Chapter 25: Consequences and the Constructive Substrate

The Hyperfactorization Theorem gives every object a unique four-tuple address. This chapter harvests the immediate consequences: constructive pairing (encoding two objects into one) and sequence encoding (encoding a finite list of objects into a single object), all without importing set theory. We also expose G"odel numbering as a special case of the ABCD encoding, revealing that G"odel’s technique implicitly imports the diagonal structure that τ earns explicitly. The chapter closes by confirming the earned dimension dim_τ = 4 from a new angle: the Hyperfactorization Theorem guarantees that the four coordinates are not merely independent but complete.