Beyond No-Good Benders Cuts: Exact Realizability for Discretely Tunable Clock Trees
Useful-skew schedules can satisfy timing constraints yet remain unrealizable by a fixed clock tree with discrete tuning choices. We formulate this mismatch as exact membership in a finite relative-latency set and develop a checkable feedback interface between the scheduler and the tree model. Arithmetic certificates explain unrealizable targets, while tree-specific contraction reduces the structural size of the exact relations projected onto selected sinks. These relations become realizability cuts that can exclude more candidates than a no-good on the same certificate support, including discrete holes that linear inequalities cannot separate. Controlled experiments confirm fewer oracle calls and faster projection construction. They also expose important limits: globally minimum certificates can cost more than they save, compact arithmetic feedback can fail on non-parity obstructions, and direct monolithic optimization remains faster on the tested additive models. The contribution is an exact, independently verifiable scheduler--tree interface, rather than a claim of universal solver acceleration or physical signoff.