kappaA
plain-language theorem explainer
kappaA supplies the golden ratio φ drawn from the Constants bundle as the base scaling factor for binary and φ-exponential constructions in the RecogSpec.Scales module. Researchers building mass ladders or recognition-cost functions cite this definition to access the self-similar fixed point required by the Recognition framework. The declaration is a one-line alias that directly references phi inside the Constants structure.
Claim. $κ_A := φ$, where $φ$ is the golden ratio supplied by the Constants structure.
background
The RecogSpec.Scales module develops binary scales and φ-exponential wrappers for quantities such as recognition costs or mass assignments on the phi-ladder. The upstream Constants structure from LawOfExistence is an abstract bundle of CPM constants that includes Knet, Cproj, Ceng, Cdisp together with nonnegativity conditions and the golden ratio phi as the self-similar fixed point forced at T6.
proof idea
The definition is a direct one-line alias that unfolds to Constants.phi. No tactics or lemmas are applied beyond the reference to the imported constant.
why it matters
kappaA anchors the φ-ladder constructions that feed the Recognition framework's T6 self-similar fixed point and the eight-tick octave. It is used by F_ofZ to define the logarithmic mapping from integer Z and by the companion lemmas kappaA_pos and kappaA_ne_zero that justify division in downstream scale expressions. This placement directly supports the mass formula yardstick · φ^(rung-8+gap(Z)) and the alpha band inside (137.030, 137.039).
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