Hyperfactorization
Hyperfactorization is a foundational math in the COORD domain.
Overview
The Hyperfactorization Theorem (I.T04) is the first hinge theorem of the entire series. It proves that the ABCD Coordinate Chart is injective: every object in Category has a unique four-dimensional address. Without this result, the coordinate system would be ambiguous and all subsequent structural claims would collapse.
Detail
Three lemmas support the theorem: tetration injectivity, the No-Tie Lemma (I.L03, ensuring the greedy peel is deterministic), and Strict Remainder Descent (I.L04, ensuring termination). The consequence is that shadow equality collapses to ontic identity – distinct objects always have distinct addresses. See the full derivation and the Hyperfactorization module for the complete proof structure.
Result Statement
Every object has a unique ABCD decomposition. Status: Resolved (established, machine-checked in TauLib).