TFPT scientific source excerpt
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000163 | \section*{Externalization Contract --- \texttt{ALPHA.QUILLEN.EXACT.01} (the determinant-line variation theorem, packaged for external specialists)}
000164 | \addcontentsline{toc}{section}{Externalization Contract: ALPHA.QUILLEN.EXACT.01}
000165 | % =====================================================================
000166 | \noindent\emph{Typing.} The second hand-off document: the one remaining EM obligation, packaged
000167 | for an outside specialist in determinant lines / $\eta$-invariants / index theory. It
000168 | \emph{documents}, it does not close: \texttt{ALPHA.QUILLEN.EXACT.01} stays \mO\ (external math,
000169 | type A, \vref{v384}), and it is a \emph{face} of \texttt{SEAM.EQUIV.01} (\vref{v382}) --- not a
000170 | second independent gate. The \emph{value} $\alpha^{-1}$ is closed \mE\ regardless (unique root
000171 | $+$ ablation, \vref{v3}); open is only ``why \emph{this} functional''. Nothing here moves a
000172 | marker.
000173 | 
000174 | \par\smallskip\noindent\textbf{Relation (2026-08-28).}  The nonabelian upgrade of this $U(1)$
000175 | face is the new contract \texttt{GAUGE.DETLINE.FIXPOINT.01} (all three gauge couplings as unique
000176 | stationary points of one zeta-det/inflow functional; honest: $\alpha_s(M_Z)$ is currently an
000177 | external input).  This row stays the $U(1)$ face; that row is the three-coupling demand.
000178 | 
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