Manuscript VIII-ST@1 · VIII-ST.tex · section · fe979f3b
Certificate table
Error budgets and finite certificates › Certificate table · lines 2498–2550
The principal finite checks can be organized without an executed numerical run:
\begin{array}{p{.34\linewidth}p{.57\linewidth}}
\toprule
\text{obligation}&\text{exact witness}\\
\midrule
\text{uniform regular spacelikeness}&
\(1-\lambda^2=1/9\)\\
\text{cap separation}&
\(h-k\ge d\rho,\quad1/d<r\)\\
\text{active nondegeneracy}&
length table and positive areas \eqref{eq:areas}\\
\text{unique transverse incidence}&
new coordinates proportional to \(s>0\), with no cap contact\\
\text{ambient matching}&
\(T_{g\leftarrow f}=A_gJ_\mu^{n_{gf}}A_f^{-1}\)\\
\text{primitive topology}&
angular lift increment \(2\pi-\mu\), retained winding one\\
\text{worldsheet fixation}&
\(J_\mu(\tau,0,\zeta)=(\tau,0,\zeta)\)\\
\text{source-off control}&
\(\mu_\theta=\mu_0\) when \(\theta\kappa\operatorname{Tr}(\rho J)=0\)\\
\text{table algebraicity}&
rational half-angle identities \eqref{eq:algebraic}\\
\text{exact event guard}&
\(j=0\), incoming mode, \(\nu_{\rm G}\ge1\)\\
\text{clock completeness}&
\(\sum_aD_a^\dagger D_a=I\)\\
\text{reversible composition}&
six retained snapshots and zero final work\\
\text{transport}&
axial communication speed \(1/8<1\)\\
\text{output arrival}&
\(9/4+1/4=5/2<3\)\\
\text{physical support}&
all controller and payload curves inside the regular tube\\
\bottomrule
\end{array}Finite matrices may store these already-defined evaluations. For example,
is an exact Boolean table, not a detector for an unknown continuum geometry.
Displayed formulas in this passage
unlabeled · line 2502
\begin{array}{p{.34\linewidth}p{.57\linewidth}} \toprule \text{obligation}&\text{exact witness}\\ \midrule \text{uniform regular spacelikeness}& \(1-\lambda^2=1/9\)\\ \text{cap separation}& \(h-k\ge d\rho,\quad1/d<r\)\\ \text{active nondegeneracy}& length table and positive areas \eqref{eq:areas}\\ \text{unique transverse incidence}& new coordinates proportional to \(s>0\), with no cap contact\\ \text{ambient matching}& \(T_{g\leftarrow f}=A_gJ_\mu^{n_{gf}}A_f^{-1}\)\\ \text{primitive topology}& angular lift increment \(2\pi-\mu\), retained winding one\\ \text{worldsheet fixation}& \(J_\mu(\tau,0,\zeta)=(\tau,0,\zeta)\)\\ \text{source-off control}& \(\mu_\theta=\mu_0\) when \(\theta\kappa\operatorname{Tr}(\rho J)=0\)\\ \text{table algebraicity}& rational half-angle identities \eqref{eq:algebraic}\\ \text{exact event guard}& \(j=0\), incoming mode, \(\nu_{\rm G}\ge1\)\\ \text{clock completeness}& \(\sum_aD_a^\dagger D_a=I\)\\ \text{reversible composition}& six retained snapshots and zero final work\\ \text{transport}& axial communication speed \(1/8<1\)\\ \text{output arrival}& \(9/4+1/4=5/2<3\)\\ \text{physical support}& all controller and payload curves inside the regular tube\\ \bottomrule \end{array}unlabeled · line 2543