[Models of how a body meets the physical world ]

Posture and landmarks are a compression we chose by hand, and every model downstream inherits its losses. The work now is a learned latent space over body–surface interaction: population-scale contact data, modalities fused, a policy initialised from rules and refined per subject inside it. The blocker was always that the forward direction could only be collected, never generated. That has changed. Load, support and adaptation become directions in a space rather than parameters on a device.

Contact has historically taken one theory per material: Hertz for elastic half-spaces, Kelvin–Voigt without geometric nonlinearity, JKR and Maugis–Dugdale for adhesion, none of them spanning the range. We put rigid, incompressible, compressible, viscoelastic and adhesive substrates inside a single finite-strain formulation, where kinematics, weak form, contact and linearisation are shared and only the constitutive subroutine changes. A substrate reduces to the question of which parameters describe it. What a sensor beneath a compliant layer reads becomes computable rather than only measurable.

Touching Solids · A Unified Finite-Strain Framework for Human Surface Interaction

A person in contact with an adaptive surface appears three times in the block diagram — as plant, as sensor, and as the compensator computing an error and applying torque — and only the third one's gain varies. Awake it is high, adaptive, and retunes itself against whatever you build underneath it. Asleep it runs at 4 × 10⁻⁴ Hz, pays an arousal for every correction, and in REM its output stage is inhibited outright. Two machines that share almost no engineering are one problem read at either end of that variable, and the hardware rate ceiling, the feedforward arbiter and the multi-rate reward stop being three safety decisions and become three consequences of one return path too slow to correct what the machine can do.

The Same Control Problem, Twice

A machine's intelligence exists in two states: computed fresh for each situation, unlimited in scope and expensive per decision, or crystallised — the stored result of a search that already ran, free at runtime and fixed in scope. Crystallise what the environment holds constant; spend the model on what varies. Gravity is constant, so holding belongs in mechanism at zero power. Where a particular body bends tonight varies, so that belongs to the model. The action space is the seam between the two, which makes it something to design rather than inherit. The first thing the rule cost was the eight-link chain below: it crystallised an answer where the answer varies, and the seat is now a platform the model commands directly.

Action Space Engineering · confidentiality: see notes

Recognising enrolled subjects is closed-set, the shape of Face ID. Estimating posture and landmarks on a body that has never been on the surface is open-set, and it is the harder claim. Across roughly fifty sessions, with every fold disjoint by session and by subject, posture reaches 90.9% out-of-fold — high-eighties once the trivially separable empty class is removed — and nine landmarks regress to 7.7 px mean error at 0.80 PCK@10px, with per-joint error tracking where the physical signal is stable. All of it on one contact geometry. Whether the structure survives a different one — different loads, a subject upright and awake — is what the second surface exists to answer.

One Sensor, Many Bodies

The first controller was thirty hand-written rules over posture, landmarks and identity. Extending it to the devices around the surface took it to eighty inside two weeks while the joint action space passed 10¹⁰, and a rule table collapses every subject onto one policy regardless. We put a language model above the learned perception stack, reasoning over semantic state rather than the raw field — then had to answer for it, because a learned policy acting on a body that cannot perceive it is covered by no published standard. We named the class, 6B, and built to it: ten independent layers between a fault and harm, an arbiter trained once and then frozen against every gradient the system afterwards produces, autonomic signals as the reward of record, and nothing a passive subject depends on placed behind a network link. The learning system is not permitted to be the safety system.

From If-Cases to Language Models · The Fourth Law · Physical Intelligence, Safely

A degree of freedom needs one mechanism to change its state and another to hold it, and those two functions separate cleanly. Make every transmission self-locking and holding costs nothing, so power only has to be present during transition. Fifteen degrees of freedom run on six motors today, four in the revision underway, and two at the architectural limit — one that powers, one that selects. Installed capacity tracks peak load on a single axis rather than the number of axes.

Multiplexing Mechanical Power

Forty-two independently commanded blocks produce a step function. A body in contact requires a continuous profile with no resolvable transition — Σ to ∫, passively, thousands of times a night. Folded geometries each generate displacement and each generate structure: Miura-ori couples adjacent zones, auxetic lattices concentrate at every hinge node, kirigami fatigues at every cut tip, and skin finds all three. What worked was passive. Constant-force springs holding ~10 N independent of extension pay out length as blocks rise and retract it as they fall, so tension across the covering layer stays uniform whatever the configuration beneath it.

From Discrete to Continuous · Flat Force Across a Moving Surface

Articulated surfaces hinge where the structure allows. A body folds at the hip. The offset between those two axes is absorbed by the person as relative sliding, and it grows with angle. We synthesised an eight-link mechanism with an exact remote centre of motion at the hip point — continuous through sixty-five degrees, not approximated at precision points — then broke two blocks out of the modular array to clear its sweep. The kinematics were the fixed constraint. The architecture moved.

The Pivot Problem Nobody Talks About

Landmark recovery had turned out not to be subject-independent. The mapping from contact field to anatomy held on unseen bodies only when the model was handed segment length and hip width, which made identity a prerequisite rather than a feature. Ninety-four features per frame — regional pressure sums, centroid, aspect ratio, eccentricity, entropy, gradient statistics — standardised, projected onto fifteen principal components, separated by an ExtraTrees classifier. 88% on sessions recorded entirely separately from training, against a 55% majority baseline, from five minutes of enrolment. A body is identifiable by how it distributes its own weight, and identifying it requires nothing of it.

Pressure ID

Treat the compliant layer as a linear shift-invariant system and recover the surface load from what reaches the sensor. Modelled as an elastic foundation — Winkler, Pasternak, Filonenko-Borodich — and attacked from Boussinesq inversion through to physics-informed networks, every route failed: a kernel too uniform to invert, physics losses the network learned to ignore, biharmonic residuals producing gradients of order 10¹⁰ on a 6 mm grid. The failure modes were the finding, and we published them in full. Then we inverted the question. A filter that cannot be removed can be specified: fourteen compositions, PSF measured at nine positions and several loads, sensor plane moved through four depths in each. What shipped is the narrowest and most position-stationary kernel that still cleared the perception threshold — selected for invertibility, not for feel.

Pressure Deconvolution Through Mattress Blocks · The Mattress as an Inverse Problem

Forty-two actuated blocks, 250 mm of travel each, 1 mm of commanded precision: a surface capable of almost any profile, and no instrument capable of saying which profile a body required. A 28 × 24 array answered part of it, at a cell pitch wider than most of the features it was looking for. Taking the array to 112 × 96 — 10,752 cells at ~25 mm, a spatial Nyquist limit near 50 mm — resolved them and exposed the dominant error term. The medium between body and sensor attenuates, disperses and delays the field before any of it is sampled.