Parity–Pattern Constraints for Collatz Cycles and a Machine–Checkable Exclusion Framework

We present a framework that imposes explicit, checkable constraints on nontrivial Collatz cycles. Working with the accelerated map on odd integers, we derive the cycle equation and a modular valuation method that excludes entire families of candidate cycles. A worked example (the 5–step, two–odd family) is carried through in detail and shown to yield no valid cycle. We also provide computational evidence for small additional families, and we outline how the constraints may be encoded for machine verification using SAT solvers and DRAT certificates. The goal is not to resolve the Collatz conjecture, but to provide a rigorous, auditable exclusion mechanism for large classes of possibilities.