An Internal Derivation of the Fine-Structure Constant

Minor numerical display correction (v1.1). A typographical inconsistency in the displayed value ofdelta_trig^(alpha,0) has been corrected in three locations:Introduction (Section A1), Appendix A (Step 9 box), and Appendix B(Section B.5). The truncated display value 0.0856731937361413...has been corrected to the full value 0.08567319373614122...,consistent with the computation in the main text (D3) and theremainder of the manuscript. No mathematical content, derivation,or conclusion has been changed. This paper presents a computational structure that internally derives the fine-structure constant \(\alpha\) as the low-energy normalized prefactor of the \(V_{p2.2}\)-EM electromagnetic channel, rather than taking it as an exogenous empirical constant.The starting point is the \(V_{p1.0}\) common event-extraction engine and the \(V_{p2.2}\)-EM channel compilation. First, the coupling-free bare electromagnetic tensor \(\widetilde T_{\mu\nu}^{(\mathrm{EM})}\) is separated from the physical electromagnetic ledger, and the position into which \(\alpha^{-1}/4\pi\) enters is sealed in advance as\[T_{\mu\nu}^{(2),\mathrm{phys}}=\frac{\alpha^{-1}(t,\Omega_\alpha)}{4\pi}\widetilde T_{\mu\nu}^{(\mathrm{EM})}+\Delta_{\mu\nu}^{(2)}+J_{\mu\nu}^{(2,\mathrm{src})}.\]On this position fixing, the electromagnetic trace-like \(U(1)\) projection-capacity certificate is produced from internal projection impedance as\[C_\Pi^{(\alpha,0)}=0.3817992348991862\ldots .\]Substituting this into the zeroth-order capsule-average loss gives the leading normalization mode\[\alpha^{-1}_{(0)}=136.9503259827925\ldots .\]Next, on the edge-trigger plateau branch selected by the time engine and the ternary implementation residual, the bounded trigger correction\[\delta_{\mathrm{trig}}^{(\alpha,0)}=0.0856731937361413\ldots\]is internally produced.Therefore, the final internal electromagnetic normalization coefficient is\[\alpha^{-1}_{\mathrm{int}}=\alpha^{-1}_{(0)}+\delta_{\mathrm{trig}}^{(\alpha,0)}=137.0359991765286\ldots .\] This paper interprets this value not as an arbitrary \(q^2\neq0\) running coupling, but as the reference value of the low-energy on-shell or Thomson-limit electromagnetic normalization branch,\[\alpha^{-1}_{\mathrm{int}}\equiv\alpha_{\mathrm{OS}}^{-1}(0;\Omega_\alpha).\]Running at \(q^2\neq0\) is separated into vacuum-polarization and higher-resolution readout-correction branches. The same zeroth-order base ledger also produces, without using \(C_\Pi^{(\alpha,0)}\) or \(\delta_{\mathrm{trig}}^{(\alpha,0)}\), the independent scale-separation readout\[R_\Omega/\ell_\Omega=1074.03933765\ldots .\]When anchored by the electron reduced Compton scale \(R_{\Omega_\alpha} = \bar{\lambda}_C = \hbar/(m_e c)\), this independent readout defines\(\ell_{\Omega_\alpha}=0.3595392216\,\mathrm{fm}\)as the electromagnetic implementation cell and minimal readout scale, namely an object-local minimal implementation cell. The claim of this paper is not that a particular number is fitted after the fact. The computational order is fixed as follows: the position of \(\alpha\), bare/normalized separation, internal derivation of \(C_\Pi^{(\alpha,0)}\), bounded production of \(\delta_{\mathrm{trig}}^{(\alpha,0)}\), low-energy QED scheme identification, independent readout, and consistency check against an external reference anchor. The later-stage readout-boundary, time-engine, support-layer, and master-action structures are presented in compressed form in the appendices to the extent required.