TFPT scientific source excerpt
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000258 | \begin{axiom}{Discrete Topological Corrections}{TC}
000259 | Additional contributions to $\phiz$ arise only from topological invariants 
000260 | that are discrete and universal.
000261 | 
000262 | \tcblower
000263 | \textbf{Status:} Consequence of gauge-invariance constraints.
000264 | 
000265 | \textbf{Consequence:} The topological surcharge is fixed by the spin lift of the
000266 | $\mathbb{Z}_2$ identification, which yields an order-4 element in the spin bundle
000267 | and hence a universal deficit factor $(1-1/4)$ per minimal sector. Cutting along the
000268 | seam yields four local corner patches $(C_1,\Gamma_+)$, $(C_1,\Gamma_-)$, $(C_2,\Gamma_+)$,
000269 | $(C_2,\Gamma_-)$ in the fundamental domain, so $F=4$ and the deficit sum is:
000270 | \begin{equation}
000271 |     \deltatop 
000272 |     = \frac{1}{256\pi^4}\sum_{p=1}^{4}\left(1-\frac{1}{4}\right)
000273 |     = \frac{3}{256\pi^4}
000274 |     = 48\cthree^4
000275 | \end{equation}
000276 | See Appendix~\ref{app:48deriv} for the explicit sector count.