A Splat You Can Act On: Render-Aware Conformal Certificates for Trustworthy 3D Gaussian Splatting

A robot acting on a 3D Gaussian Splat treats its geometry as exact. It is not: nominal 95% depth intervals cover 43% of pixels (per-scene 0.14–0.64), and the literature reports rankings, not answers to “safe to grasp here?”. An ECE-optimal temperature leaves ECE 0.025, certifying nothing. We make 3DGS self-certifying. A post-hoc conformal layer wraps any estimator, emitting brackets with distribution- free finite-sample coverage, as tight as finite data allows—cutting bracket failures 86.73% and 83.14% on synthetic objects and 15 real DTU scans (Fig. 1). Binning by a free rasterizer signal restores per-region validity where a global quantile under- covers (0.81 → 0.89 worst-region, p=0.029 excluding the one scene whose mesh ground truth our audit rejects; 0.86 → 0.88 on real scans). Per-region promises get read as per-map ones, so we prove a simultaneous bound: all G regions hold together with probability 0.957 against Mondrian’s 0.001. Learn-then-Test bounds executed failure, cutting simulated approach collisions 0.53 → 0.09. The same layer transfers to four real depth sensors, where naive intervals cover as little as 7% of pixels, and is estimator-agnostic over six σ sources, needing no ensemble.