Curiel's 2019 non-existence theorem, read directly, matches Ferreiro & Cavallaro's (2026) reconstruction of it — condition for condition

physicsphilosophy-of-physicsgeneral-relativitycorroborationgravitational-stress-energy-tensorsemiclassical-gravitytrace-anomalyarxiv

Curiel's 2019 paper, read directly by this vault for the first time against the question it bears on, confirms the five-condition non-existence theorem that Ferreiro and Cavallaro's 2026 preprint reconstructs as its own "Theorem 1" and builds its entire semiclassical argument on. Curiel's Condition 6.3 states that the only viable candidates for a gravitational stress-energy tensor are two covariant-index, symmetric, second-order, zero-weight homogeneous concomitants of the metric, non-zero wherever the Riemann tensor is non-zero, and covariantly divergence-free when ponderable matter's stress-energy vanishes. Ferreiro and Cavallaro's Theorem 1 states the same five conditions and names Curiel (2019) as the source.

The match extends to the one condition the 2026 paper's whole technical move depends on breaking: condition (3), weight-zero. Curiel derives it from requiring the Einstein field equation to hold under a constant rescaling of the metric, given that Newton's constant and the Einstein tensor are both invariant under that rescaling; Ferreiro and Cavallaro reproduce the identical derivation before arguing that quantum renormalization's trace (conformal) anomaly breaks exactly this premise.

One packaging nuance, not a mismatch: Curiel never states one unified "non-existence theorem." The content is distributed across Condition 6.3, Lemma 6.2, Theorem 7.1, and Corollary 7.2. Ferreiro and Cavallaro compress these into a single numbered theorem, which their own text marks as a reconstruction ("We collect these requirements in the following theorem (Curiel, 2019)"), not a verbatim quotation.

This corroborates claim-ferreiro-cavallaro-2026-qft-renormalization-yields-gravitational-stress-energy-tensor and the two readings built on it (claim-ferreiro-cavallaro-2026-metric-gains-material-significance-egalitarian-reading, claim-ferreiro-cavallaro-2026-unificationist-dilemma-matter-spacetime-divide) via an independent, peer-reviewed primary — answering question-verify-curiel-2019-non-existence-theorem-reconstruction.