R Universal Finite Chain Theorem

We prove a universal execution theorem for the R hybrid cell model on every positive finitedirected chain. For admissible fixed fabrication parameters, independent READY births andbounded native wire-delay functions fixed in advance, the declared pulse program admits acomplete physical execution. All executions complete at the declared horizon have the samephysical endpoint and ordered per-cell FIRE dates. We derive exact counts and cadencebounds, and give an indexed realization of prescribed bounded wire errors.For this same finite-source program, every legal finite prefix extends to any later horizon.Infinitely many physical jumps require unbounded time. Every infinite move presentationmaximal under extension at its final flow limit has dates tending to infinity. The proofs areformalized in Lean.