Full Linear Homomesy Spaces for Rowmotion on Rooted Forests

For every finite rooted forest with minimal roots, we compute the full spaces of linear order-ideal and antichain statistics that have zero average on every rowmotion orbit. The algorithm retains the orbit through the empty ideal and two affine hulls, each represented by at most n+1 vectors, instead of enumerating the orbits. A deletion lemma for Cartesian products yields scalar recursions for both zero-mesy dimensions and an exact rational basis algorithm using O(n^4) field operations, apart from integer gcd/lcm operations. The two full homomesy dimensions agree; the zero-mesy dimensions can differ by one. A known acyclic-toggle theorem transfers the ideal-indicator result to Coxeter toggle actions. The rooted-tree orbit construction is established prior work. The contribution is its affine compression and the resulting complete linear-space calculation, not a solution for arbitrary posets and actions in AIM-OTHER-0001. The cited Coxeter-transfer theorem is version-pinned to the 2021 source. No absolute priority or independent novelty certification is claimed. Unrefereed preprint prepared with AI assistance and originating-researcher self-audit. No independent peer review or formal verification is claimed. Author: Alper Ferudun, Mercury Software GmbH.