From Softmax Correspondence to Identification: The Observation Gap and a Diagnostic Template―One-Step Log-Score rEFE and RSA―

Softmax choice rules are shared by Active Inference policy selection (often written as a softmax over expected free energy, EFE) and Rational Speech Act (RSA) pragmatics, encouraging cross-context interpretations of logit/softmax slopes as differences in “precision/temperature. ” In open-ended corpora, however, the counterfactual utterance menu that fixes the softmax normalizer is unobserved. As a result, utterance policies and temperatures are not identifiable from realized strings and success outcomes alone. This preprint formalizes the observation gap and distinguishes it from a diagnostic gap (policy assumptions are assessed only through outcome-level GLMs) and a proxy gap (unobserved cost/decoder terms require imperfect proxies). As a controlled case study, we define rEFE, a restricted one-step instrumental objective whose hard-goal log-score (reverse-KL) term matches RSA informativeness under channel identification. The rEFE–RSA softmax correspondence is treated as an identification target, not as a general “EFE = RSA” claim. We derive two outcome-level diagnostics for heterogeneous contexts: A2ₒutcome: a comparability gate for cross-context coefficient/temperature readings (slope×condition block tests). A5ₒutcome: a residual-baseline check consistent with offset-style calibration (condition-intercept block tests, especially conditional on slope heterogeneity). These are interpretability checks for outcome models under missing menus, not policy-level correspondence tests. Using Colors in Context, pre-specified multiverse robustness and multiway cluster-robust block tests frequently reject A2ₒutcome, indicating that cross-condition slope/precision interpretations are not licensed in these success models without explicit scale anchors or calibration models. Held-out gains are dominated by geometry and coarse condition baselines rather than a length proxy.