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Inspired by the deep insights revealed in the recent work around the Amplituhedron, a new and deeper mathematical principle has revealed itself. While the amplituhedron caused quite a buzz even outside of the world of theoretical particle physics, thus far it is restricted to $\mathcal{N}=4$ supersymmetry. In contrast, this new object is able to represent all known predictions for physical observables. The new object, outlined in a recent paper is being called "The Realineituhedron".

The key observation is that at the end of the day, everything we measure can be represented as a real number. The paper outlines a particular way of projecting these observations onto the realineituhedron, in which the "volume" $\Omega$ of the object represents the value of the observation.

In fact, the physically observable quantity must be a real number, a feature foreshadoewed by the Hermitian postulate of quantum mechanics.

The paper is full of beautiful hand-drawn figures, such as the ones below:

Is it possible that there is some geometrical object is able to capture the Hermitian nature of these operators--indeed, is it able to represent all fundamental observables?

This masterful work will take some time to digest -- it was only released today! One of the most intriguing ideas is that of a "The Master Realineituhedron", denoted $\mathbb{R}^2$, in which all realineituhedrons can be embeded.

It would be interesting to see whether this larger space has any interesting role to play in understanding the m = 1 geometry relevant to physics.