Erratum to the Erratum to the Erratum: On the Structure of the Catullan Transform in the Sappho 31 Reconstruction — Correction of the Compression/Inversion Mischaracterization is a philological erratum; correction of transform-structure characterization; documentary artifact of the reconstructive method's own precisification chain; cross-linked companion to the prior errata in the sappho 31 stanza-numbering chain in the Crimson Hexagonal Archive, by Lee Sharks (2026-07-07). The mistake in STANZA-02 was to describe Catullus 4 as compression because its outward appearance (semantic redirection, register change, temporal shift) resembled the compressive operation at the middle stanzas. But those surface features do not entail loss. They entail transformation. Compression loses; inversion transforms without loss. The two operations are structurally different and have different reconstructive consequences. The archive's evolving accuracy about its own reconstructive method is itself an object of philological interest. Each erratum tightens the account. The original erratum corrected the numbering. The second-order erratum accounted for the methodological reason the numbering error arose in the first place. The present third-order erratum corrects the second-order erratum's mischaracterization of the transform-structure. Together the three deposits document not merely the corrected result but the trajectory of the corrections — the sequence of increasingly precise formulations by which the archive arrives at a stable characterization of what the reconstruction actually does. — Article composed 2026-08-05 from the work's own prose so that every record carries an encyclopedic entry; a fuller editorial treatment belongs to the description/wiki review stream.