A Genealogy and Interface Audit of QCD-Sector Truncations in History-Dependent Gravity (Paper LXXVIII-B-02)

Abstract

This work presents a systematic genealogy and interface audit of the quark and gluon sector truncations within the History-Dependent Gravity (HDG) framework. We map the currently activated operational interfaces, specifically the gluon interface (K → Q_{G,op}, Paper XXXII) and the quark-vertex interface (K/M → Γ_{DSE}, Paper XXIX). The operational relation W_{op}^{XXIX}=0 is validated within the truncation of Paper XXIX. The audit further demonstrates that the three-gluon construction of Paper XXXV cannot be directly inherited from the activated XXXII gluon interface: the two papers employ different propagator realizations, and the cross-paper identification of the corresponding inverse propagators has not been established. These results do not imply a physical incompatibility of the underlying HDG constructions. Rather, they define the current boundary of admissible cross-paper inheritance. A common master formulation, for example at the level of a unified effective action, is identified as a natural future route for establishing such compatibility, but is not assumed or claimed to follow uniquely from the present audit. This work serves as a reviewer-safe boundary map for subsequent unification efforts (forthcoming as the LXXIX master formulation).