BRIDGE COMPLETION OF THE AIT PROGRAM FOR CYCLIC-DEFECT BLOCKS: THE BRIDGE FUNCTOR, CONJECTURE 4.8, AND GEOMETRIC-CATEGORICAL COMPATIBILITY

This preprint presents a scoped bridge-completion result for the AIT program in cyclic-defect blocks (Coxeter-prime regime), with explicit claim governance labels [P]/[PC]/[C]/[Obs]. The manuscript consolidates corrected incidence-kernel analysis, an integrality-squeeze uniqueness mechanism for regularized projections, and a block-normalized trace framework compatible with Brauer-tree structure. It constructs the bridge-functor layer and formulates geometric–categorical compatibility in a single commutative diagram, while explicitly isolating the conditional finite-field BZSV descent input. Unconditional algebraic/categorical components are separated from conditional geometric identification, and scope boundaries (including Coxeter-only statements such as e=h-dependent identities) are stated explicitly for verification.