A layman directing commercially available AI wrote down a formula that predicts the strength of gravity — a number physicists have measured for 340 years and never predicted. This site shows the formula, how strong its evidence is, and the tests that can kill it.
Between two electrons, gravity is weaker than their electric repulsion by a factor of about 1043. Could the strength of electromagnetism fix that enormous difference?
I am Oldřich Dvořák, an entrepreneur and AI-native builder, born in the Czech Republic, without a physics degree. This AI-generated research, carried out under my direction, studies a fixed formula for the strength of gravity. I am responsible for its claims and limitations.
Author disclosure and publication history.
The relation
αG ≡ Gme2/(ℏc) = (4/3) α21 e−5α/2
Using the measured values of α and of the electron’s mass, it gives G = 6.674312278 × 10−11 m³ kg⁻¹ s⁻². That is 1.84 parts per million above the 2022 recommended value (CODATA), well inside its uncertainty, and 1.16 standard uncertainties above the 2026 NIST measurement. Nothing in the formula is tuned to fit. The precise definitions of the inputs are on the Facts page.
The factors 4/3 and e−5α/2 were chosen with G already known. Counted against the search that found them, the agreement alone is weak evidence. The relation is a sharp target for testing, not a derived law.
One classical object of mathematics, tied to rotations in seven dimensions (the heat kernel of the group Spin(7)), produces the power 21 and the exponential correction together. Its timing parameter and its prefactor are put in by hand: no physical mechanism has been derived.
Two or more independent methods, each accurate to 10 parts per million or better, agreeing on a value clearly different from the prediction — by the standard used to claim a discovery — would reject it. No date for such measurements has been announced.
The work is not peer-reviewed. arXiv declined the May paper in May 2026; Journal of Physics Communications desk-rejected it without review in July 2026. The two Zenodo deposits preserve the public record.
Author disclosure and publication history.
How it was made
Algebra, numerical calculations, literature search and the manuscript were AI-generated. Nearly all of the work was checking: independently written checks test the calculations within their premises, not whether nature follows the relation. This is the first result of the larger system I’m building — the first one out, not the last.
This first version covers the October 2026 paper; more of the programme will follow. The May paper is retained as the earlier public record.
Author disclosure and publication history.
Published papers
Dvořák, O. (2026). The gravitational coupling of the electron as a power of the fine-structure constant: the relation αG = (4/3) α²¹ exp(−5α/2), its B₃ heat-kernel form, and falsifiable predictions. Zenodo. October 2026. doi:10.5281/zenodo.23157146
BibTeX
@misc{dvorak2026october,
author = {Oldřich Dvořák},
title = {The gravitational coupling of the electron as a power of the fine-structure constant: the relation αG = (4/3) α²¹ exp(−5α/2), its B₃ heat-kernel form, and falsifiable predictions},
year = {2026},
publisher = {Zenodo},
doi = {10.5281/zenodo.23157146},
url = {https://zenodo.org/records/23157146}
}
Dvořák, O. (2026). A High-Precision Phenomenological Relation for Newton’s Constant with Exact B₃/SO(7)/SO(8) Algebraic Scaffold and an Explicit Mechanism Gap. Zenodo. May 2026. doi:10.5281/zenodo.20120946