TFPT scientific source excerpt
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000239 | \section*{Research Contract --- \texttt{SEAM.DETLINE.UNIFICATION.01} (the determinant-line unification hypothesis)}
000240 | \addcontentsline{toc}{section}{Research Contract: SEAM.DETLINE.UNIFICATION.01}
000241 | % =====================================================================
000242 | \noindent\emph{Typing.} A research \emph{hypothesis} contract \mO\ (ledger row
000243 | \texttt{SEAM.DETLINE.UNIFICATION.01}) --- a precise conjecture, \emph{not} a result.
000244 | \textbf{Observation.}  Three separately open structures may be projections of \emph{one}
000245 | geometric object: \textbf{(1)}~the seam extension is described by a Q-system/simple current
000246 | (\texttt{SEAM.SIMPLECURRENT.GENERATOR.01}); \textbf{(2)}~the chiral fermion measure lives on a
000247 | determinant line (\texttt{CHIRAL4D.NOMIRROR.01} demand C1); \textbf{(3)}~anomalies and CP
000248 | phases appear as holonomies of that determinant line --- the \emph{finite} Quillen identity is
000249 | already two-sided (\veri{v974\_alpha\_faces\_computed.py}: Berry integral $=$
000250 | Poincar\'e--Lelong divisor integral $=+1$), and the continuum Bismut--Freed identification is
000251 | the named missing step of \texttt{ALPHA.QUILLEN.EXACT.01}.  \textbf{Demand (the compatibility
000252 | theorem).}
000253 | \[
000254 | \operatorname{Res}_{\rm seam}\det D_{4D}\;\cong\;\det D_{\rm seam}
000255 | \]
000256 | as line bundles \emph{with connection}, and the holonomy of the bulk determinant line equals
000257 | the discrete TFPT orientation phase (the classically invisible $\operatorname{sgn}J$
000258 | orientation bit, now machine-checked at matrix level with the Wilson-plaquette interference
000259 | readout as its minimal observable, \veri{v977\_transfer\_unistochastic\_wilson.py}; the
000260 | bulk-determinant identification demanded here stays open).  If such a theorem exists, seam extension, chiral
000261 | anomaly freedom, the generation index and the discrete CP orientation become different
000262 | projections of the same object.  \textbf{Kill tests.}  The two determinant lines differ by a
000263 | nontrivial local factor no counterterm removes; the bulk holonomy disagrees with the discrete
000264 | orientation phase on a computable family.  \emph{Honest boundary:} the continuum
000265 | Quillen/Bismut--Freed identification is exactly the critical missing step; nothing in the
000266 | corpus proves any part of the 4D side.  Status: \texttt{SEAM.DETLINE.UNIFICATION.01} \mO.
000267 | 
000268 | \par\smallskip\noindent\textbf{Executed update (2026-08-28, promote round): a finite $2{+}1$D/$1$D
000269 | bulk--edge shadow is executed
000270 | (\veri{v991\_\allowbreak detline\_\allowbreak bulk\_\allowbreak edge.py}; continuum
000271 | Bismut--Freed stays \mO).}
000272 | On the QWZ collar, bulk twist-torus curvature $2\pi\cdot(+1)$ equals the seam holonomy winding
000273 | $+1$ (difference $5.6\times10^{-16}$); the $M=3$ control is zero on both sides; a conjugation
000274 | mutant flips both signs coherently.  Honest: finite shadow \mE, not the 4D Bismut--Freed
000275 | identification.  Display marker stays \mO.
000276 | 
000277 | \par\smallskip\noindent\textbf{Executed update (2026-08-30, late-evening harvest;
000278 | \veri{v1014\_\allowbreak bridge\_\allowbreak refinements.py}; the contract stays \mO).}
000279 | The finite restriction isomorphism $\operatorname{Res}_\Sigma L_{\mathrm{bulk}}\cong L_\Sigma$
000280 | is verified ($c_{\mathrm{phase}}$ constancy $3.7{\times}10^{-16}$, conjugation covariance exact,
000281 | $C=W_{\mathrm{bulk}}=W_{\mathrm{seam}}=+1$ / mirror $-1$).  Orientation fixes only the
000282 | conjugate-pair branch ($2\to1$); a constant $U(1)$ anchor remains, fixed by the $A_0$
000283 | reference normalization of \texttt{ALPHA.QUILLEN.EXACT.01}.  Continuum Bismut--Freed stays \mO.
000284 | 
000285 | % =====================================================================