Charlot Lab · EFA · one energy, both roles

The controller is the certificate.

A single learned scalar energy over a saturated double integrator. The agent acts by descending it, and because that same energy provably contracts along the descent, the act of controlling is the stability guarantee. One object, two roles, no separate model to check.

Companion to Energy Is the Certificate §7 · verified in Rust (research/efa-unification) · re-proven on the fabric (ebm_unified_verify)

energy V(x,v), the bowl proven Lyapunov basin (certified R=1.35) agents descending to the goal

one energy · controller = argmin_u V(step) · certificate = ΔV+α‖s‖²<0, proven reached goal: 0 / 0 unification tax: zero

saturated torque |u|≤3 · greedy over 31 candidates · certified by affine Taylor+CROWN (959 boxes, audited)

The bowl is the energy V. Every agent picks, from 31 saturated torques, the one whose next state has lowest V, pure descent, and rolls to the goal. The gold ring is not drawn by hand: it is the region where a sound proof (2nd-order Taylor + per-box CROWN, the greedy controller handled as an OR over torques) guarantees V strictly decreases every step. Training a second energy only to certify buys no larger ring and still controls at 100%, so the two roles cost nothing to unify. Nano, in simulation; the scope is in the paper.