Chapter 18: The Normal-Form Address Encoding

the relevant chapter defined tower atoms and the greedy peel-off algorithm. The peel produces a single tuple (A, B, C, D) from any X ≥ 2. But the remainder D is itself an element of τ-Idx — it may be non-trivial and admit further structure. This chapter defines the normal-form address encoding: the result of applying the greedy peel once, recording the extracted tower atom and the remainder. The NF address is the canonical description of X in terms of the arithmetic hierarchy. Existence of the NF is established here; uniqueness is the subject of Part V.