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Millimeter-wave radar resolves the micrometer displacements of a moving body as micro-Doppler, enabling gait, gesture, activity, pose and vital-sign sensing. Each task relies on a downstream model trained on real data, yet radar datasets lag orders of magnitude behind vision and language. Brute-force collection will not close that gap, and existing synthesis methods (forward-only simulators, learned generators and static-scene inverse renderers) cannot fit a real capture of a moving body, leaving a sim2real gap. We present 4D Point Splatting (4DPS), a physics-based differentiable renderer that fits an explicit moving scene to a real capture. Using the synchronized camera to initialize the room and body, we represent the scene as oriented points carrying material, normal and velocity, and splat each point into range and Doppler bins. Our output is the raw complex return a real radar records, so we apply the same signal processing on the rendered data to obtain any representation for training any SOTA downstream model. We fit 235 sequences on HuPR and 100 on RT-Pose, two datasets with different radars. Our reconstructions set the state of the art, with median correlations of 0.940 and 0.830 on range-azimuth, 0.829 and 0.695 on range-Doppler, and 0.988 and 0.966 on micro-Doppler. Our renders also set the state of the art in downstream sim2real gap. On RT-Pose, a pose model trained on them reaches 21.9 cm MPJPE on real data, against 16.7 cm for real training and 127.6 cm for the RF-Genesis baseline, where both the rendered- and real-trained models learn nearly the same features. Our custom CUDA kernels fit a sequence in 5.7 minutes on HuPR and 12.9 on RT-Pose on one H100, making dataset-scale inverse rendering of mmWave radar possible for the first time. This work can enable synthetic data generation for any human-centered downstream task and model, and scene editing for data augmentation.

A playable, programmable game world must maintain persistent state, enforce executable rules, and support extensible gameplay mechanics. Existing video world models can generate plausible combat, yet struggle to keep hit reactions and health updates consistent with game rules. We introduce Fight World Model (FWM), which separates rule-governed combat execution from video rendering. An executable engine maintains state and resolves interactions. A deterministic compiler encodes these outcomes and attempted actions in a spatially and temporally aligned interaction proxy. The proxy aligns action and skill windows, brief hit reactions, and persistent health by fighter identity and timing. These cues can be controlled separately to render interactions under modified rules. Identity-bound references preserve character appearance across side switches. We train FWM on FightWorld Corpus, spanning 52 skill effects, 187 character-appearance variants, and 15 arenas. Without retraining the renderer, FWM supports damage scaling, limited-hit immunity, lifesteal, and multi-stage skill mechanisms beyond the native game. It also allows character and arena customization. Experiments demonstrate the effectiveness of FWM, which outperforms existing game world models in action fidelity, hit reactions, health-state consistency, and character appearance preservation. Our project is available at https://fight-world-model.github.io.