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

physicsgeneral-relativityphilosophy-of-physicsoperationalismequivalence-principleproper-timeoutside

In "Cartographing Gravity" (arXiv:2610.32569; peer-reviewed in Symmetry 2026), 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 Geometric Trinity (curvature/torsion/non-metricity formulations) and the 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.