The Wu-Wei Sampling Theorem: Event-Triggered Monitoring Carries One-Third the Error of Fixed-Cadence Sampling

Staged thematic record of the Viridis Canon (route: S2 (Monitoring) ). 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. Settles when to observe an ecosystem. At equal mean rate, event-triggered (send-on-delta / Lebesgue) monitoring carries exactly one-third the mean-square error of fixed-cadence (clock / Riemann) sampling, and the advantage grows with burstiness. A unique optimal trigger threshold Δ*= (b/a) ^1/4 sits between over-monitoring and illegibility; monitoring efficiency equals cos²Θ and forcing debt equals sin²Θ. The temporal dual of the Monitoring Water-Filling Theorem (the Surveyor) ; 20th IB self-application (the Listener). The 10 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 Working record; paper pending; not peer-reviewed.