TRIM: Trocar-Referenced Instrument Motion for Physically Grounded Surgical World Models

World models for Physical AI should represent dynamics in coordinates that remain physically meaningful when observation conditions change. In minimally invasive surgery, endoscope motion changes an instrument’s image coordinates even when its motion relative to the surgical scene is unchanged. We introduce TRIM (Trocar-Referenced Instrument Motion), a metric surgical state anchored at the laparoscopic trocar or remote center of motion (RCM), a persistent physical anchor that generic video lacks. Given calibration and geometry, the TRIM pose is invariant to pure camera-coordinate reparameterization, allowing predictions from any world model to be expressed and evaluated in a stable physical frame. On SurgPose, we certify the recovered state against da Vinci robot signals, obtaining 1.1–2.2 mm wrist RMSE, median jaw $|r|=0.935$, and insertion $r\geq0.98$. On 14 held-out recording setups, a camera-frame inverse-dynamics model and a 3B surgical vision-language-action model, both zero-shot and fine-tuned in-setup, fail to beat a no-motion persistence floor; their residual error is traceable to predicted motion directions that carry little information about the true motion. In contrast, a compact state-space forecaster reaches 2.85 mm error against a 6.36 mm persistence floor with a 1.9× validation-to-test gap, compared with 12× for the pixel model. Adding the current frame widens this gap, while training directly on trocar-frame targets is slightly worse for both model families; geometric transformation nevertheless grounds predictions exactly. Finally, generated trajectories can satisfy RCM geometry while exhibiting 95th-percentile speed and acceleration approximately 11× and 31× those of real motion. TRIM therefore serves as a physically grounded interface for world-model prediction and evaluation rather than as a privileged training target, separating coordinate correctness, predictive accuracy, and rollout fidelity in surgical world models.