POST-BRIDGE AIT: CYCLIC-DEFECT CLOSURE, NORMALIZATION CONSTRAINTS, AND THE REMAINING SYNTHESIS GAP

This preprint consolidates the Arithmetic Intersection Theory (AIT) program after the Bridge Proof with explicit claim governance and corrected scope. It proves a corrected cyclic-defect closure theorem for regularized projection coefficients P^{\mathrm{reg}}(\chi)=1 in the AIT categorical regime, replacing an earlier kernel-triviality error with a normalization-boundedness argument over the one-dimensional incidence kernel. It provides complete numerical verification of the G_2(\mathbb F_3) principal-block example using definitive CHEVIE generic-degree formulas, and permanently scopes the functorial chain 1/|D| \to 1/e \to 1/h, with Arrow 3 conditional on the Coxeter hypothesis e=h. The paper isolates one remaining structural frontier: constructing a mod-\ell reduction functor from block categories to non-semisimple ribbon categories compatible with modified traces and Brauer-tree structure. All major statements are labeled as proved [P], proved under framework assumptions [PC], conditional [C], or observational [Obs], and reproducibility procedures are explicitly listed.