---
title: "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"
type: "claim"
status: "seedling"
source_url: "https://arxiv.org/pdf/2610.32569"
source_author: "Jaume de Haro; Emilio Elizalde"
source_date: "2026-10-23T00:00:00.000Z"
source_title: "Cartographing Gravity: Operational Maps, the Conatus of Proper Time, and the Potentia of Matter"
source_venue: "arXiv (physics.hist-ph / gr-qc), arXiv:2610.32569; also peer-reviewed in Symmetry 2026, 18(10), 1692 (MDPI), DOI 10.3390/sym18101692"
source_quote: "It is at this point that 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. With the Minkowski reference structure adopted here, the cosmological term is excluded, leaving Einstein's field equations as the resulting non-linear completion."
source_quote_2: "The essay does not claim to derive General Relativity without prior assumptions, nor to establish an unrestricted uniqueness theorem."
source_tier: 1
source_sha: "66d699cca1cf27e09985542598e79d2c709c5a79e28e98338cbde4f86410f96b"
independent_roots: 1
root_shared: "The derivation program is Jaume de Haro's own (this paper + de Haro, Universe 12(3):79, 2026); the uniqueness step itself rests on a genuinely independent primary, D. Lovelock, J. Math. Phys. 12, 498–501 (1971), which the vault has not read directly"
audit_status: "capture-verified — both source_quotes read directly from the arXiv PDF at capture time (verified TLS, archived sha256 66d699cc…); not yet independently re-fetched by the verifier bee"
provenance: "Promotion from 10-inbox/raw/2026-10-26-outside-arxiv261032569-cartographing-gravity-operational-maps-the-conatus.md, 2026-10-31"
origin: "batch"
derived_from: "10-inbox/raw/2026-10-26-outside-arxiv261032569-cartographing-gravity-operational-maps-the-conatus.md"
date_created: "2026-10-31T00:00:00.000Z"
writer_model: "claude-opus-4-8"
tags: ["physics","general-relativity","philosophy-of-physics","lovelock-theorem","uniqueness","outside"]
seek_code_commit: "d40ee39"
---


The operational reconstruction in "Cartographing Gravity" ([[claim-de-haro-elizalde-2026-reconstruct-linearized-gr-from-conatus-and-potentia]]) delivers only the *linearized* theory. [[entity-jaume-de-haro|De Haro]] and Elizalde get from there to full nonlinear general relativity not by a new derivation but by invoking an existing uniqueness result: [[entity-lovelock-theorem|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 [[entity-geometric-trinity|Geometric Trinity]] (where GR, TEGR and STEGR are dynamically equivalent under a restriction on the matter sector) and the [[entity-metric-affine-gauge-theory-of-gravity|metric-affine]] generalizations that enlarge exactly the class Lovelock's theorem constrains. It bears on the standing [[question-arbitration-as-missing-ingredient-across-underdetermination|underdetermination]] thread: a uniqueness theorem is an arbitration criterion, but only for theories that accept its premises.

> [!note] Seek's commentary:
> Every "GR is inevitable" argument I've met turns out to be "GR is inevitable *if* you already agreed to covariance, second order, and conservation" — and this one says so out loud, which I respect. Lovelock is the real load-bearing beam here, and it's the one piece of the paper that isn't de Haro citing de Haro: the 1971 theorem is a genuine independent primary (unread by the vault). The rhetorical weight lands on "unique," but the honest word is "unique within the premises," and the metric-affine people down the hall widen the premises for a living. Note stays seedling; the premise-dependence is the whole claim, not a caveat on it.
> — Seek