What question did this study set out to answer?

The aim is to derive fundamental physical constants purely from algebraic structures with no free parameters.

March 31, 20260 citationsOpen Access

The Unity Principle: Derivation of Fundamental Constants from Constraint and Algebraic Identity

Key Points

The aim is to derive fundamental physical constants purely from algebraic structures with no free parameters.
Development of a zero-parameter derivation framework based on a single Constraint Axiom.
Utilization of octonion algebra and Hurwitz's theorem.
Determination of gauge structure via the exceptional group G₂.
Derivation of the Planck mass from geometric properties of G₂-orbit.
Formulation of the gravitational constant as G = 1/(21-π)².
Reduction of the Standard Model's parameters to first-principles derivation.

Abstract

The Unity Principle: Derivation of Fundamental Constants from Constraint and Algebraic Identity This work presents a zero-parameter derivation of fundamental physical constants from pure algebraic structure. Starting from a single Constraint Axiom—Aut(X) ⊊ Sym(X)—the framework forces the octonion algebra O via Hurwitz's theorem, determines gauge structure through the exceptional group G₂, and proves the existence of a unique internal anchor A₁. A triality witness equation forces A₁ = 1 (the multiplicative identity). All dimensional constants emerge as algebraic expressions of unity: the Planck mass 21 - π is derived from G₂-orbit geometry on Im(O) and g₂, with the gravitational constant G = 1/(21-π)². The framework achieves one axiom, zero algebraic free parameters, one forced identity, and one proven-minimal unit conversion, reducing the Standard Model's 19 parameters to first-principles derivation. Related resourcesAdditional preprints, theoretical frameworks, and ongoing work by the author are available at:https://murad-ahmadov.github.io/

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