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2026
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| Accés en línia: | https://doi.org/10.5281/zenodo.20071321 |
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| _version_ | 1866902230295117824 |
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| author | Requiere, Frederic |
| author_facet | Requiere, Frederic |
| contents | <div> <div>We derive the absolute masses of the electron, the u quark, and the complete neutrino mass spectrum from first principles with zero free parameters. The universal fermion mass formula is: <strong>m_f = α · v_n · K_f · (1 + δ_f)</strong>, where α = 1/(2π²N_eff + corrections) is the fine-structure constant (Theorem 22), v_n is the n-th scale of the informational cascade (Theorem 82), K_f is a channel-dependent geometric projection factor, and δ_f encodes radiative corrections. The three inputs (α, v_n, K_f) are each derived from the axioms. For the electron, three levels of radiative corrections (vertex, self-energy, participation) are derived from the axioms, achieving sub-ppb precision: m_e = 0.510998950 69 MeV vs. 0.510998950 69(16) MeV [CODATA 2022], a residual error of −0.002 ppb. This residual is well within the ~11,000 ppb uncertainty that G imposes on M_Pl, making the formula structurally exact to the precision currently testable. The u quark is derived at m_u = 2.144 MeV vs. 2.16 ± 0.07 MeV (−0.76%, 0.24σ), and the heaviest neutrino at m_ν₃ = 49.904 meV vs. 50.28 ± 0.35 meV [NuFIT 5.3] (−0.75%, 1.1σ). The neutrino mass hierarchy is derived via a transition mechanism: m_ν₂/m_ν₃ = 1/√(p₂·min(P_W)·(1+η)) (0.05σ), giving m_ν₂ = 8.607 meV vs. 8.68 ± 0.10 meV. The lightest neutrino mass m_ν₁ = 0 follows from the Pascal layer structure. The predicted sum Σm_ν = 58.5 meV is testable by CMB-S4. The derivation requires the neutrino to be a Majorana fermion (K_ν = 1/k_max), testable via neutrinoless double-beta decay. Combined with the companion paper on charged lepton mass ratios, all six lepton masses are obtained from first principles. A complete Python validation script reproducing all numerical results is provided in the appendix.</div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20071321 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Absolute Lepton Masses from the Informational Cascade: Correlation Density Times Arithmetic Scale Requiere, Frederic electron mass lepton masses neutrino mass quark mass arithmetic cascade radiative corrections sub-ppb Planck mass Koide formula <div> <div>We derive the absolute masses of the electron, the u quark, and the complete neutrino mass spectrum from first principles with zero free parameters. The universal fermion mass formula is: <strong>m_f = α · v_n · K_f · (1 + δ_f)</strong>, where α = 1/(2π²N_eff + corrections) is the fine-structure constant (Theorem 22), v_n is the n-th scale of the informational cascade (Theorem 82), K_f is a channel-dependent geometric projection factor, and δ_f encodes radiative corrections. The three inputs (α, v_n, K_f) are each derived from the axioms. For the electron, three levels of radiative corrections (vertex, self-energy, participation) are derived from the axioms, achieving sub-ppb precision: m_e = 0.510998950 69 MeV vs. 0.510998950 69(16) MeV [CODATA 2022], a residual error of −0.002 ppb. This residual is well within the ~11,000 ppb uncertainty that G imposes on M_Pl, making the formula structurally exact to the precision currently testable. The u quark is derived at m_u = 2.144 MeV vs. 2.16 ± 0.07 MeV (−0.76%, 0.24σ), and the heaviest neutrino at m_ν₃ = 49.904 meV vs. 50.28 ± 0.35 meV [NuFIT 5.3] (−0.75%, 1.1σ). The neutrino mass hierarchy is derived via a transition mechanism: m_ν₂/m_ν₃ = 1/√(p₂·min(P_W)·(1+η)) (0.05σ), giving m_ν₂ = 8.607 meV vs. 8.68 ± 0.10 meV. The lightest neutrino mass m_ν₁ = 0 follows from the Pascal layer structure. The predicted sum Σm_ν = 58.5 meV is testable by CMB-S4. The derivation requires the neutrino to be a Majorana fermion (K_ν = 1/k_max), testable via neutrinoless double-beta decay. Combined with the companion paper on charged lepton mass ratios, all six lepton masses are obtained from first principles. A complete Python validation script reproducing all numerical results is provided in the appendix.</div> </div> |
| title | Absolute Lepton Masses from the Informational Cascade: Correlation Density Times Arithmetic Scale |
| topic | electron mass lepton masses neutrino mass quark mass arithmetic cascade radiative corrections sub-ppb Planck mass Koide formula |
| url | https://doi.org/10.5281/zenodo.20071321 |