A confident pseudo-label can be wrong and remain fixed

Take $\mathcal{X}=\{0,1,2,3,4,5\}$ with distance $d(x,y)=\mathrm{\mid }x-y\mathrm{\mid }$ and classes $\{1,2\}$. The true labels at $0,1,2,3,4,5$ are $1,1,1,1,2,2$, but only the examples $(0,1),(1,1),(2,1),(3,1),(4,2)$ are labeled for the procedure. Run the finite confidence-threshold pseudo-labeling algorithm with unlabeled set $\{5\}$, $k=5$, threshold $\tau =4\mathrm{/}5$, pseudo-label weight $\lambda =1$, and round cap $T=1$. The nearest labeled examples to $5$ have labels $2,1,1,1,1$, so confidence $4\mathrm{/}5$ assigns the wrong label $1$; the no-relabel rule retains that assignment.

The nodes lie at their feature coordinates on the real line. Labels after a colon are observed labels for positions 0 through 4; the question mark at 5 is unlabeled to the algorithm. The hidden true class at 5 is 2. The drawn line shows distance order only, not a graph edge set.

diagram failed to render:
\begin{tikzpicture}
\node[draw,circle] (x0) at (0,0) {$0:1$};
\node[draw,circle] (x1) at (1.5,0) {$1:1$};
\node[draw,circle] (x2) at (3,0) {$2:1$};
\node[draw,circle] (x3) at (4.5,0) {$3:1$};
\node[draw,circle] (x4) at (6,0) {$4:2$};
\node[draw,circle,dashed] (x5) at (7.5,0) {$5:?$};
\draw (x0)--(x1)--(x2)--(x3)--(x4)--(x5);
\node at (7.5,-0.75) {true class 2};
\end{tikzpicture}