5 problems

Bounded barcode-chain conjecture. There exists a number $M(n)$ such that for any $y_0,y_1\in\mathrm{MT}_n$, there exist $x_0,\ldots,x_k$ with $k<M(n)$, $y_0=x_0$, and $y_1=x_1$ sat…

Restricted interleaving metric conjecture. When $n=1,2$,

Non-geodesicity conjecture. The space of isomorphism classes of Reeb graphs with metric $d$ is not a geodesic space.

Geometric lifts conjecture. There exists a CW-complex $X$ and continuous functions $$gammaM, $$ $\gamma_N:X\to \mathbb R^n$ $ such that

Interleaving optimality conjecture. For any field $k$ and $i\in\mathbb Z_{\geq 0}$, $d_I$ is $i$-optimal.