Plate XX defines trajectory governance over the unified system functional. Plate XIX measures the system through 𝓛(x,t); Plate XX constrains the evolution of that measure. A trajectory remains admissible only when the audit scalar decreases or remains invariant over time. If d𝓛/dt > 0, the system is diverging from closure and the trajectory is not admissible. This plate does not redefine execution authority; it governs the temporal behavior of the measured system.

System evolution is admissible only when the unified audit scalar descends or remains stable over time.

Convergence & Closure Dynamics

The unified system functional integrates biology (Φ), geometry (Δ^p), and physics (E_k + E_p) into a single scalar measure. Convergence occurs when 𝓛 → 0, indicating alignment with the invariant reference I*.

A single scalar unifying biological coherence, geometric deviation, and physical energy into one audit function.

The Unified System Functional

The pre-execution governance plate. Identity is fixed as invariant reference (I* = constant, dI*/dt = 0). State projects to xᵢ; coupling field K relates components; admissibility gate Φ(x; I*) ≤ 0 permits or denies execution; safety latch L is monotone non-decreasing under the disjunction L(t+1) = L(t) ∨ spike(t); recovery K_auto restores state without erasing breach memory; inadmissible paths terminate at †. Coherence Q reveals structure but does not define truth — neighbor consensus cannot define ground truth when intrinsic variation is part of the signal. Lattice is structure; reference is invariant law. The Lyapunov bound V = Σ‖xᵢ − x̂ᵢ‖² with dV/dt ≤ 0 constrains drift through gating. Final law: only the admissible may execute, only the coherent may propagate, only the violating is permanently remembered.

Reference-anchored, constraint-gated, coherence-resolved, safety-latched. The seven-stage pipeline that governs whether execution may occur.