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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2506.12859 |
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| _version_ | 1866914391880892416 |
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| author | Washburn, Jonathan Allahyarov, Elshad |
| author_facet | Washburn, Jonathan Allahyarov, Elshad |
| contents | We present a first-principles derivation of the masses of all twelve known fermions -- three charged leptons, six quarks, and three neutrinos -- and the fine-structure constant $α^{-1}$, from a single discrete functional equation, the Recognition Composition Law (RCL), with \textbf{zero continuously adjustable parameters}. The mass spectrum follows from the RCL supplemented by four regularity conditions and eight structural theorems (T1--T8): the golden ratio $φ=(1+\sqrt{5})/2$ emerges as the unique hierarchy base (T6); an 8-step period is fixed by the 3-cube Hamiltonian cycle (T7); three spatial dimensions are selected by a unique combinatorial identity (T8). All integers entering the mass formula are the six combinatorial invariants of the 3-cube $Q_3$; none is fitted. The sole empirical input is the electron mass, which fixes an irreducible unit-conversion constant~$τ_0$.
Predictions are confronted with PDG measurements. Charged-lepton masses are reproduced at sub-ppm accuracy for the muon and $\sim\!10^{-4}$ for the tau (Table~\ref{tab:lepton_validation}). All six quark masses are predicted at integer level; first-generation quarks agree to better than $1\%$, while second/third-generation residuals of $2$--$16\%$ are expected integer-precision effects (Table~\ref{tab:quark_validation}). Neutrino mass-squared splittings agree with NuFIT~5.3 within $1$--$2σ$, normal ordering is predicted, and $Σm_ν\approx 0.063$~eV satisfies cosmological bounds.
All structural claims are machine-verified in Lean~4 (179 files, 0~\texttt{sorry}; \texttt{github.com/\allowbreak jonwashburn/\allowbreak recognition-science}). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12859 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Complete Derivation of the Fermion Spectrum from the Recognition Composition Law Washburn, Jonathan Allahyarov, Elshad General Physics High Energy Physics - Phenomenology We present a first-principles derivation of the masses of all twelve known fermions -- three charged leptons, six quarks, and three neutrinos -- and the fine-structure constant $α^{-1}$, from a single discrete functional equation, the Recognition Composition Law (RCL), with \textbf{zero continuously adjustable parameters}. The mass spectrum follows from the RCL supplemented by four regularity conditions and eight structural theorems (T1--T8): the golden ratio $φ=(1+\sqrt{5})/2$ emerges as the unique hierarchy base (T6); an 8-step period is fixed by the 3-cube Hamiltonian cycle (T7); three spatial dimensions are selected by a unique combinatorial identity (T8). All integers entering the mass formula are the six combinatorial invariants of the 3-cube $Q_3$; none is fitted. The sole empirical input is the electron mass, which fixes an irreducible unit-conversion constant~$τ_0$. Predictions are confronted with PDG measurements. Charged-lepton masses are reproduced at sub-ppm accuracy for the muon and $\sim\!10^{-4}$ for the tau (Table~\ref{tab:lepton_validation}). All six quark masses are predicted at integer level; first-generation quarks agree to better than $1\%$, while second/third-generation residuals of $2$--$16\%$ are expected integer-precision effects (Table~\ref{tab:quark_validation}). Neutrino mass-squared splittings agree with NuFIT~5.3 within $1$--$2σ$, normal ordering is predicted, and $Σm_ν\approx 0.063$~eV satisfies cosmological bounds. All structural claims are machine-verified in Lean~4 (179 files, 0~\texttt{sorry}; \texttt{github.com/\allowbreak jonwashburn/\allowbreak recognition-science}). |
| title | A Complete Derivation of the Fermion Spectrum from the Recognition Composition Law |
| topic | General Physics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2506.12859 |