justification is a direct reflexivity step on the noncomputable definition.
Claim. The dimensionless bridge ratio satisfies $K = varphi^{1/2}$, where $varphi$ denotes the golden ratio.
background
The module sets the fundamental RS time quantum to one tick. The golden ratio arises as the self-similar fixed point forced by the T5-T6 steps of the unified forcing chain. K is introduced explicitly as the square root of phi to provide a dimensionless scaling factor for later constant expressions such as G = phi^5 / pi.
proof idea
The proof is a one-line wrapper that applies reflexivity to the noncomputable definition of K given in the same module.
why it matters
The declaration fixes the bridge ratio used in all subsequent constant derivations inside the Recognition framework. It supports the phi-ladder mass formula and the eight-tick octave structure. No downstream theorems are recorded in the used-by graph, leaving open how K will be invoked in curvature or defect-distance calculations.
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