When Apparatus Sharpens Taxonomy: What Implementation Granularity Reveals About Type A, B, and C Failures

cafebedouin@gmail.com — Abstract The trifurcation framework classifies reasoning failures into three operationally distinct types: Type A (drift across reasoning stages), Type B (axiomatic inconsistency), and Type C (indexical underspecification). The taxonomy was originally diagnostic: each type has a corresponding repair (frame-fix, axiom-revise, index-specify), and the diagnostic move is to identify which repair the failure calls for. A subsequent paper, The Asymmetry of Failure Types, extended the taxonomy architecturally: the same three types divide unevenly along treatment lines when built into a working apparatus, with Type B detected by formal computation, Type C prevented by required indexing, and Type A governed by paired synchronic and diachronic discipline. This paper extends the architectural move with what an audit chain on a working apparatus revealed about the internal architecture of each type — granularity the diagnostic and architectural framings did not anticipate.…