Gauge Fixing as Admissible Section Selection in Modal Triplet Theory Faddeev–Popov Determinants, Ghosts, BRST, and Gribov Ambiguity as Projection Geometry

Gauge theory contains an explicit version of the projection architecture developed in Modal Triplet Theory. The full field space contains redundant representatives related by a gauge group, while the physical configuration space is their quotient. A gauge condition is therefore a local representative section of the quotient map rather than a physical law imposed on the quotient itself. This paper interprets gauge fixing as admissible section selection. The gauge-fixing delta is the singular zero-width limit of a representative-selection kernel, the Faddeev-Popov determinant is the Jacobian from gauge-orbit coordinates to slice coordinates, ghost fields encode quotient-measure bookkeeping, BRST cohomology implements admissible quotienting algebraically, and Gribov ambiguity obstructs a global admissible section. We prove a finite-dimensional local-slice formula, state the regularized functional identity under the usual formal path-integral assumptions, and give a typed MTT interpretation. The section language is exact, but the assignment of lens, circle, and nil roles is an encoding dictionary rather than a derivation of gauge theory. A gauge section chooses a representative of an orbit; it neither globally inverts the quotient nor recovers a unique ontic configuration. The global obstruction depends on the topology and orbit stratification of the declared gauge bundle.