TFPT scientific source excerpt
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000208 | \subsection*{2026-07-20 (II) (\texttt{v490} --- the $T^2$ spin-structure parity census: $\mu_{\mathrm{pre}}{=}4$ witnessed on the lattice, the 16-fold-way bridge $\theta_v{=}1$ on measured numbers, and the honest TEE non-discriminator fence; \emph{no gate closes, no marker moves})}
000209 | \begin{itemize}[leftmargin=1.5em]
000210 | \item \textbf{\texttt{v490\_seam\_parity\_census.py} (\texttt{SEAM.MU.01}).} The $T^2$ ground-state fermion
000211 | parity of the \texttt{v367} $p{+}ip$ collar, resolved per spin structure $(AA,AP,PA,PP)$ and determined
000212 | TWICE --- Read--Green TRIM product AND real-space Majorana Pfaffian (Schur), relative to the trivial
000213 | $M{=}3$ phase, with the twisted real-space spectra matching the Bloch bands to $9\times10^{-15}$. \mE\
000214 | per layer $(+,+,+,-)$ (the $\nu{=}1$ Ising signature, TRIM $\equiv$ Pfaffian in every sector); \mE\ the
000215 | $16$-layer carrier has $\mathrm{parity}^{16}={+}$ in ALL FOUR sectors $\Rightarrow$ gauged torus
000216 | $\mathrm{GSD}=4=\mu(SO(16)_1)=|\det\mathrm{Cartan}(D_8)|$ --- the lattice ground-state witness of
000217 | ``$\mu_{\mathrm{pre}}{=}4$ before condensation'' (step 1 of the \texttt{v378} KLM chain); \mE\ the
000218 | 16-fold-way bridge on MEASURED numbers: $\theta_v=e^{2\pi i\nu/16}=1$ exactly at $\nu=2c_-=16$
000219 | (\texttt{v489}), rivals $\nu=1,2,8$ not holomorphically condensable; \mE\ honest fence: the fermionic
000220 | Kitaev--Preskill TEE is identically zero for BOTH $M{=}1$ and $M{=}3$ ($\gamma_f{=}0.000001/0.000000$) ---
000221 | it does NOT discriminate $(E_8)_1$ vs $SO(16)_1$. \mC\ the KLM step $\mu:4\to4/2^2=1$ stays the cited
000222 | theorem (the condensed model is interacting); the numerics pin only the premise package
000223 | $\{c_-{=}8,\ \mu_{\mathrm{pre}}{=}4,\ \theta_v{=}1\}$. \mO\ \texttt{SEAM.EQUIV.01} stays \mO\ (continuum
000224 | existence, MMST \texttt{v336}). Integrated in \texttt{tfpt\_research\_contracts} (new S3-stack paragraph);