Recurrence dimension conjecture for alternating multiple s-values

For each weight $n$, let $\mathsf{AMSV}_n$ denote the rational vector space of alternating multiple $s$-values. Recurrence dimension conjecture.

$$\dim_{\mathbb Q}\mathsf{AMSV}_1=1,\qquad \dim_{\mathbb Q}\mathsf{AMSV}_2=3,$$

and, for every $n\ge3$,

$$\dim_{\mathbb Q}\mathsf{AMSV}_n=2\dim_{\mathbb Q}\mathsf{AMSV}_{n-1}-2\left\lfloor\displaystyle\!\frac{n+1}{2}\right\rfloor+4.$$

The paper presents this as one of three dimension conjectures based on theoretical and numerical evidence and describes the resulting problems as unsolved.