This work presents an exploratory analysis of prime gaps using a dyadic remainder transformation. For each gap between consecutive primes, the largest power of two not exceeding the gap is subtracted, and the remainder is recorded. When the frequencies of these remainders are plotted across widely separated prime ranges, a qualitatively similar shape emerges. The manuscript provides fully reproducible examples drawn from seven distinct prime segments, each precisely defined with extensive metadata, figures, and remainder-frequency distributions. The purpose of this document is descriptive and methodological: it records the transformation and its resulting distributions with sufficient clarity that independent researchers may reproduce, critique, or extend the observations. No theoretical explanation is claimed for the observed shapes; the focus is solely on presenting stable, repeatable empirical patterns in dyadic-conditioned prime gap data.