Chapter 20: Geometry from Generators

Space, metric, dimension, and locality are not postulated but derived from the five generators of Category τ. Distance is address-comparison cost: two NF addresses are close when they share a long common prefix. Dimension—specifically, dim(τ³) = 3—is a structural consequence of the fibered product construction, not an empirical input. Locality is the sheaf condition applied to the kernel’s covering families: a property is local when it can be checked on patches and glued. The philosophical import is decisive: space is not a container that precedes its contents; it is a structural consequence of the generators that constitute those contents.