Lookahead Bias From Universe Membership Leakage

You are building an alpha signal using a feature $x_i(t)$ to predict the next-day return $r_i(t+1)$. The feature itself never directly uses $r_i(t+1)$, so at first glance it looks clean. But you discover that $x_i(t)$ was constructed using a cross-sectional normalization that references the day-$(t+1)$ universe membership list $U(t+1)$ -- for example, it excludes stocks that were halted on day $t+1$, information that is only known at $t+1$. 1. Explain why this creates lookahead bias even though $r_i(t+1)$ never appears in the formula for $x_i(t)$. 2. Design an explicit, reproducible audit test that would detect this leakage using only logged feature values and timestamps. Describe the test procedure step by step. 3. Describe how to rebuild $x_i(t)$ to eliminate the bias while preserving the spirit of the cross-sectional normalization.