The chord-word formula for singular height of planar knotoids

Let $D$ be a linear chord diagram with one chord for a planar knotoid, and write its corresponding word as $c=a^{n_1}b^{m_1}\dots a^{n_k}b^{m_k}$, where $k<\infty$ and $n_i,m_i\in\mathbb{Z}$, subject to the stated reduced-word conditions. Let $d$ be the integer determined by the first consecutive pair of exponents with the same sign, using the four cases described in the construction preceding the conjecture. Chord-word formula for singular height. The singular height of the corresponding singular planar knotoid diagram is

$$\displaystyle{sh(k)=\left[\sum_{i=1}^k\left(|n_i|+|m_i|\right)\right]-2d}.$$

This conjecture proposes that singular height can be detected directly from the word associated with a linear chord diagram. The supplied text does not state whether the formula has been proved or disproved.