The averaging kernel and the lagged trend gate are separate specifications

Two published buy rules

A published stiffness-style buy setup stated two conditions rather than one. One published buy rule required a stiffness reading computed with lookbacks of 100 and 60 to cross above 90. That stiffness filter is a lookback-based trend-quality measure.

A second published buy rule compared a 100-period exponential average of a broad market proxy with the same average two sampling intervals earlier.

The omitted lookback lag

Correspondence identified that the second buy condition as first printed omitted the two-interval lag on the exponential average. A lookback lag is a fixed shift of a series by a stated number of sampling intervals so a comparison is not contemporaneous with itself.

The intended second condition is therefore a comparison of the 100-period exponential average with the same series two sampling intervals earlier, not a comparison of that average with itself at the same time.

Substituting the averaging kernel

A robustness check replaced the simple moving average inside the indicator with volume-weighted, sine-weighted, triangular-weighted, and recursively weighted averages. Those substitutions change the averaging kernel, the weighting scheme inside the moving average.

The volume-weighted moving average was formed from typical price, the arithmetic mean of a bar's high, low, and close, rather than from the close alone. In that kernel, each price observation is scaled by that period's volume before dividing by total volume.

One stated variant subtracted two-tenths of the lookback standard deviation of the close from that volume-weighted typical-price average.

Replication and follow-up windows

An independent replication applied the indicator to a large-capitalization index universe after attempting to remove survivorship bias. Follow-up tests of the volume-weighted substitution were described over five-year and ten-year windows.