De Haro and Elizalde (2026) argue the nonlinear completion of their operational gravity is forced to be Einstein's field equations specifically, by Lovelock's 1971 uniqueness theorem under covariance, second-order, and conservation assumptions

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The operational reconstruction in "Cartographing Gravity" (claim-de-haro-elizalde-2026-reconstruct-linearized-gr-from-conatus-and-potentia) delivers only the linearized theory. De Haro and Elizalde get from there to full nonlinear general relativity not by a new derivation but by invoking an existing uniqueness result: Lovelock's theorem (D. Lovelock, "The Einstein Tensor and Its Generalizations," J. Math. Phys. 12, 498–501, 1971). Once general covariance, locality, and second-order field equations are imposed together with general energy–momentum conservation, they argue, "the Einstein tensor emerges as the unique divergence-free covariant structure within the class of theories satisfying the assumptions of Lovelock's theorem, up to a cosmological term"; their Minkowski reference structure excludes the cosmological term, "leaving Einstein's field equations as the resulting non-linear completion." The intended force of the argument is that GR's field equations are not postulated but are the only option left standing in that class — not merely "something GR-like."

Crucially, the authors frame this as restricted and assumption-dependent, not an unconditional proof: "The essay does not claim to derive General Relativity without prior assumptions, nor to establish an unrestricted uniqueness theorem." The uniqueness therefore lives entirely inside Lovelock's premise set; relax covariance, second-order, or the conservation condition and the conclusion is not claimed.

This is the same logical shape as the vault's other gravitational-uniqueness and alternative-formulation material — the Geometric Trinity (where GR, TEGR and STEGR are dynamically equivalent under a restriction on the matter sector) and the metric-affine generalizations that enlarge exactly the class Lovelock's theorem constrains. It bears on the standing underdetermination thread: a uniqueness theorem is an arbitration criterion, but only for theories that accept its premises.