TFPT scientific source excerpt
Original repository path: documents/tfpt_research_contracts/sections/006-source.tex
Original file SHA-256: a93b3c1fd9be52521a3eea6ca82b6bddd16e15c2447382f274d3542a36a0382b
Inclusive original lines: 236-258
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000236 | resolvent factor) does \emph{not} reproduce the lepton amplitudes $(0.475,1.107,0.917)$. So the precise
000237 | $\Gamma^{\min}_{ij}$ geodesic-to-word dictionary (how the $6$-site hypercharge hexagon combines with the
000238 | $3$-dim family $\rho^\star$) was the genuine remaining analytic input --- it is \emph{not} fixed by a
000239 | natural guess, and we do \emph{not} fish for $55/117$. \emph{Resolved since (\vref{v118}): the correct
000240 | extraction is the resolvent determinant of the $W(A_3)$ monodromy, not the diagonal dressing --- the
000241 | probe's failure is thereby explained, and the dictionary is exact.}
000242 | 
000243 | 
000244 | \begin{keybox}[Theorem U --- the four-way split (sharper than one monster gate) \mE/\mO]
000245 | $D_4$ \emph{fixes the admissible chamber, not the physical point} (the $D_4$-fixed locus is
000246 | positive-dimensional, U3); the discrete selectors $\det R=8$, $\operatorname{SNF}(R)=(1,1,8)$,
000247 | $\operatorname{Spec}(Q_+)=\{1,2,3\}$ do the cutting. The gate splits into four pieces, three of them
000248 | essentially closed:
000249 | \begin{itemize}
000250 | \item $U_{\mathrm{unitary}}$ \mE: parabolic degree $0$ $+$ polystable $\Rightarrow$ unitary (Mehta--Seshadri)
000251 |   $\Rightarrow\Phi=0$; the harmonic metric is the \emph{finite} invariant form $H$ ($M_k^\dagger HM_k=H$),
000252 |   not a Hitchin PDE (\veri{v40\_harmonic\_metric.py}).
000253 | \item $U_{\mathrm{H2}}$ \mE: $R,Q,K$ are read off the bundle (splitting type $=a$, $\det R=8$,
000254 |   $\operatorname{Spec}(Q_+)$) (\veri{v39\_uwall\_selectors.py}).
000255 | \item $U_{\Lambda^2}$ \mE: \textbf{Readout Rigidity} --- on the discrete stratum
000256 |   $\mathcal S_{8,Q}=\{\det R=8,\operatorname{SNF}(R)=(1,1,8),\operatorname{Spec}(Q_+)=\{1,2,3\}\}$ the
000257 |   anchor-plane readout is \emph{constant},
000258 |   $\mathcal C_{ud}(\rho)=\gcar\|\operatorname{Pl}_{\mathbf1,a}(K)\|_1/(\Nfam^2\Delta_Q)=\tfrac{55}{117}$,