phi_code_distance
plain-language theorem explainer
The φ-code distance is the J-cost of the golden ratio φ, which equals (√5 - 2)/2. Researchers working on Recognition Science error correction cite it as the minimum defect cost on the φ-ladder. The definition is a direct one-line abbreviation that applies the Jcost function to the constant supplied by the PhiForcing module.
Claim. Let $d_φ := J(φ)$ where $J(x) = (x + x^{-1})/2 - 1$ and $φ = (1 + √5)/2$, so $d_φ = (√5 - 2)/2$.
background
The Error Correction module treats ledger dynamics as a fault-tolerant stabilizer code. Recognition defects are deviations from the J=0 ground state; defect energy measures the cost of creating them; error syndromes are their detectable signatures; and correction dynamics restore equilibrium. The φ-ladder supplies the code distance in this analogy, while the eight-tick cycle acts as the correction period.
proof idea
This is a one-line definition that applies the Jcost function directly to the golden ratio φ from the PhiForcing module.
why it matters
The definition supplies the code distance required by the error-correction viewpoint of RS thermodynamics and is used immediately by the positivity theorem phi_code_distance_pos. It realizes the module statement that the φ-ladder structure provides the code distance in the stabilizer-code analogy. The quantity anchors the minimum defect cost at the self-similar fixed point φ, consistent with the T6 forcing step.
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