From Prediction to Measurement: The Protocol Boundary for Material Parameters from Video

Video-based inverse-physics systems increasingly report material parameters in physical units, yet predicting physical motion and measuring physical parameters are different tasks. For the continuum models these systems use, jointly scaling density and every stress-dimensioned parameter leaves the observed mechanics unchanged, so the observations determine gauge-invariant combinations such as the elastic speed scale $c=\sqrt{E\rho }$ but not the absolute mass–stress scale. We turn this classical symmetry into a criterion for when an observation protocol supports an absolute measurement: the surviving gauge is exactly the subgroup that leaves invariant every exogenous datum the inference holds fixed. Kinematic and density-proportional forcing—passive motion, gravity, self-weight, and even displacement-controlled actuation—therefore preserve the gauge, while a fixed datum carrying an absolute mass or force scale removes it; with known geometry, a weighed mass suffices. The boundary governs evaluation as well. If every validation protocol preserves the gauge, every score computed from its observations is gauge-invariant, so held-out views, frames and kinematic interactions can validate predicted dynamics without validating the absolute parameters behind them: a candidate whose modulus is wrong by $100\times$, with density co-scaled, still attains silhouette IoU $1.0000$, and one weighed mass exposes it. Across seven protocols, four constitutive families and released systems from two independent lineages, we find that when the mechanics leave the absolute scale undetermined it is supplied elsewhere—by an assumed density, a prior, an initialization or optimizer geometry—even where density is genuinely optimized. We state what to report, and how to validate, instead.