The Pythagorean Three-Body Conjecture remains unresolved. But not for lack of effort on the part of the models.

In a nutshell, the assertion is that there exist no three-body zero-velocity conditions which have integer masses, a, b, c placed opposite the legs of an a-b-c right triangle that admit a periodic solution — that is, a trajectory that perfectly, certifiably returns to its starting state.

Arbitrarily close in the sense of numerical precision is no cigar:

The pythagorean starting conditions can be ordered by a single parameter, u, which admits every valid integer triple. The triangles are nicely organized by u, viewed as an angle, and the logarithms of the hypotenuses, plotted radially. Each triangle defines an orbit, and as u is made narrower, the orbits converge.

A strategy that has occupied a great deal of the model’s attention consists of rigorously excluding finite discreet ranges of u from harboring a periodic solution. So far, only a small region of the full u-wedge has been excluded.

The full interim report (written by GPT-6 Astra) is here in the unlikely event that anyone cares to read it.