kappa
plain-language theorem explainer
Assigns the thermal conductivity scaling factor on the phi-ladder by setting the value at rung k to the golden ratio raised to the power k. Materials researchers modeling transitions among the five regimes would cite this for the discrete adjacent-regime ratios. The assignment is introduced as a direct power expression using the pre-established golden ratio constant.
Claim. The conductivity scaling factor on the golden-ratio ladder is given by $k(k) = phi^k$ for each natural number $k$.
background
The module identifies five canonical thermal-conductivity regimes for configDim equal to 5: ballistic, diffusive, phonon-dominated, electron-dominated, and interface-limited. Adjacent-regime ratios are realized as powers on the phi-ladder. This definition extends the stiffness constant from annular cost theory, where the base stiffness equals the square of the logarithm of phi.
proof idea
One-line definition that directly sets the conductivity parameter indexed by rung k to the power of the golden ratio constant.
why it matters
This supplies the discrete scaling steps used by the unique lambda determination theorem in the lambda recurrence derivation and by the discreteness, per-turn ratio, and step-ratio lemmas in flight geometry. It realizes the phi self-similar fixed point for materials conductivity ratios and connects to the eight-tick octave and spatial dimension structure in the Recognition Science framework.
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