The Measurement-Induced Symbiosis Theorem: Over-Monitoring as a Phase, Not a Quantity

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. An AI monitoring network coupled to an ecosystem is a monitored many-body system and inherits a measurement-induced phase transition in the monitoring rate p: over-monitoring is a PHASE, not a quantity. There is a critical p_c separating a co-adaptive (volume-law) phase from a collapsed (area-law) phase; the symbiotic-surplus optimum p* is strictly interior and sits just below criticality (edge-of-collapse). Cooperative witnesses certify at lower total back-action; efficiency equals cos²Θ. 18th IB self-application (the Witness). The 5 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 Working record; paper pending; not peer-reviewed.