degreeExponent
plain-language theorem explainer
The definition assigns the degree exponent γ the value 1 + φ. Network theorists modeling scale-free graphs via preferential attachment cite it to obtain the Zipf-Pareto tail exponent from sigma conservation. The definition is a direct substitution of the golden ratio constant into the expression for γ.
Claim. $γ = 1 + φ$
background
The module derives network topology from sigma conservation under Recognition Science at D = 3. Scale-free networks obey P(k) ∝ k^{-γ} with measured γ ≈ 2.1-2.3. The RS prediction sets γ = 2 + 1/φ ≈ 2.618 for any σ-conserving preferential-attachment network. Each attachment step is a recognition cost decision; σ-conservation forces the exponent to equal 2 + J(φ)/J(φ) = 2 + 1/φ, where J is the J-cost function from the Recognition Composition Law.
proof idea
The definition is a direct abbreviation that substitutes the golden ratio constant phi into 1 + phi.
why it matters
This definition supplies the core value for the NetworkTopologyCert structure and its supporting theorems degreeExponent_eq_two_plus_inv, degreeExponent_gt_two, and degreeExponent_val_band. It fills the RS prediction for the Zipf-Pareto exponent in σ-conserving networks, linking directly to the phi self-similar fixed point and the eight-tick octave in the forcing chain T0-T8.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.