The Electron Mass, the Fine Structure Constant, and Newton's Constant\\ from a Finite-Information Framework

The finite-information framework of~\cite{FoundationPaper} supplies a carrier, a balanced coin, three frames, Koide's ratio $Q=2/3$ and corrolaries (collectively "Retained Structure Dynamics"). Given that foundation, this paper derives the framework values that correspond to the electron mass, the fine structure constant, Newton's constant, and the lepton mass ratios, with no free dimensionful input beyond the framework's own. The chain runs through framework-internal values---the screen's capture fraction $8/15$, the lock length $L_0=\log(15/8)$, the hop length $\ell=0.6358598660$, the electron's closed loop action $A_e=-23.3215823152$, the primitive charged packet's UV recurrence modulus $\eta_e=e^{-A_{\rm UV}}$, and the lattice spacing $a=\eta_e\lambda_e$---and at each measured quantity to a correspondence. The screen's positive-frequency Bose occupancy takes the value $137.03599917628$, corresponding to $\alpha^{-1}$; the loop action takes the value that corresponds to $m_ec^2=0.510998950686$~MeV; the structural chain $ch\eta_e^2/(4\pi^2m_e^2)$ gives $6.674329\times10^{-11}$~SI, corresponding to Newton's constant; and the family weights take values corresponding to the lepton mass ratios $m_\mu/m_e=206.7682825$ and $m_\tau/m_e=3477.4416$. No measured mass is an input to any derivation; each correspondence is tested against CODATA~2022~\cite{CODATA2022}, at or below $0.2\sigma$ except $m_\tau$ at $+0.43\sigma$. All results not derived here are cited to~\cite{FoundationPaper}.