Gorde:
| Egile nagusia: | |
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| Formatua: | Recurso digital |
| Hizkuntza: | |
| Argitaratua: |
Zenodo
2026
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| Gaiak: | |
| Sarrera elektronikoa: | https://doi.org/10.5281/zenodo.20071349 |
| Etiketak: |
Etiketa erantsi
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Aurkibidea:
- <div> <div>We derive the masses of four pseudoscalar mesons (π, K, D, B) from the informational axiom system with zero free parameters. The central tool is a unified bridge formula: <strong>m² = G(channel) · vᵢ · vⱼ</strong>, where vᵢ, vⱼ are cascade scales (Theorem 82) and the bridge coupling G is selected by the variational principle (Axiom 13, least perturbation) among three channels: pairing, self, and inter-level. The four formulas are: <strong>m_π = √(C(3)·v₃·v₄)</strong> = 139.60 MeV, <strong>m_K = √(D(3)/k_max)·v₃</strong> = 492.2 MeV, <strong>m_D = √(α·C(2)·v₂·v₃)</strong> = 1852.7 MeV, <strong>m_B = √(α·C(2)²·v₂·v₃)</strong> = 5240.3 MeV, where C(n) and D(n) are the arithmetic cascade depth and gauge structure, α = 1/137.036 is the fine-structure constant (Theorem 22), and k_max = 2 is the projective cutoff. The PDG values are: m_π = 139.57 MeV (+0.024% error), m_K = 493.68 MeV (−0.29% error), m_D = 1864.84 MeV (−0.65% error), m_B = 5279.65 MeV (−0.75% error). The RMS error is 0.52% across a mass range spanning a factor of 38. Each formula uses only cascade quantities (C(n), D(n), v_n), the fine-structure constant α, and the projective cutoff k_max = 2. No experimental hadronic input is required. Key structural results: (i) the pion mass formula m_π² = C(3)·v₃·v₄ is the informational analog of the Gell-Mann–Oakes–Renner relation, expressing m_π² as a product of a symmetry-breaking scale and a coupling constant, (ii) the pairing condition C(3) = C(4) = 10 selects the pion channel uniquely (no other adjacent level pair satisfies this condition), (iii) the ratio m_B/m_D = √(C(2)) = √8 = 2.828 is a pure structural prediction (experimental: 2.831, error +0.10%). All four formulas are formally derived from the axioms via the spectral decomposition (Theorem 82.3), the inter-level impedance (Theorem 51), and the variational selection rule (Axiom 13). A complete Python validation script reproducing all numerical results is provided in the appendix.</div> </div>