Does drift-aware spectral conformal prediction (DASC) narrow the intervals of adaptive conformal inference (ACI) when all methods share one forecaster per data set and one tuning criterion? Not with the projected update. At DASC's step size, projected DASC and ACI widths differ by at most 0.43 per cent on electricity and weather; DASC is wider on finance. With DASC's step size tuned at a larger budget, or with wider step-size sets and scaled bandwidths, paired width intervals against ACI include zero or lie above it. Coverage is near nominal for the adaptive methods, with some under-coverage at the selected settings. The paper contributes a reproducible simulation and resampling design, released with code and saved results: twelve simulated scenarios and three real streams, paired moving-block bootstrap intervals with block-length and seed checks, a perturbation test that every interval uses only past observations (0 failures in 630 checks), and one-at-a-time measurements of how evaluation choices move widths. An earlier preprint reported width reductions of 28 and 42 per cent that came from centring DASC on a different forecast from the baselines. The replacement theory states the status of each result; the earlier long-run theorem was false for the projected update.

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