Deterministic Detection of All Documented Human Transcription Error Classes via Phase-Coupled D3 5 Decimal Folds

Abstract—The companion paper [1] constructs a two-digit decimal checksum on G = D₅ × D₅ that deterministically detects all single-digit substitutions and all adjacent transpositions of distinct digits, with a proven miss bound of at most 1/100 for uniform random noise. That construction leaves two practically important error classes—twin errors (aa → bb) and jump transpositions (a_b → b_a)—with empirical but not deterministic detection guarantees. We show that the natural generalisation to G = D₅³ with two phase parameters (k₁, k₂) closes this gap. An exhaustive empirical search over all 72 non-degenerate phase pairs at 100,000 codewords per pair identifies 42 pairs for which twin errors and jump transpositions are detected with zero misses, in addition to the deterministic substitution and adjacent-transposition guarantees inherited from the m = 2 theory. The construction uses three decimal check digits, provides 1/1000 asymptotic miss probability, and operates entirely within the decimal alphabet. Exhaustive finite verification confirms that twin-error and jump-transposition detection at the 42 perfect pairs is deterministic, not merely empirical. To the author's knowledge, this is the first purely decimal check-digit construction for arbitrary-length identifiers that achieves deterministic detection of all four documented human transcription error classes simultaneously.