First lets go back 300 years to what Newton really said
The Constant of Proportionality: Newton's Deliberate Omission of G and the Lost Principle of Invariance
And Einstein agreed that c^2 in E=mc^2 was unit scaling and the reality was E~m.
Let's look at what the constants are really:
G as a Metrological Artifact: A Formal Proof of Newton's Principle of Invariance
The main work on this blog is this post:
The Structure of Physical Law as a Grothendieck Fibration
This shows how conscious beings fragment a unified reality into shards that it can perceive. The being then chooses a unit chart for the measurement and this projects the form of the physical law into their physics framework.
The calculus of physical law from that document is implemented as a github page:
Law Forge
This is a meta theory not just about physics, but it can be seen to describe the structure of all human knowledge as perception of conceptual axes, those axes are scaled relative to all other knowledge, and combined into vectors in knowledge spaces.
The Universal Architecture of Human Knowledge: A Categorical Framework for Epistemic Construction
You can focus on just solving the constants as a system of equations and defining them with the factors you found.
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