Appendix B: Reference Tables

Symbol	Value	Tree Expression
$G$	$6.674 \times 10^{-11}$ m$^3$ kg$^{-1}$ s$^{-2}$	$M_\text{Pl}^{-2}$
$\hbar$	$1.055 \times 10^{-34}$ J$\cdot$s	Fundamental distinction quantum
$c$	$2.998 \times 10^8$ m/s	Emergent from tree automorphisms (symmetries of the distinction manifold)
$\Lambda$	$\sim 10^{-52}$ m$^{-2}$	$\Lambda_\text{bare} \cdot q^{-d_\text{max}}$ — residual from finite distinction depth
$\alpha$	$\approx 1/137.036$	$q^{-d_\text{EM}}$ — electromagnetic distinction depth

Parameter	Symbol	Typical Range	Distinction Interpretation
Scaling ratio	$q$	$e, \pi, \varphi, \alpha^{-1}$	Ratio between adjacent distinction levels
Branching parameter	$N$	$2, 3, p+1$	Number of sub-distinctions per distinction
Planck depth	$d_\text{Pl}$	$\sim 60$	Finest distinction level
EW depth	$d_\text{EW}$	$\sim 30$	Electroweak distinction level
Optimal depth (QEC)	$d_\text{opt}$	$10-30$	Distinction depth for fault tolerance

Symbol	Meaning	Chapter
$\mathbb{Q}_p$	$p$-adic numbers — distinction space at prime $p$	4
$\mathbb{Z}_p$	$p$-adic integers — the unit distinction ball	4
$v_p(x)$	$p$-adic valuation — distinction count at $p$	4
$\|x\|_p$	$p$-adic absolute value — distinction size at $p$	4
$T_{N,q}$	Bruhat-Tits tree — the geometric form of nested distinctions	5
$\partial T$	Tree boundary — the continuum limit of distinctions	5, 9
$\mathbb{A}_\mathbb{Q}$	Adele ring — the space of all distinctions at all primes	8
$D_p^\alpha$	Vladimirov operator — distinction-respecting Laplacian	6
$M_p$	Monna map — distinction-to-Archimedean projection	6