Scoped full-termination conjecture for pure recursive calculi

Let $R$ be an operator-only Pure Recursive Calculus with a recursor rule of the form

$$\mathrm{rec}(b,s,\sigma(n))\to f(s,\mathrm{rec}(b,s,n)).$$

The step argument $s$ is unrestricted, and an internally definable measure means a measure satisfying Definition~, without external axioms, imported arithmetic, or meta-level encodings. Scoped full-termination conjecture. No internally definable measure currently known proves termination of such an $R$ for the full calculus when $s$ is unrestricted. The audited family excludes additive and polynomial methods, as well as standard path orders such as LPO, RPO, and MPO when they rely on the universal subterm property $f(t)>t$ as an imported structural axiom.

This is a scoped impossibility claim rather than a theorem of absolute nonexistence: the cited machine-checked barriers cover the audited families, while the canonical computable SafeStep certificate remains available as an internal measure for the relevant restricted setting. Whether some other internally definable method proves full-calculus termination under unrestricted duplication remains open.