Reading the Gate, Not the Interference: Output-Side Interference Measurement Does Not Track Merge Collapse
Task-arithmetic merging works until it doesn't, and the field diagnoses why by measuring interference inside the merged model. We take the most direct such measure, the exact layerwise activation cross-term of a factorial ledger, establish its causal anatomy, and then ask what it tracks. The anatomy is clean: each block mostly transports and amplifies the cross-term rather than generating it; erased, it is regenerated by the untouched marginal paths to 99% of its norm unless removed late; its output effect varies monotonically with the displacement's angle (orthogonal displacements make interference worse), and a two-assumption model derives the angle law and retro-dicts the dose curve (R^2 >= 0.99). What the measure tracks is not what the field assumes. Behavioural expert-likeness is decoupled from it across four instruments. Its cross-condition behaviour is denominator-dominated: an instruction template pins the main effect to within 1% while the absolute interaction grows 111x from two to six merged tasks, suppressing expressed interference at k=2 and amplifying it at k=6. And where merging actually collapses, the cross-term is a bystander, not the carrier: across two collapse parameterizations at two scales, even erased persistently at every position, removing it entirely repairs none of the collapse. There the output-side ratio carries no method information under a common counterfactual, while two state-space measures the field already uses rank methods correctly at both scales. All 81 predictions were frozen before their data; falsifications are reported as such. Output-side interference measurement reads the gate, the denominator, and the displacement budget, not the interference. What fails a merge is the carrier-bystander split: collapse rides in the marginal displacements while the cross-term merely accompanies it, and only state space sees the carrier.