Extending Single-Minus Amplitudes to Gravitons

OpenAI researchers used GPT-5.2 Pro to discover a new mathematical result describing interactions between particles in quantum gravity. This research extends a previously obtained result for gluons to the graviton setting.

The core of the research is the finding that single-minus graviton tree amplitudes are not zero under certain conditions. Existing theory held that these amplitudes vanish, but it was confirmed that they exist as a valid mathematical distribution when the particles' momenta form a special alignment called the half-collinear regime.

This result shows how the infinite-dimensional w-(1+∞) symmetry discovered by Penrose acts on gravitons. This is regarded as important progress toward solving the key problem of unifying quantum mechanics and general relativity.

During the research process, GPT-5.2 Pro was given the prior gluon research results as context, and carried out the construction of the graviton amplitudes—work that would have taken a human researcher considerable time. The model not only solved the problem using a technique called the directed matrix-tree theorem, but also drafted the paper itself.