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 $mathrm{Ly}tomathrm{HS}tomathrm{Ru}$ predicts a chain of lattice dimensions $44to 34to 24$, 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}.