Theorem. A summary-only harness cannot distinguish summary-equivalent archives [ftip-00CS]
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    Fix the claim ledger \(q\), goal \(g\), and proposal \(p\). Suppose a research-decision kernel uses the complete archive only through \(C(A)\). If \(A\sim _C A'\), then its decision laws under \(A\) and \(A'\) are equal.

    This finite information-boundary result follows from the displayed setup. It does not assume that the two complete archives induce the same independent utility.

    Proof. 

      By hypothesis, the two decision laws are related by

      \[ J(C(A),q,g,p)=J(C(A'),q,g,p). \]

      Summary equivalence makes the first arguments equal, while every other argument is fixed. The two probability laws are therefore identical.