The Recursive Actuation Mandate: Semiotic Closure of the G − I Cycle and Universal Underdetermination

This note formally establishes the semiotic and normative interpretation of the Structural Severance Theorem, demonstrated within Dynamic Epistemic Logic (DEL) by [Your Name, Date of DEL Upload]. The theorem proves that knowledge alone cannot guarantee actuation (Kaϕ ̸|= ⟨α⟩⊤), revealing a structural gap between cognitive analysis (G) and executive command (I). We propose that this logically necessary Executive Operator (I) must be interpreted as Peirce’s Legisign, a general rule or conventional law. This mandates that the Actuation Gap is closed through a G−I recursive cycle where I’s Normative Authority intervenes to resolve G’s theoretical underdetermination, establishing a framework where Weak Authority (logical reasoning) is always subservient to Strong Authority (normative choice)