Develop an average-case theory for the learned performance advantage

Develop an average-case theoretical analysis that explains the measured operation-count advantage of the learned Shellsort gap sequence over the tested classical gap sequences.

Background

The paper reports that the learned sequence has the lowest equal-task average operation count among seven tested classical baselines on 25 large sorting tasks, with gains measured across random, reversed, nearly sorted, duplicate-heavy, and block-permuted inputs.

The asymptotic analysis in the paper concerns worst-case operation counts and does not explain why the learned finite prefix performs better empirically on the tested input mixture. The authors therefore identify an unresolved need for an average-case theory connecting the sequence's arithmetic structure and its observed practical advantage.