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| Format: | Recurso digital |
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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17771453 |
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Table of Contents:
- <p>This document presents a complete derivation of the proton rest energy within the Harmonic Scale Framework (HSF). <br>In HSF, inertial mass corresponds to energy stored in the Neutrofield (K4) depot. The proton is modeled as a <br>(K1_p, K3_p, K4_p) composite on a shared oblate-spheroid geometry (flattening f = 0.02), with Dirichlet boundary <br>conditions for K1 and K3, Robin conditions for K4, and guided in-surface timing for K5.</p> <p>Only one experimental observable is used as an anchor: the proton charge radius r_p = 0.84 fm. This single anchor <br>fixes the absolute K4 depot normalization rho_K4^(p) without retuning the gravitational coupling parameters <br>(lambda_45, alpha_4) already established in the HSF gravity derivation. The proton rest energy then follows as:</p> <p> m_p c^2 = E_K4^(p)[rho_K4^(p)] + DeltaE_{K1_p,K3_p}</p> <p>Dirichlet-mode corrections are small, and no additional free parameters are introduced. Combined with the previously <br>derived electron closure m_e c^2 = 2 * E1 / alpha^2, the proton-to-electron mass ratio m_p/m_e emerges directly.</p> <p>The document includes geometric corrections, uncertainty propagation from the r_p band, and consistency checks <br>against magnetic moment trends and hydrogen finite-size effects. This completes the proton mass derivation in HSF <br>and demonstrates a single-parameter closure for a composite mass, complementing the earlier HSF derivations of c, h, G, <br>alpha, and m_e.</p>