phiBit
plain-language theorem explainer
phiBit defines the base unit of recognition information as the reciprocal of the natural logarithm of phi. Researchers extending Shannon entropy to phi-weighted systems cite this when measuring information in binary choices with self-similar branches. The declaration is a direct one-line definition with no lemmas or reductions.
Claim. The phi-bit is the quantity $1 / (ln phi)$, the information content of a binary choice whose branches are weighted by the golden ratio phi.
background
Recognition entropy is Shannon entropy computed in base phi rather than base 2. The module states that phi-bits are more fundamental for the recognition channel capacity of CP6, which scales as phi^12 and exceeds ordinary Shannon capacity for the same space. Upstream results define entropy of a configuration as its total defect, with the zero-defect state as the minimum-entropy initial condition; related structures calibrate J-cost and derive phi-forcing constants used in the logarithm.
proof idea
Direct definition: phiBit is assigned the value 1 divided by the real logarithm of phi. No lemmas are invoked; the declaration is a noncomputable constant definition.
why it matters
This definition supplies the information-theoretic unit required by the Recognition Entropy module and its key results on phi-bit capacity and phi_bits_exceed_shannon comparisons. It anchors the phi-based scale to the golden-ratio fixed point from the forcing chain and supports entropy calculations H_R(p) = -sum p_i log_phi(p_i). No open questions are closed here; the definition remains available for capacity theorems that follow.
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