A complete first-principles derivation: axioms → ħ, c, G → MP = √ (ħc/G) with full non-circularity proof and SI unit equivalence Abstract: The Planck mass MP = √ (ħc/G) ≈ 2. 176×10 ⁸ kg ≈ 1. 2209×10⁻ ¹⁹ GeV/c² is thefundamental mass scale of nature — the point where quantum mechanics and gravity areequally strong. In standard physics, MP is computed from the measured values of ħ, c, and G;no framework derives these three constants from first principles. This paper presents thecomplete Pattern Algebra (PA) derivation of MP from axioms A1–A11 and the Hurwitz theorem, without circular reasoning and without free parameters.
Mario Sorce (2026) studied this question.