A Quasipolynomial Research Program for the Wang Framework: Deep Integration with Babai's Local–Global Symmetry Method

The fifth paper of the Wang-framework series is conceived as a research-program paper rather than a completed complexity theorem. Its purpose is to formulate, with explicit mathematical interfaces, a route from the slice-wise fixed-parameter complexity established in the fourth paper to a quasipolynomial-time global framework compatible with Babai's graph-isomorphism architecture. The guiding idea is that Wang-framework quotient packets on logarithmic supports should serve as concrete, canonically computable local certificates in the sense of Babai's local–global symmetry method, while Babai's recursion should provide the top-level mechanism that replaces full support enumeration by recursive symmetry reduction. We therefore isolate the exact objects imported from the third and fourth papers, define Wang local-certificate packets, formulate the bridge principles needed for affected/unaffected propagation, aggregation, Johnson-type obstruction recognition, and inverse synthesis of large local symmetry, and derive a conditional quasipolynomial recurrence from these principles. The paper is intended as a rigorous blueprint for subsequent theorem-proving work: it records what must be proved, in what order, and through which precise interfaces, in order to lower the Wang framework from the current supportwise complexity O (nᵏ f (k) ) to a Babai-compatible quasipolynomial regime