# Verification of the forest quota decomposition

The written proof establishes the convex-hull identity and integer decomposition for every finite forest with one unweighted interval quota on a neighbor subset per vertex. It constructs local circular schedules and glues them with integer mass matching. The support is at most 3n-1 and the construction runs in polynomial binary input time.

A separate checker validates output witnesses against the original independence and conditional quota definitions, coordinate marginals, total mass and support bound. Exhaustive tests include all labeled forests on at most four vertices, all nonempty edge directions including antiparallel arcs, and q<=4 for ordinary kernels. General-quota tests use all forests on at most three vertices, all neighbor subsets, all intervals with endpoints in [0,|S_v|+1], and q<=3.

There are 6,012 feasible ordinary cases, 86,142 feasible general-quota cases and 80 larger cases with very large integer weights. All 92,234 decompositions pass. Two invalid graph inputs and five corrupt witnesses are rejected. Three boundary examples demonstrate failure without the forest, interval or unweighted assumptions. Normal and optimized Python executions agree exactly, with diagnostic digest 15bcb7086572e9a6c20588df7a58939786ce59cd2bd098294e8e65b39acf4e79.

The five PDF pages were visually inspected for legibility, equation layout, author footnote, pagination and bibliography. The manuscript compiles with the built-in editor and Tectonic without undefined references or missing-character errors. The package build record records a separate portable archive build and replay when completed.

This is an originating-researcher self-audit, not independent peer review or proof-assistant verification. Finite tests do not establish the universal theorem or novelty. The ordinary forest kernel hull is credited to prior literature; the source's broader classification programme remains PARTIALLY_SOLVED, with zero whole-source closure increment.