Stiffness Fields on Skeleton--Surface Lines: Structured Physical Inference for AI-Driven Dynamics of Gaussian-Splat Entities

Abstract

Physics-integrated Gaussian Splatting either prescribes material parameters by hand or estimates them point-wise from appearance, leaving unstructured numbers that inherit appearance confounding. We show that stiffness can instead be carried by structure: a two-dimensional field $F(s,t)$ on skeleton--surface lines, with solid skeleton elements, typed joints (type, degrees of freedom, angular limits), and connection lines carrying radial stiffness profiles with stretch/compression limits. We validate three claims. \textbf{(i) Inference: anchor--propagation turns colour-template agreement and geometric consistency into stiffness anchors that correct confounded regions, cutting synthetic RMSE by $40%$ ($1.029\to0.618$) and, on $9$ validated real objects, per-object error by a median of $1.67\times$ ($2.44\times$ where per-view names conflict). \textbf{(ii) Joint typing: the nullspace of the interface stiffness matrix identifies the joint type --- $7/7$ on synthetic bundles and $7/7$ on real captured meshes --- with a sampling gate that refuses to type when the interface cannot support it, and an interpretable failure order ($4/7$ at $1^\circ$ direction noise). \textbf{(iii) Boundaries, measured: the same layer cannot repair a density prior or a volume convention; against a real external pipeline on official ABO-500 objects our aggregation changes its field by $\sim\!10^{-3$ of its mass while our full pipeline is $5.8\times$ closer, and the volume convention alone moves the error ratio by $\sim\!20\times$; six appearance cues explain none of the residual. Where appearance is insufficient --- same shape, different material --- drive-and-compare probing cuts stiffness recovery error from $51$--$115%$ to $1$--$8%$ within $10$ probes, and joint-limit error from $25.0^\circ$ to $1.75^\circ$. The contribution is a representation, a typing module, and a measured boundary map.