Obstructed MDS Identification in the Lyons Carabiner and the Prediction of Λ₄₄

We present a self-contained exposition of the Lyons carabiner, focusing on the triple obstruction mechanism arising in Section~\ref{sec:triple}. Three independent numerical obstructions---phantom coupling $\pi$, holonomy defect $\rho$, and braid deficit $\beta$---together form the triple $(\pi,\rho,\beta)=(3,4,9)$, which uniquely recovers the MDS code $[6,4,3]_5$ over $\mathbb{F}_5$. This identification is not a postulate but a provable consequence of the weight distribution and the complement involution. We then develop the Pontryagin--Heegner bridge: phantom weights are ``silent frequencies'' in the Pontryagin dual of $\mathbb{R}_+^\times$, and their vacuum generates the $20$-dimensional \emph{inverse Heegner space} $\mathcal{H}_{20}$. This yields a candidate $44$-dimensional lattice $\Lambda_{44} = \Lambda_{24} \oplus \mathcal{H}_{20}$ with Lyons group symmetries. The phantom resolution cascade $\mathrm{Ly}\to\mathrm{HS}\to\mathrm{Ru}$ predicts a chain of lattice dimensions $44\to 34\to 24$, terminating at the Leech lattice $\Lambda_{24}$, with the Rudvalis level providing independent numerical evidence through striking orbit coincidences. All numerical claims are verified by machine-checked computation. ( The Lean~4 formalization is available as the \texttt{HatsuYakitori} library; the key files are \texttt{MachineConstants.lean}, \texttt{LyonsCarabiner.lean}, and \texttt{RudvalisCarabiner.lean}. Remaining \texttt{sorry}s are listed explicitly in Section~\ref{sec:conclusion}.