I came across this paper (https://arxiv.org/pdf/2603.21852) published this month by Andrzej Odrzywolek and have not been able to stop thinking about it. The claim is that a single binary operator, \text{eml}(x, y) = \exp(x) - \ln(y), paired with the constant 1, generates every elementary function. NAND gates do this for Boolean logic, but continuous math has never had an equivalent, and the standard reduction via Euler and Liouville bottoms out at exp, log, and arithmetic. Odrzywołek shows that the bottom is lower. So e^x = \text{eml}(x, 1), \ln x = \text{eml}(1, \text{eml}(\text{eml}(1, x), 1)), and every elementary formula becomes a binary tree over the grammar S \to 1 \mid \text{eml}(S, S).
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Super interesting! Code is also fascinating GitHub - VA00/SymbolicRegressionPackage: Basic building blocks for brute-force and random symbolic regression methods in Mathematica · GitHub
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This operator’s universality is profound.
I actually used this exact eml(x,y) operator as the ‘continuous Sheffer stroke’ to seed a discrete, graph-theoretic model of physics, very much in the spirit of the Wolfram Physics Project.
If you minimize its relational Landauer cost, a single 100-line, zero-dependency Python file computes the fine-structure constant and fundamental mass ratios from pure geometry.
Full write up markdown file is also in the vault. But check the script first!
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