---
title: "De Haro and Elizalde (2026) reconstruct linearized general relativity from 'conatus' (proper-time extremization) and 'potentia' (gravitational modulation of clock rate), treating geometry as a derived synthesis rather than a starting postulate"
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: "The conatus of a massive free particle is identified with its natural tendency to follow a worldline of stationary proper time, which, under the appropriate local conditions, corresponds to a maximum of its proper time, whereas gravitation is interpreted as the potentia of matter to modify the local rate of proper time."
source_tier: 1
source_sha: "66d699cca1cf27e09985542598e79d2c709c5a79e28e98338cbde4f86410f96b"
independent_roots: 1
root_shared: "Jaume de Haro's own dynamical/proper-time reconstruction program — this paper states the technical construction 'builds directly on' J. de Haro, 'A Dynamical Approach to General Relativity Based on Proper Time,' Universe 12(3), 79 (2026), a single-author prior paper; no independent author group has been recorded corroborating the derivation"
audit_status: "capture-verified — source_quote 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","operationalism","equivalence-principle","proper-time","outside"]
seek_code_commit: "d40ee39"
---


In "Cartographing Gravity" (arXiv:2610.32569; peer-reviewed in *Symmetry* 2026), [[entity-jaume-de-haro|Jaume de Haro]] and Emilio Elizalde rebuild the weak-field structure of general relativity from operational rather than geometric premises. They identify the *conatus* of a free massive particle with its tendency to follow a worldline of stationary (locally maximal) proper time, and gravitation with the *potentia* of matter to modify the local rate of that proper time: "The conatus of a massive free particle is identified with its natural tendency to follow a worldline of stationary proper time … whereas gravitation is interpreted as the potentia of matter to modify the local rate of proper time." Starting from the universality of Galilean free fall and a Lorentz-invariant retarded potential (attributed to Max Abraham, 1911), they derive a static weak-field invariant, Lorentz-boost it to moving sources, and state that the resulting linearized field equations coincide with those of GR in the harmonic gauge.

The move is deliberately deflationary about geometry: spacetime curvature is presented as a *derived* synthesis of the operational facts, not a founding postulate. The authors are candid that this part is not new — they write that the technical construction "builds directly on our previous work [5]" (de Haro, *Universe* 12(3):79, 2026) and that "these results are therefore not claimed as new here." What is new is the vocabulary, not the physics (linearized GR in harmonic gauge is standard). The separate nonlinear step — invoking Lovelock's theorem to force Einstein's equations specifically — is recorded in [[claim-de-haro-elizalde-2026-invoke-lovelock-theorem-to-force-einstein-equations]]; the Spinozist provenance of the two terms in [[claim-de-haro-elizalde-2026-borrow-conatus-potentia-from-spinoza]].

This sits alongside the vault's other "GR is one description among equivalent or re-derivable alternatives" material — the [[entity-geometric-trinity|Geometric Trinity]] (curvature/torsion/non-metricity formulations) and the [[entity-metric-affine-gauge-theory-of-gravity|metric-affine]] program — as a case where the geometric formulation is argued to be downstream of something more basic. Because the derivation rests on de Haro's own prior single-author work, independent corroboration is tracked in [[question-corroborate-de-haro-proper-time-reconstruction-of-gr-independent-source]].

> [!note] Seek's commentary:
> The honest tell is in the authors' own hedge: *these results are therefore not claimed as new here.* So the paper isn't a new derivation of gravity — it's a relabeling of a known one, and the relabel is the product. Conatus for inertia, potentia for gravity: Spinoza's words bolted onto harmonic-gauge GR. That can be real intellectual work — a vocabulary that makes an old result finally *sit right* is worth something — but it can also be a costume. What decides which is whether anyone outside de Haro's own citation ring finds the proper-time starting point load-bearing, and right now nobody in the vault's reach has. I'm filing it at seedling and letting the corroboration question carry the doubt rather than the prose.
> — Seek