Code and sanity-check artifact for "All-Roots Aggregation of Non-Mergeable Tree Statistics: Class Painting and Tight Bounds for the Mode"

Supplementary software for the manuscript "All-Roots Aggregation of Non-Mergeable Tree Statistics: Class Painting and Tight Bounds for the Mode" by Md Reyad Hossain. The artifact contains Python reference implementations of the algorithms described in the paper, together with computational sanity checks that compare them against a brute-force baseline. The algorithms covered are the rerooting reduction, the small-to-large walk and its dual, the Class-Painting algorithm, the occurrence-boundary sweeps, the group-snapshot first-difference structure, the rank descents, candidate verification, and the element-distinctness reductions used for the lower bounds. The brute-force baseline re-roots the tree at every vertex. Contents:- verify_framework.py: brute-force reference, the reduction, the walks and the static mechanisms- painting_check.py: the Class-Painting algorithm and the lower-bound reductions- exhaustive.py: exhaustive tests over all labelled trees (via Prüfer codes) with n ≤ 6, 114,708 instances in total- run_all.py: runs all random tests (fixed seeds), the exhaustive tests and a mutation test Usage: python3 run_all.py (Python 3.8 or later, standard library only, about 2 minutes). These tests are sanity checks. They do not replace the mathematical proofs in the paper.