The Cognitive Throughput Theorem: An Inverse Square-Root Bound on Cognitive Information Acquisition and the Cognitive Face of the Intelligence Bound

Standalone record of the Viridis Canon (Cognition / Intelligence-Bound self-application) — the core IB canon spine is unchanged (frozen at v9). Proves the Cognitive Throughput Theorem (CTT): an embodied cognitive system modeled as an open quantum (GKSL/Lindblad) process on a Fisher–Rao manifold, performing simultaneous Pierra–Censor–Elfving Bregman multiprojection onto sensory, model, and motor constraint sets, has a maximum certified information-acquisition rate that obeys an inverse square-root envelope dI_cog/dt|max(N) = K_cog · N^(−1/2), with throughput constant K_cog = √(2·W_attn·Φ_eco/(k_B T ln 2)). The decoupled/coupled dichotomy — Φ_eco = 0 ⇒ K_cog = 0 versus Φ_eco > 0 ⇒ K_cog > 0 — is the cognitive face of the Intelligence Bound: cognitive throughput is gated by physical/ecological coupling, giving a thermodynamic foundation for the necessity of AI–ecology co-evolution. The 13th Intelligence-Bound self-application (the Knower). Scope. Lean 4 (Aristotle-verified, zero sorry, axioms ⊆ {propext, Classical.choice, Quot.sound}) certifies the structural results — the inverse-√ scaling law, the conserved throughput invariant, strict antitonicity (the attentional iris), and the decoupled/coupled coupling dichotomy — not empirical magnitudes. Working paper; not peer-reviewed.