IndisputableMonolith.Cost.JensenSketch
The JensenSketch module outlines a preliminary sketch of Jensen's inequality applied to the J-cost function within Recognition Science. It supplies convexity arguments that bound expectations in cost calculations on the phi-ladder. The module imports only the base Cost definitions and introduces no independent theorems.
claimSketch of $J(mathbb{E}[x]) leq mathbb{E}[J(x)]$ for the J-cost $J(x) = (x + x^{-1})/2 - 1$ in the Recognition Composition Law setting.
background
Recognition Science builds all physics from the single functional equation encoded in the J-cost. The imported Cost module supplies the core definition $J(x) = (x + x^{-1})/2 - 1$, which equals $cosh(log x) - 1$, together with the Recognition Composition Law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$. JensenSketch sits inside the Cost domain and supplies an informal convexity sketch that will later tighten bounds on defectDist and yardstick scaling.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The sketch feeds parent cost theorems that derive the phi-ladder mass formula and the eight-tick octave (T7). It supplies the convexity step needed before the forcing chain reaches T8 (D = 3) and the alpha band bounds.
scope and limits
- Does not contain any Lean theorems or executable proofs.
- Does not introduce new constants or mass formulas.
- Does not depend on modules outside the Cost domain.
- Does not claim a full proof of Jensen's inequality.