Interventional Commutativity: Effect Preservation and Reference Selection Under Weight-Only Quantisation

Can an intervention discovered before quantisation be reused after deployment? This question has two targets: preserving its original effect and matching an intervention re-discovered on the deployed model. We formalise the latter as interventional commutativity and audit both on behaviourally matched inputs. A round-to-nearest construction proves that exact functional equivalence can coexist with complete source-effect loss; an effect-mass bound separates mean sign agreement from magnitude retention. Empirically, a corrected 504-cell FP16/INT8 audit finds median native-relative retention 0.999 across 245 informative INT8 cells, with eight severe gaps in four configurations. However, the 243 cells whose source-effect magnitudes exceed the same descriptive guard have source-fidelity point estimates between 0.792 and 1.186. Crossed execution explains the distinction: on 117 matched template-held-out Qwen prompts, 4.481 logits of a 4.497-logit native-reference gap already exist before quantisation; only 0.016 comes from different responses to deployment. Thus a large native gap can diagnose reference selection while the transported effect's point estimate stays near its source value. Control-calibrated floors, paired gaps and cluster uncertainty make the comparison measurable; sequence checks show that its verdict remains endpoint-specific. The resulting audit quantifies preservation against the chosen reference and clarifies the target of repair.