diff --git a/docs/phd/appendix/B-falsification.tex b/docs/phd/appendix/B-falsification.tex
index 624c3a562d..4a0f2c0aa6 100644
--- a/docs/phd/appendix/B-falsification.tex
+++ b/docs/phd/appendix/B-falsification.tex
@@ -14,6 +14,7 @@ \chapter*{Appendix B: Falsification Ledger — Popperian Audit Across 33 Chapter
 
 \addcontentsline{toc}{chapter}{Appendix B: Falsification Ledger}
 \label{app:falsification}
+\label{ch:appendix-B-falsification}
 
 \begin{quote}\itshape
 ``A theory which is not refutable by any conceivable event is non-scientific.
diff --git a/docs/phd/appendix/D-golden-mirror.tex b/docs/phd/appendix/D-golden-mirror.tex
index 360965d672..a7f6d41634 100644
--- a/docs/phd/appendix/D-golden-mirror.tex
+++ b/docs/phd/appendix/D-golden-mirror.tex
@@ -29,7 +29,7 @@ \section*{D.0  Preface and Scope}
 \[
   \varphi^{2} + \varphi^{-2} = 3,
   \quad \varphi = \tfrac{1+\sqrt{5}}{2}.
-  \tag{D.0}
+  \tag{D.0}\label{eqn:D0}
 \]
 The three strands are:
 
@@ -282,7 +282,7 @@ \section*{D.4.5  Mirror-Conjugate Closure Theorem (Main Theorem)}
 \emph{mirror coordinate formula}:
 \[
   \boxed{\sigma(a + b\varphi) = (a+b) - b\varphi.}
-  \tag{D.1}
+  \tag{D.1}\label{eqn:D1}
 \]
 This is the algebraic core of the ``golden mirror'' metaphor:
 the coefficient $b$ is negated, while the integer part accumulates $b$
@@ -635,7 +635,7 @@ \subsection*{D.8.2  Lucas Mirror Identity}
 Therefore:
 \[
   \boxed{L_n L_{-n} = 2 + (-1)^n(\varphi^{2n} + \varphi^{-2n}).}
-  \tag{D.2}
+  \tag{D.2}\label{eqn:D2}
 \]
 \end{lemma}
 
diff --git a/docs/phd/appendix/F-coq-citation-map.tex b/docs/phd/appendix/F-coq-citation-map.tex
index f68310d846..aefb609f89 100644
--- a/docs/phd/appendix/F-coq-citation-map.tex
+++ b/docs/phd/appendix/F-coq-citation-map.tex
@@ -352,7 +352,7 @@ \subsection{The 15 \texttt{Admitted} passports}
 time $> 27 \log 27 / (1 - \varphi^{-1}) \approx 297$ steps for the
 canonical seed $1597$.
 
-\paragraph{F.7.C KART $\leftrightarrow$ GF16 isomorphism ($\times$1).}
+\paragraph{F.7.C KART $\leftrightarrow$ GF16 isomorphism ($\times$1).}\label{thm:gf16-kart}
 \filepath{trinity-clara/proofs/igla/kart\_gf16\_isomorphism.v}, theorem
 \texttt{kart\_gf16\_exact}. The Kolmogorov--Arnold ternary representation
 $\mathrm{KART}_n$ is isomorphic as an $\mathbb{F}_2$-algebra to