PAI-250 · Education

Energy First Architecture

The physics-first thesis, built in the browser: one scalar energy a body descends to act — and the same energy is the proof it will not diverge. Descend it to control, read its decrease as the certificate, get that certificate for free by structuring the energy as a port-Hamiltonian (at any number of joints, where a box proof cannot), and gate a task policy so it verifies before it commits. No bolted-on verifier; one energy, and the proof is the objective. This is an active research line, not ours alone (co-learned port-Hamiltonian models with passivity-based safety certificates, arXiv 2604.26172 and 2512.24493, and physics-driven world models like PH-Dreamer); what you build here is the open, on-device, readable version of it.

Skilled → Frontier·3 modules · 4 labs·4 lessons
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Module 1

One energy, both roles

Act by descending an energy, and see that the same energy is the stability certificate.

  1. SkilledTo act is to descend an energyControl a pendulum by descending a shaped energy — the energy IS the controller, not a policy bolted to one.→
  2. SkilledThe same energy is the proofSee that the energy you descended is, unchanged, a Lyapunov certificate: it provably decreases along the closed loop.→
Module 2

Structure, not proof

Earn the certificate by construction — at any number of joints, where proving it walls out.

  1. FrontierStructure, not proofEarn the certificate by CONSTRUCTION at any number of joints — where proving it box-by-box is astronomically infeasible.→
Module 3

Verify before you commit

Gate a real task policy with the energy certificate: a guarantee before the action commits.

  1. FrontierVerify before you commitPut a certificate gate on a task policy: veto an unsafe action before it commits — a guarantee, not a score.→