We introduce a local data-driven statistical framework (L2–L4) for analyzing prime gaps. Across ranges up to 11 million primes, this framework consistently explains approximately 98–99% of gap distributions using variance-band filtering, short-range repulsion, and rare-jump identification. The residual ~1–2% exhibit significant clustering and near-linear alignment under spiral-lift mapping, suggesting possible geometric order beyond current local models.

"prime gaps", "number theory", "statistical analysis", "residual order