A named evaluation experiment records the artifact, task law, inference protocol, evaluator, seed kernel, budget, and sampling unit. Two reported scores are comparable only after these coordinates and their intended target have been stated.

For a fixed evaluation interface from Convention [ftip-005D], an evaluation law is a probability measure \(\mathsf Q\) on the finite outcome space \(\mathcal Z=\mathcal X_{\mathsf T_{\rm ev}}\times \mathcal O_{\mathsf T_{\rm ev}}\) with random pair \((X,O)\sim \mathsf Q\). Its score for artifact \(M\) is a bounded measurable map \(s_M:\mathcal Z\to [0,1]\). Write \(J_{\mathsf Q}(M)=\mathbb E_{\mathsf Q}[s_M(X,O)]\).

A matched evaluation pair is \((\mathsf Q,\mathsf I,b,\Lambda )\) and \((\mathsf Q',\mathsf I',b',\Lambda ')\) together with a coupling \((Z,Z')\) whose marginals are the two laws. The pair is matched on the declared coordinates when the task, utility, evaluator version, and sampling unit are shared; any changed coordinate is named.

For iid coupled draws \((Z_j,Z'_j)_{j=1}^m\), define \(\widehat \Delta _m=m^{-1}\sum _{j=1}^m(s_M(Z_j)-s_{M'}(Z'_j))\). The pairing is part of the estimator specification; it does not silently identify the two evaluation laws.

Under the iid coupling in Definition 4, \(\mathbb E[\widehat \Delta _m]=J_{\mathsf Q}(M)-J_{\mathsf Q'}(M')\).

If \(s_M(Z)=s_{M'}(Z')\) almost surely under a common-seed coupling, then \(\widehat \Delta _m=0\) for every sample even when independent sampling would have nonzero variance. This is a variance statement, not evidence that the two artifacts have equal behavior on a different law.

The result in Theorem 5 follows from its displayed hypotheses. A shared seed can make a paired comparison precise while the changed task law, evaluator, or inference budget still changes the estimand. No causal effect follows without a declared intervention and matched coordinates.