Axiomatic Model

What might an axiomatic model of our universe look like?

A working document, not even a first draft. Assuredly under construction.

What if we start within number theory? Instead of the Planck units, we somewhat arbitrarily build out with positive and negative numbers in a grid that is the outline for our chart of the universe, yet without the Planck numbers.

Might such an exercise already have been accomplished?  Is this ostensibly what the  Langlands programs attempted to do?  Might another flavor of such a model be found within string theory? Where does each start?  Can our UniverseView be outlined with just simple mathematical constructs?

We have an advantage because we ultimately know that we will be trying to find the absolutely right hook from within the empirical to apply to it. For example, we will have in mind the actual measurements defined for the Planck base units.

Notes:

In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica

In mathematics, a binary operation or dyadic operation is a calculation that combines two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two.

https://en.wikipedia.org/wiki/Binary_operation#References

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Felix Klein (1849-1925) said “Physics is geometry.” John Wheeler from about 1952 to 1972 also made the statement, “Physics is geometry.”

https://en.wikipedia.org/wiki/Binary_operation