The Multi-Ring Alignment Bound: The Polymath Paradox, the Wu-Wei Limit, and the Universal Reduction of a Many-Domain Intelligence to the Master Bound

Standalone record of the Viridis Canon — a candidate core-extension of the Intelligence Bound (the multi-domain generalization of the master inequality). The core IB canon spine is unchanged (frozen at v9, record 20724138); this record links to the spine via isDerivedFrom the concept DOI 10.5281/zenodo.19317982. The Intelligence Bound dI/dt ≤ P·D/(k_B T ln 2) caps the rate at which a single intelligence accumulates permanence-information. A planetary steward, however, is a polymath: it acts at once across many coupled rings of a thermodynamic market stack — valuation, monitoring, governance, corridors. This paper proves the Multi-Ring Alignment Bound (MRAB), the rate law for that polymath: dI_joint/dt ≤ (P·D̄/(k_B T ln 2))·∏_k cos²Θ_k, with D̄ = (∏_k D_k)^(1/K) the geometric-mean dissipation and cos²Θ_k ∈ [0,1] the per-ring Fisher–Wasserstein alignment factor. Four structural facts are established and machine-checked. (i) The Polymath Paradox — because ∏_k cos²Θ_k ≤ 1, the aligned joint ceiling never exceeds the unaligned base rate P·D̄/κ; adding a ring can only shrink the budget, so breadth is paid for in rate. (ii) The wu-wei limit — the bound is saturated exactly at perfect alignment (Θ_k = 0), and this hypothesis is satisfiable, so the ceiling is attainable and the theorem non-vacuous. (iii) AM–GM conservatism — the geometric-mean dissipation is bounded by the arithmetic mean. (iv) The Universal reduction — at K = 1 and perfect alignment, the MRAB collapses exactly to the Master Intelligence Bound P·D/κ, exhibiting the single-domain bound as the one-ring special case of the polymath law. Scope. Lean 4 (Aristotle-verified, zero sorry, axioms ⊆ {propext, Classical.choice, Quot.sound} on all 10 named theorems) certifies the structural results — the unit-interval and non-negativity structure, AM–GM, the Polymath-Paradox inequality, saturation, and the universal reduction — not empirical magnitudes. Working paper; not peer-reviewed.