gamma
plain-language theorem explainer
The definition fixes the power-law exponent γ at 3 for the degree distribution on recognition graphs. Network scientists working with preferential attachment and small-world scaling would cite this value as the self-similar fixed point of the σ-conservation equation. The assignment is introduced directly as a constant matching the quadratic solution (γ-1)(γ-2)=2.
Claim. In the degree distribution $P(k)∝k^{-γ}$ on the recognition graph, the exponent satisfies $γ=3$.
background
The module re-derives the Barabási-Albert result inside Recognition Science by treating γ as the self-similar fixed point of the φ-recurrence. It states that γ=3 is the unique positive solution of the σ-conservation fixed-point equation (γ-1)·(γ-2)=2, with average path length scaling as log_φ N and clustering ratio 1/φ. The local setting is Track F9 of Plan v5, which obtains the small-world property from the same recurrence that forces D=3 and the eight-tick octave elsewhere in the framework.
proof idea
Direct constant definition that assigns the real number 3.
why it matters
The definition supplies the exponent required by the module's derivations of path-length scaling and clustering ratio. It fills the fixed-point step in the power-law claim whose falsifier is any network class with best-fit exponent outside [2.5,3.5]. The value aligns with the φ-recurrence fixed point that also produces the alpha-band frequency φ^5 and the mass-ladder spacing in the broader Recognition Science chain.
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