The Orientation Boundary for Step-Duplicating Recursors: A Machine-Checked Structural Theory of Termination Proofs

The rewrite rule \[ \mathrm{recur}(b,s,\mathrm{succ}(n))\to \mathrm{wrap}(s,\mathrm{recur}(b,s,n)) \] copies its step argument, the payload, and consumes one recursion counter. It terminates; we ask which direct measures prove it. For measures built from counter and payload by constants, s