Charlot Lab · PINN × EFA · the physics gate

A certificate on every action.

A frozen, imperfect policy drives a nonlinear pendulum. A physics gate checks each proposed torque against the plant's energy certificate, does it make the energy provably contract, $\Delta V + \alpha\lVert s\rVert^2 < 0$?, and substitutes the certified action only when the policy would violate it. Same policy, same behavior, now with a per-step stability guarantee, at microseconds per step.

The capstone of Energy Is the Certificate × PINN: the energy is the computable certificate on any policy's action · companions: unified pendulum, PINN trust-meter

certificate satisfied (ΔV+α‖s‖²<0) raw policy violates the certificate gate fired, certified action substituted

certificate satisfied: raw — · gated 100% gate fires — of steps gate cost ~2 µs/step (<1 ms)

frozen policy = linear PD (imperfect on the nonlinear, saturated plant) · certificate + certified action from the verified pendulum energy

Both pendulums reach the goal, on a plant with enough authority, the raw policy usually gets there. That is the point: the gate's product is not task success, it is the guarantee. The raw policy satisfies the stability certificate on only ~⅔ of steps (its energy jumps upward, red, whenever a hallucinated or off-model action pushes the wrong way); the gate holds the certificate on 100% of steps, its energy descending monotonically, by substituting the certified action only on the steps where the policy's action would fail the check, and leaving the policy untouched otherwise (fewer, when you switch the hallucination spikes off). This is the PhysVLA pattern with a formal certificate underneath: a per-step, deterministic, microsecond physical-consistency guarantee bolted onto a black-box policy. Nano, single-seed, one plant, in simulation; the certificate is the per-step contraction proven for this basin, scope in the paper.