What question did this study set out to answer?

To derive four fundamental constants of nature using a gated cubic recursion with no free parameters.

March 31, 20260 citationsOpen Access

Four Fundamental Constants of Nature from a Gated Cubic Recursion with Zero Free Parameters

Key Points

To derive four fundamental constants of nature using a gated cubic recursion with no free parameters.
Utilized gated cubic recursion f(x) = Γ·tanh³(x) − λx.
Employs Diophantine and modular arithmetic along with spectral constraints.
Implemented 106 computational verification scripts.
Four constants: proton-to-electron mass ratio, neutron-to-electron mass ratio, inverse fine-structure constant, and muon-to-electron mass ratio derived.
All constants emerge from the integers (3,5).

Abstract

First paper of the RASP series. Derives four fundamental constants of nature — proton-to-electron mass ratio, neutron-to-electron mass ratio, inverse fine-structure constant, and muon-to-electron mass ratio — from a single gated cubic recursion f(x) = Γ·tanh³(x) − λx with zero free parameters. All constants emerge from the integers (n,p) = (3,5) through Diophantine, modular arithmetic, and spectral constraints. Includes 106 computational verification scripts. Research began June 2025.

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