Abstract

We introduce Lambda Geometry, a computational framework that extends lambda calculus from function transformation to dimensional transformation.

By treating dimensions as structured 4-tuples encoding weight, depth, density, and feature count, we establish a formal calculus where derivatives become dimensional quotients and force emerges as their natural gradient.

This formwork marries disparate phenomena—from physical dynamics to blockchain consensus like geometric diverification to cognitive verification—under a common topological structure governed by the fundamental progression r → r² → r³ → R.