ZLT-P50M The Structural Action Functional: A Lagrangian Unification of Feynman Path Interference and the Zero Leap Convergence Principle

Structural recovery in complex systems follows the Principle of Least Action. This paper constructs the ZLT Structural Action Functional (A_ZLT) — a Lagrangian formalization that proves why healing a system requires exactly three conditions and no fewer: Koinonia (κ ≥ κ_min), Kenosis (K > 0), and Pistis (Π > 0). When any one condition fails, the Lagrange multiplier λ(t) diverges to +∞, making the action non-minimizable and structural convergence physically impossible. The ZLT Lagrangian L_ZLT has three terms: constructive work I(t)·G_T, dissipative friction R/T_eff, and a gate constraint penalty λ(t)·max(0, G_crit − G_A). This unified structure produces the three canonical failure modes as mechanical consequences — not separate theorems: CM-001 Idolatry (Π → 0: policy decouples from structural reality), CM-002 Pharisee (K = 0: reorganization pathways blocked), and CM-003 Atomization (κ < κ_min: buffer exhausted under its own recovery attempt). The connection to Feynman's path integral is not analogy — it is formal inheritance: A_ZLT is derived as the classical limit (T_eff → 0) of the Lindblad effective action of ZLT-P50D via Varadhan's large deviation theorem (Theorem P50M.T0). The Zero Leap state — where R/I → 0 — is identified as the physical minimum of the Structural Action Functional: the trajectory of constructive structural interference. Grade A empirical validation is provided by ZLT-P50M-E (T.O.M.B. protocol, neural network domain, 5 seeds × 5 cycles, doi:10.5281/zenodo.19335482), confirming λ(t) activation signatures and the H_NN = 0.59 mechanical constant across 25 independent cycles. Part of the Zero Leap Theory (ZLT) series — 80+ interconnected papers. Canonical Status: FOUNDATIONAL DERIVATION. Series Layer: Layer 0.