Appendix A

Notation and Conventions

From A Source-to-Readout Architecture for a Theory of Everything, Version 1.0 (July 2026) · doi:10.5281/zenodo.21366204

This appendix collects only notation used across more than one chapter. Sector-specific symbols are defined where they first occur.

Symbol	Meaning
$\mathsf S_0$ , $\mathsf S_{\rm adm}$	raw and admitted source categories
$\mathcal W_0$ , $\mathbb L_{\rm src}$	witness class and source-closure operator
$X$ , $Y\in\operatorname{RealPrep}_{\Omega}[X]$	an admitted source and a supported realization
$\Omega$	fixed target-neutral, source-local realization convention containing no Tier-1 target or physical-success predicate
$\mathsf{Comp}_{T1}$	compatible Tier-1 readout object
$Q$ , $\mathcal A$ , $M$ , $G$ , $C$ , $A$ , $O$	quantum, QFT, matter, gravity, cosmology, arrow and observer sectors
$\rho$ , $E_Y$ , $\mathcal I_Y$	quantum state, POVM and instrument
$R^{\rm pre},R^{\rm cand},R^{\rm sel},R^{\rm act},R^{\rm obj}$	record stages
$D_i^{\rm obj}$ , $\mathcal A_Y^{\rm obj}$	an objective record and the objective archive of realization $Y$
$\kappa^{\rm inf}$ , $d_{\rm rel}$	intervention-derived influence and relational distance
$d_{\rm str}^{C}$ , $d_C^{\rm cmp}$ , $d_{\rm ref}$	strong metric on a Lorentzian comparison region, induced cell Hausdorff distance, and refinement path pseudometric
$\operatorname{Rec}_{\rm met}$	set-valued metric reconstruction relation
$\operatorname{Norm}_Y$ , $s_Y$	metric-scale normalization functional and normalized section
$G_R$ , $\Lambda_{\rm br}$ , $\mathcal Q_{\mu\nu}^{\rm grav}$	renormalized Newton coupling, branch cosmological constant and pure-metric higher-curvature correction
$S_M^{\rm dyn}$ , $\Gamma_{\rm QFT,dyn}^{\rm ren}$	disjoint matter action and normalized state-dependent QFT influence functional
$\mathfrak m_R$	EFT matching datum fixed before the gravitational solution
$\Gamma_{R,\rm CTP}$ , $T_{\mu\nu}^{R,\rm tot}$	matched record-exclusive influence and total record contribution $T_{\mu\nu}^{R}+\chi_{MR}T_{\mu\nu}^{MR}$
$q=6Y$ , $g_q=g_Y/6$	integer hypercharge and its compact-group coupling, with $g_q q=g_Y Y$
$g_Y$ , $g_2$ , $g_3$	hypercharge, weak and strong gauge couplings
$\mathcal K_{\rm FLRW}$ , $k_{\rm com}$	physical FLRW curvature scale and comoving perturbation wavenumber
$\chi$ , $\varrho=f_{\mathcal K}(\chi)$	radial geodesic distance and areal comoving curvature radius
$\Phi,\Psi,V_i,h_{ij}$	scalar Bardeen potentials, vector shear and tensor perturbation
$\prec_D$ , $(\mathcal T_Y,\preceq_t)$ , $\Theta_A$	strict event-dependency order, temporal carrier and order embedding
$\mathcal H_{Y,o}$ , $\mathfrak O_{Y,o}(t)$	common objective/arrow history and structural observer-readout family
$d_{\rm 1P}$ , $d_H^{\rm 1P}$	metric on individual observer structures and its Hausdorff metric on closed output sets

Unless stated otherwise, the spacetime signature is $(-+++ )$ , units satisfy $c=\hbar=1$ , Greek indices are spacetime indices and Latin indices are spatial or internal indices according to context. Curvature conventions are fixed by

[\nabla_\mu,\nabla_\nu]V^\rho =R^\rho{}_{\sigma\mu\nu}V^\sigma, \qquad R_{\mu\nu}=R^\rho{}_{\mu\rho\nu}, \qquad G_{\mu\nu}=R_{\mu\nu}-\frac12Rg_{\mu\nu}.

The relation arrow $\rightsquigarrow$ denotes a possibly partial or set-valued relation. A quotient by redescription identifies presentations of the same candidate; physical coarse-graining is a separate operation performed afterward.