Two demonstrations on a compliant body certify its whole operating region while five hundred and twelve on a stiff one do not, because what the body contributes never appears in the observations. That is the measured form of a claim three mathematics now make independently: coherence across a body’s local models is a gluing condition rather than a data-volume condition, token-level learning pays exponentially in compositional depth for what predicting your own latents gets at constant cost, and action labels reconstructed by an observer absorb the body’s work in exact proportion to how much the body does, turning fatal the moment the substrate holds a load. The unlock is architectural and every part exists: declare the substrate, log the efference copy, learn from your own latents, and check the gluing instead of pooling the data.
One of eight, and only one of them is physics. How we read a frontier →
Most of the loop was never a data object.
Hold your arm out and close your eyes: it stays up, and nothing about staying up ever crosses your attention. A body runs two systems. A substrate of muscle mechanics, reflexes and pattern generators acts in milliseconds, before any signal is processed, and carries most of the behaviour at most of the energy budget. An information system rides on top, expensive and sparing. The perfect-storm thesis says enough recorded experience will unlock Physical AI, and its best evidence is real: a measured scaling law from twenty thousand hours of human video. But a camera records what the information system did, never what the substrate held, and an observer reconstructing actions from motion attributes the body’s work to the policy. We measured what that costs. Two demonstrations on a compliant body certify its whole operating region; five hundred and twelve on a stiff body reach a quarter of it. And the moment the substrate holds a steady load, policies cloned from reconstructed labels die where policies cloned from true ones hold everything.
The bench registered four predictions before running and published the score: two confirmed, two falsified. The falsifications taught the most. Misattributed labels are benign while the substrate’s work is zero-mean, because doubling a restoring force forgives. Add a steady 1.5 newton load and the reconstructed-label clone collapses to region 0.000 where the true-label clone holds 1.000: it re-applies the holding force the spring already supplies, twice. For pipelines built on reconstructed hand pose, the failure concentrates on load-bearing contact, which is where Physical AI most needs to work.