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This paper aims to provide a unifying principle that explains the derivation of the Standard Model from a 59-dimensional framework using group theory.

May 25, 2026Open Access

The 59-Dimensional Framework as the Gauge Group: A Complete Zero-Parameter Derivation of the Standard Model from 59 = 11 + 6×8

Key Points

This paper aims to provide a unifying principle that explains the derivation of the Standard Model from a 59-dimensional framework using group theory.
Derivation of 33 dimensionless Standard Model quantities using four operations on the integers {1, 3, 4, 6, 8, 11}.
Linking the QCD beta-function to hidden dimensions through the equation β₀ = D_CY + D_0.
Numerical verification of predictions against experimental data from PDG 2022.
All 33 results verified against PDG 2022, with four achieving better than 0.1% accuracy.
Prediction of neutrino mass sum Σm_ν ≈ 58.7 meV and baryon resonance N*(1685) at 1680.6 MeV.
Framework reaches zero experimental free parameters compared to ~25 in the Standard Model.

Abstract

v2 — May 2026: Corrected the group-theory expression for DCY in Tables 1–2 and Figure 1 (now dim SU (3) − rank SU (3) = 6). No numerical result changed. This paper (Paper E of the 59-Dimensional Series) presents a single unifying principle explaining why the 59-dimensional framework reproduces the Standard Model: the number 59 = 11 + 6×8 is the unique embedding of the Standard Model gauge group GSM = SU (3) ×SU (2) ×U (1) in M-theory for which Dₜotal is simultaneously prime and odd, while observable spacetime equals the rank of the gauge group, Dₛpace = rank (GSM) = 4. This condition fixes DM = 11 uniquely. From this single structural fact, every dimension of the framework is determined by group theory alone — no free choice remains. We derive 33 dimensionless Standard Model quantities using four elementary operations (ratio, binary exponential, square root, integer sum) on the six integers 1, 3, 4, 6, 8, 11 that are themselves the dimensions and ranks of GSM. New results beyond Papers A–D: (i) the QCD beta-function coefficient satisfies β₀ = DCY + D₀ = 7, linking asymptotic freedom to the hidden dimensions; (ii) observable spacetime is four-dimensional because rank (GSM) = 4; (iii) three fermion generations arise because they equal half the Calabi-Yau dimension, DCY/2 = 3; (iv) cos (θW) = exp (−D₀/DSO8) achieves 0. 12% accuracy — thirty times better than sin²θW; (v) with the geometric value αₛ = 4/34, the framework reaches zero experimental free parameters, against ~25 in the Standard Model. All 33 results are verified against PDG 2022 — four to better than 0. 1% — and none uses a fitted constant. Three quantities remain genuinely open (ΩDM, the cosmological constant, and the PMNS CP phase), stated honestly. Two falsifiable predictions are highlighted: the neutrino mass sum Σm_ν ≈ 58. 7 meV and the baryon resonance N* (1685) at 1680. 6 MeV. Numerical verification was performed with the assistance of Claude (Anthropic). All scientific ideas and responsibility rest with the author.

The 59-Dimensional Framework as the Gauge Group: A Complete Zero-Parameter Derivation of the Standard Model from 59 = 11 + 6×8

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