Task Synergy Does Not Certify State Non-Additivity: An Exact Decomposition and an Audit Checklist

A pair of components is called synergistic when adding both to a system lowers a task loss by more than the sum of the gains from adding each alone. Reading this quantity as evidence of non-additive interaction is not licensed: the task synergy S splits exactly into a curvature term (what the loss alone would give if the two components' effects on the state were perfectly additive) and an interaction term (the part attributable to genuine non-additivity of the state). We prove that (i) for a continuous loss on a full vector space, curvature synergy vanishes for every additive system if and only if the loss is affine; (ii) feed-forward relational updates with additive drive produce exactly additive trajectories, so all task synergy from such structures is curvature; and (iii) S = 0 can coexist with strongly interacting states. Four exact worked examples are verified in rational arithmetic. Applied to an archived relational-dynamics audit (7,776 records, recomputed exactly, post hoc), 98.1% of the 431 strong records are non-chain pairs whose raw-weight interaction is exactly zero and whose synergy is almost entirely the threshold crossing at the effective-weight level, while the 8 genuinely interacting records are two orders of magnitude weaker. A short audit checklist follows. Companion to doi:10.5281/zenodo.23006539. Unpublished; not peer reviewed. Includes verification script, case-study files and a self-contained reproduction bundle.