OTAZ: Exponentially Weighted Fusion—Algebraic Structure, Numerical Stability, and Reproducible Experiments

This technical preprint studies a pair-valued exponentially weighted fusion operator whose value component is a softmax-weighted mean and whose score component is a scaled log-sum-exp. For a fixed finite nonzero coefficient and compatible finite inputs, a mass–moment transformation establishes closure, commutativity and associativity. The analysis develops convex-hull and score bounds, coefficient limits, derivatives, entropy identities, perturbation bounds and explicit information-loss counterexamples. A max-shifted formulation and a mergeable block state provide practical evaluation strategies. A reproducibility suite evaluates 12 property categories comprising 10,859 comparison cases, complemented by 26 public-API unit tests, 300 independent-baseline comparisons, 100-digit reference cases, precision stress tests and CPU timing and traced-allocation measurements. A clean-directory rerun on the same host is assessed separately from independent replication. The work is an integrated mathematical and computational exposition of established softmax and log-sum-exp machinery; it does not claim discovery of those functions, universal indispensability, or application-level efficacy. Source-available noncommercial code and synthetic-result tables accompany the manuscript. Software is separately licensed under PolyForm Noncommercial 1.0.0. If you archive the software as another record, select Software and do not reuse the manuscript DOI.This JSON is a legacy-deposition API representation and a metadata reference, not an automatically submitted record. The web form may use different field labels.