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v = −κ∇ₐE + w for a coupled 2-link arm: one scalar potential Eθ(s,a,t) that actuates (descend its action-gradient)
and verifies (Eθ(·,1): low = valid action), plus a small ℓ2-penalized correction net w that absorbs the residual a
scalar fit cannot express.Eθ(s,a,t): relu/linear MLP over [cos(θ₁−g₁), sin(θ₁−g₁), ω₁, cos(θ₂−g₂), sin(θ₂−g₂), ω₂, sin θ₁, sin θ₂, a₁, a₂, t] → scalar.wφ(s,a,t): same inputs → 2-D velocity residual, trained jointly with an ℓ2 penalty (λ in config.json) so the potential must carry all the field it can.a←0; for k in 0..K { t=k/K; a += (−κ∇ₐEθ(s,a,t) + wφ(s,a,t))/K } — the action is energy descent plus a small correction. ∇ₐEθ is exact (analytic backprop through the relu net).Eθ(s, a, t=1) — lower is more valid.config.json)config.json); the policy is meaningless without that env.config.json.config.json; a pure-potential variant costs actuation (ledger §VII).experiments/efa_release.rs (train → gate → save → reload → re-verify) from the EFA validation program
(65 measured experiments, negatives included): see WHITEPAPER.md §3.9 and docs/RESULTS.md §VII, including the 2026
frontier check that produced this architecture (docs/FRONTIER-CHECK-2026.md).