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Observer Determinacy of Termination Certificates: Sufficient Statistics, Blackwell Comparison, and Simple Projections for Step-Duplicating Recursion
The recursor $F(x,y,0)\to x$, $F(x,y,S(n))\to G(y,F(x,y,n))$ terminates and is confluent under all contexts, yet every orienting expression of the stated direct-measure grammar ignores the copied argument $y$; a payload-sensitive orienter exists outside it. An observer $q:X\to Q$ licenses a target $
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