Physics-AI World Model — a Deterministic Operator Machine

A Deterministic Operator Machine, Not a Probabilistic Transformer

Conservation by construction • Calibrated confidence • Measured on RTX 5080

6.0 G state-steps/s  |  energy conserved to 1×10⁻¹⁴  |  155× control improvement  |  0% confidently-wrong decisions

A Transformer is high-dimensional statistical curve-fitting — it predicts the next token's probability. The Physics-AI World Model is an operator machine: state evolves under a fixed linear unitary operator, and the output is the physically-evolved state. There is no sampling, no temperature, no probabilistic drift.

Conservation is structural, not trained. The propagator is M = (I − ds/2·O)−1(I + ds/2·O) with O skew-symmetric ⇒ M orthogonal ⇒ the state norm ‖Ψ‖² is conserved to machine precision. Semantic instructions are Cayley rotations of an so(N) generator; the readout is a fixed projection. You cannot ask a conservation law to hallucinate.

As a control core, the engine rolls out 100,000 candidate action-futures in parallel each step and applies the one that best hits the target readout (one-step MPC).

Measured (RTX 5080): ~3.2 ms per decision (evaluating 100k futures) → ~300 Hz; steady-state tracking error 0.0015 vs 0.236 uncontrolled = 155× improvement. (Model-perfect MPC — a control simulation on synthetic dynamics, not a hardware loop.)

The decision gate does not commit every step. It accumulates a Fisher information angle Θ = arccos(2√(p(1−p))) and only collapses to a decision once Θ ≥ π/3 (60°), reporting its true confidence — not a forced 1.0. This is the same calibration principle that runs through the V131 field theory: reported confidence must equal measured hit-rate.

Reported confidence 0.945 ≈ measured hit-rate 0.945 (calibrated). In the control loop the calibrated gate halves the control error and never once locks confidently onto the wrong target — the cost is honest abstention on the hardest ~20% of cases. In a safety setting, abstaining beats confidently hitting a wall.

With online system identification (each step re-estimates the true operator from observed state transitions), the engine recovers from an 80% initial model mismatch down to ‖error‖ ~0.02, pushing the failure point from 20% (open-loop) to >80% mismatch. It self-repairs.

The differentiator of this work is that the limits are published, not hidden:

• The nonlinear wall: this is a linear unitary operator machine. When state-dependent nonlinearity reaches operator scale, control degrades and online linear identification cannot compensate — breaking through requires nonlinear identification (Koopman lifting cuts the residual 2.4–3.6× but does not eliminate it).
• Two kinds of uncertainty: epistemic (wrong model) is removable; aleatoric (genuinely tied outcomes) is not — forcing <5% abstention on a true coin-flip is just relabeled overconfidence. The gate abstains instead.
• GPU = digital simulation of the engine, not photonic hardware. The MZI-mesh physical executor is a design spec (robust to σ≲3°/3% fabrication tolerance), not yet fabricated.
• A published null result: a drift detector was built, tested head-to-head, found no better than the baseline, and reported as such rather than buried.

Not a replacement for nonlinear deep nets / LLMs on their turf. It is a deterministic, conserved, calibrated core for control, evolution, and physical-front-end computing — where being right or honestly silent matters more than being fluent.