The Mutualistic Entropy-Driven Learning Theorem: A Mutualism Trichotomy for Joint Learning Efficiency

Staged thematic record of the Viridis Canon (route: standalone NEW-CATEGORY). The Intelligence-Bound spine is unchanged (frozen at v10.0.0, record 20801185); this record links to it via isDerivedFrom the concept DOI 10.5281/zenodo.19317982. Establishes a genuine mutualism trichotomy over joint learning efficiency η_joint = η_L+η_E+2µ_LE/√(λ_Lλ_E): strict super-additivity when the stewardship coupling µ>0, exact additivity when µ=0, and parasitic sub-additivity when µ<0. The mutualistic cross-term obeys AM–GM with rank-1 saturation iff the two learners' capacities are equal. Pairs with the Dissipative Generalization Theorem and the Symbiotic Intelligence Bound. Candidate seed for a Learning / Information-Thermodynamics series. The 6 core theorems are machine-checked in Lean 4 (Aristotle, zero sorry, axioms ⊆ {propext, Classical.choice, Quot.sound}, statements verbatim and non-vacuous). Scope: the Lean proofs certify the validity of the discrete reasoning, not empirical magnitudes. Working record; paper pending; not peer-reviewed.