Deterministic Detection of Four Human Transcription Error Classes via Phase-Coupled (D5)^3 Decimal Folds

Abstract

v2 clarifies the systematic encoding rule and adds a proof of error detection within the check block and across the check/payload boundary. It corrects the twin-error argument and the comparison with MOD 97-10, and distinguishes the uniform-word acceptance probability from the asymptotic payload-collision probability. The construction, the 42 successful phase pairs and the reported Monte Carlo results remain unchanged and have been independently reverified. The supplementary material includes a self-contained verifier and machine-readable results. The title now explicitly identifies the four error classes considered. The exposition and author affiliations have also been updated.-- Abstract We construct a three-digit decimal checksum on the direct product G = D53 that deterministically detects four human transcription error classes throughout the systematic codeword. The classes are single-digit substitution, adjacent transposition, twin error (aa → bb), and jump transposition (a_b → b_a). We previously constructed a phase-coupled D5 × D5 fold [1]. Here we add a third dihedral factor with phase offsets (k1, k2) and store each coordinate of the inverse payload fold as one check digit. Injectivity and anti-symmetry give substitution and adjacent-transposition detection. For twin errors, the two anomalous phases act on different pairs in the T0-collision set C0, so every one of the 72 non-degenerate phase pairs gives deterministic detection. Exhaustive verification of 9,000 local jump configurations per phase pair gives 42 pairs with no simultaneous collision in all three factors. We extend these payload guarantees to the complete codeword through a separate argument for errors within the check block and across its boundary. For independent uniform payloads, the collision probability decreases to 1/1000 as payload length grows, while uniform replacement of the complete received word gives acceptance probability exactly 1/1000 at every length. All payload and check symbols are decimal digits.