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| Formato: | Recurso digital |
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Zenodo
2026
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| Acceso en liña: | https://doi.org/10.5281/zenodo.20071345 |
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Table of Contents:
- <div> <div>We derive the current masses of the three heavy quarks (c, b, t) from the informational axiom system with zero free parameters. The central mechanism is the gauge depth coupling: a heavy quark at QCD level acquires mass proportional to the electroweak gauge depth D(2) attenuated by the projective cutoff k_max. The three formulas are: <strong>m_c = v₃ · (d · D(2))/(k_max · C(3)) · (1 + α_s/(dπ)) </strong>= 1.2686 GeV, <strong>m_b = v₃ · D(2)/k_max </strong>= 4.1766 GeV, <strong>m_t = v₂ · (1 − 1/π) </strong>= 172.74 GeV, where v₃ = M_Pl · α^g(3) and v₂ = M_Pl · α^g(2) are cascade VEVs (Theorem 82), D(2) = (k_max · d)² = 36 is the gauge depth factorization, C(3) = 10 is the arithmetic cascade depth, α_s is the strong coupling, and k_max = 2 is the projective cutoff. All three predictions lie within one standard deviation of PDG 2024 values: m_c = 1.27 ± 0.02 GeV (−0.07σ), m_b = 4.18 ± 0.03 GeV (−0.11σ), m_t = 172.57 ± 0.29 GeV (+0.59σ). The RMS error is 0.095% across a mass range spanning a factor of 136. Key structural results: (i) the factorization D(2) = (k_max · d)² = 36 reveals the gauge depth as a square of projective modes, (ii) the ratio m_b/m_c = C(3)/d = 10/3 is a pure structural prediction (experimental: 3.29, error +1.3%), (iii) the top quark mass equals the electroweak VEV minus the combined Haar depletion of SU(2)_L × U(1)_Y: m_t = v₂(1 − 1/π). All three masses are formally derived. The top quark formula uses the maximal torus rank theorem: gauge depletion equals rank(G)/(2π), and additivity follows from rank(G₁ × G₂) = rank(G₁) + rank(G₂). Each formula uses only cascade quantities (C(n), D(n), v_n), the strong coupling α_s, and the projective cutoff k_max = 2. No experimental hadronic input is required. A complete Python validation script reproducing all numerical results is provided in the appendix.</div> </div>