In 54 network summaries, a 1.67% allowance for separate weights permits a half response in 30 years at the published fit limit

We test how a common rate mixture limits the inferred response of thermal composition. We use the same 54 network summaries and 40 published positive rates plus zero as earlier studies. Each network can put an amplitude eta into separate weights; the rest must share common weights. At the common best score plus 4, the 30-year mean unit-step response range grows from 0.195-0.413 at eta=0 to 0.005-0.965 at eta=1. A convex calculation shows that eta about 0.016663 is enough to permit a half response at that score limit. A direct model witness and a global certificate verify this threshold. Separate models improve fit. At each class own best score plus 4, fully separate mixtures still allow 0.221-0.653. Thus re-centering the fit set does not restore the below-half result. Independent code checks 60 endpoint certificates and five reference fits. These are conditional model sensitivity bounds, not confidence limits, forecasts or evidence for a lag mechanism. Fixed spatial slopes, summary errors, the rate grid, detection and habitat confounding remain limits. Code, aggregate results, model witnesses, proof and provenance are included.