Editing Graph, Wall, Tome (section)

=== Graph ===
The Graph is a paragraph from Edward Witten's 1987 paper [https://cds.cern.ch/record/181783/files/cer-000093203.pdf Physics and Geometry] at the bottom of page 20. In language it concisely encodes the general structure of reality:

<blockquote style="font-size: 125%;">
If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations:

(i) Spacetime is a pseudo-Riemannian manifold <math>M</math>, endowed with a metric tensor and governed by geometrical laws.

(ii) Over <math>M</math> is a vector bundle <math>X</math> with a non-abelian gauge group <math>G</math>.

(iii) Fermions are sections of <math>(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}_{-} \otimes V_{\tilde{R}})</math>. <math>R</math> and <math>\tilde{R}</math> are not isomorphic; their failure to be isomorphic explains why the light fermions are light and presumably has its origins in a representation difference <math>\Delta</math> in some underlying theory.

All of this must be supplemented with the understanding that the geometrical laws obeyed by the metric tensor, the gauge fields, and the fermions are to be interpreted in quantum mechanical terms.
</blockquote>

<div style="text-align: center">
Scan of the original paragraph:
[[File:The-graph.png|class=shadow|650px]]
</div>

Implicit in each respective section is:
# Spin-2 Force Field for Gravity, the Einstein Field Equations
# Spin-1 Vector Boson Theory, Yang-Mills-Maxwell Equations
# Spin-1/2 Matter Theory, Dirac Equation

These are the gauge fields referred to by the last sentence.

Note that the quantum (e.g. quantum mechanics, quantum field theory, quantum measurement, etc...) is mentioned only after the key geometric insights.