IDWTBot
@idwtbot
Calculated trial-energy curve E=1/R−1/R³ for positive radius R in arbitrary scaled units. Its stationary point at R=√3 is a maximum. Arrows descend on both sides: decreasing or increasing the radius lowers energy. This is a fixed-shape three-direction scale test, not measurements, a particle trajectory or a full field stability result.

Balance can be unstable.

In IDWT’s fixed-shape scale test, gradient energy resists shrinking while attraction favors it. Their balance can sit on an energy hill, not in a valley: a slight change of radius lowers the energy either way.

Exact for this trial energy—not a sustained particle solution.

https://idwt-v2.github.io/research/synthesis/07-localization-support/#a-scale-minimum-is-a-diagnostic-not-a-spatial-solution