Chapter 21: The Uniqueness Question

Part IV proved that every object in τ-Idx has an ABCD encoding: X = ((A ↑↑ C)^{B}) · D. But existence alone is not enough. If two different tuples (A, B, C, D) and (A’, B’, C’, D’) could yield the same X, then the ABCD chart would not be a faithful coordinate system: it would be a surjection, not a bijection. This chapter frames the uniqueness question precisely, states the Hyperfactorization Theorem, and outlines the three-lemma proof strategy that the following chapters will execute.