The SATOR Matrix - Plastic-Number Regularities in Selected Standard Model Mass Ratios: A Phenomenological and Statistical Analysis
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2026
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| author | Somma, Massimo Michele Edoardo |
| author_facet | Somma, Massimo Michele Edoardo |
| contents | <p>We examine whether selected, precisely measured Standard Model mass ratios exhibit anomalously simple fits in powers of the plastic number ρ, defined by ρ³ = ρ + 1. Motivated by the (2,3) pentagonal Pisot hierarchy, we predefine a primary dataset consisting of the ratios m_μ/m_e, m_τ/m_e, and m_Z/m_e, and a secondary dataset consisting of the electroweak ratios m_H/m_W and m_t/m_W. For the primary dataset, the fixed base ρ ≈ 1.3247 yields the integer exponents (19, 29, 43) with relative errors 1.13%, 0.08%, and 0.05%, together with exact additive consistency in exponent space. A continuous base scan on b ∈ [1.2, 1.5] has its minimum at b* = 1.3246, within 0.01% of ρ. Under a null model in which four masses are drawn log-uniformly over the observed e-to-Z range and then ordered, only 2.8 × 10⁻⁴ of samples achieve a fixed-ρ exponent-space score at least as small as the observed one. By contrast, optimizing over the base removes most of the anomaly, showing that the signal is specifically about the plastic number rather than about generic exponential fitting. In the secondary dataset, the ratios m_H/m_W and m_t/m_W admit low-complexity φ^a ρ^b fits, namely φ⁻²ρ⁵ and φρ, at the 10⁻⁴ and 10⁻³ levels. The exponent n_Z = 43 identified here serves as the electroweak anchor depth in the companion neutrino paper. We frame these findings as regularities in selected mass ratios, not as a derivation of the Standard Model spectrum. Part of the SATOR Matrix programme.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19412085 |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | The SATOR Matrix - Plastic-Number Regularities in Selected Standard Model Mass Ratios: A Phenomenological and Statistical Analysis Somma, Massimo Michele Edoardo <p>We examine whether selected, precisely measured Standard Model mass ratios exhibit anomalously simple fits in powers of the plastic number ρ, defined by ρ³ = ρ + 1. Motivated by the (2,3) pentagonal Pisot hierarchy, we predefine a primary dataset consisting of the ratios m_μ/m_e, m_τ/m_e, and m_Z/m_e, and a secondary dataset consisting of the electroweak ratios m_H/m_W and m_t/m_W. For the primary dataset, the fixed base ρ ≈ 1.3247 yields the integer exponents (19, 29, 43) with relative errors 1.13%, 0.08%, and 0.05%, together with exact additive consistency in exponent space. A continuous base scan on b ∈ [1.2, 1.5] has its minimum at b* = 1.3246, within 0.01% of ρ. Under a null model in which four masses are drawn log-uniformly over the observed e-to-Z range and then ordered, only 2.8 × 10⁻⁴ of samples achieve a fixed-ρ exponent-space score at least as small as the observed one. By contrast, optimizing over the base removes most of the anomaly, showing that the signal is specifically about the plastic number rather than about generic exponential fitting. In the secondary dataset, the ratios m_H/m_W and m_t/m_W admit low-complexity φ^a ρ^b fits, namely φ⁻²ρ⁵ and φρ, at the 10⁻⁴ and 10⁻³ levels. The exponent n_Z = 43 identified here serves as the electroweak anchor depth in the companion neutrino paper. We frame these findings as regularities in selected mass ratios, not as a derivation of the Standard Model spectrum. Part of the SATOR Matrix programme.</p> |
| title | The SATOR Matrix - Plastic-Number Regularities in Selected Standard Model Mass Ratios: A Phenomenological and Statistical Analysis |
| url | https://doi.org/10.5281/zenodo.19412085 |