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000001 | \subsection{Relative objects}
000002 | 
000003 | The adjective \enquote{relative} is used in one fixed sense throughout the paper: every operator or action is compared to a declared reference object.
000004 | 
000005 | \begin{table}[t]
000006 | \centering
000007 | \small
000008 | \begin{tabularx}{\linewidth}{@{}>{\raggedright\arraybackslash}p{0.22\linewidth}YY@{}}
000009 | \toprule
000010 | Relative object & Definition or schematic form & Role \\
000011 | \midrule
000012 | $D_{\mathrm{rel}}$ & $D-D_{\mathrm{ref}}$ or a specified relative pair $(D,D_{\mathrm{ref}})$ & fermionic comparison operator \\
000013 | $\Gamma_{\mathrm{grav}}$ & $-6\chigeo^2\mathcal E_D+\Gamma_D^{(4)}$ with $\mathcal E_D=\operatorname*{Res}_{s=1}\mathcal Z_{\mathrm{rel}}$ and $\Gamma_D^{(4)}=\operatorname{FP}_{s=0}\mathcal Z_{\mathrm{rel}}$ & canonical spectral Einstein functional from relative residues \\
000014 | $\Gamma_{\mathrm{rel}}$ & admissible relative action preserved by the sheet antiunitary involution & strong-CP and reflection-symmetry package \\
000015 | $\Ind_{\mathrm{rel}}$ & APS-type index of a relative pair or superconnection package & carrier and bosonic counting \\
000016 | $Z_{\mathrm{rel}}$ & $Z_{\mathrm{adm}}[J,\eta,\bar\eta]/Z_{\mathrm{ref}}[0,0,0]$ & normalized admissible generating functional \\
000017 | $\Padm$ & $\operatorname*{s-lim}_{\beta\to\infty}e^{-\beta\Kadm}$; factorized form when the elementary projectors commute & operative admissibility selector on the closed branch \\
000018 | $\langle W(C)\rangle_{\mathrm{rel}}$ & Wilson observable after subtraction of the declared reference sector & confinement diagnostics \\
000019 | $\mathcal H_{\mathrm{rel}}$ & relative Hamiltonian used in admissible-sector minimization & optional record extension \\
000020 | \bottomrule
000021 | \end{tabularx}
000022 | \caption{Conventions on relative objects.}
000023 | \label{tab:relative-objects}
000024 | \end{table}