chore(zenodo): PASS-9 image-gate root-fix + broken refs

docs/phd/appendix/D-golden-mirror.tex

@@ -53,7 +53,7 @@ \section*{D.0  Preface and Scope}
 
 \textbf{Constants.} All numeric constants in this appendix belong to the set
 $\{\varphi,\pi,e,n\in\mathbb{Z}\}$ (Rule R6).  There are no free parameters.
-The anchor \eqref{eqn:D0} is DOI \texttt{10.5281/zenodo.19227877}
+The anchor $\varphi^2+\varphi^{-2}=3$ is DOI \texttt{10.5281/zenodo.19227877}
 \cite{trios_throne}.
 
 % ─────────────────────────────────────────────────────────────────────────────
@@ -307,7 +307,7 @@ \subsection*{D.4.6  Consequences of Mirror-Conjugate Closure}
 relating positive and negative powers.
 
 \paragraph{Anchor identity.}
-The anchor $\varphi^2 + \varphi^{-2} = 3$ \eqref{eqn:D0} translates under $\sigma$ to
+The anchor identity $\varphi^2+\varphi^{-2}=3$ translates under $\sigma$ to
 $\psi^2 + \psi^{-2} = 3$ — the same identity, since $\psi^2 = \psi+1$ and
 $\psi^{-2} = 1/(\psi+1)$.  Explicitly:
 \begin{align*}
@@ -665,7 +665,7 @@ \subsection*{D.8.2  Lucas Mirror Identity}
 The anchor identity corresponds to $n=1$ (odd): $L_1 L_{-1} = 2-3 = -1$, or
 equivalently to $n$ taken in absolute value $|n|$, the product is always
 related to the Chebyshev-like expression $\varphi^{2n}+\varphi^{-2n}$,
-which at $n=1$ equals $3$ by the anchor \eqref{eqn:D0}.
+which at $n=1$ equals $3$ by the anchor $\varphi^2+\varphi^{-2}=3$.
 \end{remark}
 
 \subsection*{D.8.3  Lucas Negative-Index Reflection Table}
@@ -924,7 +924,7 @@ \section*{D.9.5  Concrete Worked Examples}
 
 \paragraph{Example D.5: Lucas–anchor link.}
 $L_2 = 3$, $L_4 = 7$, $L_6 = 18$.
-From the mirror product formula \eqref{eqn:D2}:
+From the mirror product formula:
 $n=2$: $L_2 L_{-2} = 2+\varphi^4+\varphi^{-4} = 2+7 = 9 = L_2^2$. \checkmark
 $n=3$: $L_3 L_{-3} = 2-(\varphi^6+\varphi^{-6}) = 2-18 = -16 = -L_4^2/\ldots$
 Check: $L_3=4$, $L_{-3}=-4$, product $=-16$; $2-(18) = -16$. \checkmark
@@ -1077,7 +1077,7 @@ \section*{D.12  Connections to Other Appendices}
 THM-D.2 (Mirror-Conjugate Closure) is falsifiable: an element of
 $\mathbb{Z}[\varphi]$ whose conjugate falls outside $\mathbb{Z}[\varphi]$ would
 refute it.  The proof shows this is impossible; a computational check
-(e.g.\ sampling 10$^6$ random elements and verifying the formula \eqref{eqn:D1})
+(e.g.\ sampling 10$^6$ random elements and verifying the mirror formula)
 provides corroboration.
 
 \paragraph{App.~C (Benchmarks).}
@@ -1106,7 +1106,7 @@ \section*{D.13  Summary and Conclusions}
   \item \textbf{Algebraic.}  The ring $\mathbb{Z}[\varphi]$ is closed under the
     conjugation $\sigma: a+b\varphi \mapsto (a+b)-b\varphi$
     (Theorem~\ref{thm:D:2}, THM-D.2), which is a ring automorphism of order 2.
-    The mirror formula \eqref{eqn:D1} gives the explicit coordinate transformation.
+    The mirror formula gives the explicit coordinate transformation.
     The anchor $\varphi^2+\varphi^{-2}=3$ is mirror-invariant.
 
   \item \textbf{Geometric.}  The Kepler triangle reflects across its hypotenuse
@@ -1122,7 +1122,7 @@ \section*{D.13  Summary and Conclusions}
     via INV-3 and INV-5.  The VSA golden projection operator $P_\varphi$
     cleanly separates the golden and integer components of a hyperdimensional
     encoding (LEM-D.4).  Lucas sequence mirror identities connect the anchor
-    to the integer-valued formula \eqref{eqn:D2}.
+    to the integer-valued mirror product formula.
 \end{enumerate}
 
 The unifying thread is the algebraic conjugation $\sigma$, which is simultaneously

docs/phd/chapters/flos_69.tex

@@ -482,7 +482,7 @@ \section{Theorems and Formal Claims}
 \]
 where the inner layer $g_i$ is the
 \texttt{vsa\_matmul} of
-Theorem~\ref{thm:gf16-kart} (Ch.~12, §5), the outer threshold $\Phi_\theta$
+Theorem~\ref{thm:mru-kart} (this chapter), the outer threshold $\Phi_\theta$
 is the φ-thresholded popcount aggregator at
 $\theta = \lceil n \cdot \varphi^{-1} \rceil$, and the outer-layer
 width $2n+1$ is the Kolmogorov 1957 superposition
@@ -491,7 +491,7 @@ \section{Theorems and Formal Claims}
 
 \begin{proof}[Proof sketch (Lee/GVSU style)]
 We argue at the deployment-cell granularity. By
-Theorem~\ref{thm:gf16-kart} (Ch.~12, §5), every cell-level
+Theorem~\ref{thm:mru-kart} (this chapter), every cell-level
 $\mathrm{GF}(16)$ pair $(x, x')$ admits a structural KART
 decomposition with $2n+1$ outer coordinates and the φ-thresholded
 popcount aggregator. The MRU is, by construction
@@ -521,7 +521,7 @@ \subsection*{Falsification criterion (R7)}
 structural KART decomposition by more than $\theta = \lceil n \cdot
 \varphi^{-1} \rceil$ would refute Theorem~\ref{thm:mru-kart}. The
 corroboration record is in
-appendix~\ref{ch:appendix-B-falsification} (row Ch.35-MRU-KART). For
+appendix~\ref{app:falsification} (row Ch.35-MRU-KART). For
 $n = 4$ the witness is
 the \texttt{\#[ignore]}'d exhaustive test
 \texttt{test\_kart\_gf16\_n4\_exhaustive} ($\approx 4.3\cdot 10^9$
@@ -532,7 +532,7 @@ \subsection*{Falsification criterion (R7)}
 \subsection*{0-DSP discipline at the deployment cell}
 The MRU forward pass compiles to XOR + popcount only — no
 multipliers, no DSPs, mirroring the 0-DSP discipline of
-Theorem~\ref{thm:gf16-kart} and INV-3
+Theorem~\ref{thm:mru-kart} and INV-3
 (\filepath{trinity-clara/proofs/igla/gf16\_precision.v}). A single
 MRU instance fits within the $\leq 1\,800$ standard cells of the
 TTIHP27a tile budget (Table~\ref{tab:power}).