Conjectural dimensions of finite multiple mixed-value subspaces

Let $F_w$ denote the $w$-th Fibonacci number, and let the symbols $\mathsf{FMZV}^{(2)}_w$, $\mathsf{FMMVe}_w$, $\mathsf{FMMV}_w$, $\mathsf{FES}_w$, $\mathsf{FMMVo}_w$, $\mathsf{FMtV}_w$, and $\mathsf{FMTV}_w$ denote the finite multiple-value subspaces of weight $w$ defined in the paper. Finite multiple mixed-value dimension conjecture. (i) For all $w\geq1$,

$$\mathsf {FMZV}^{(2)}_w=\mathsf {FMMVe}_w=\mathsf {FMMV}_w=\mathsf {FES}_w=\mathsf {FMMVo}_w=\mathsf {FMtV}_w$$

all have dimension $F_w$. (ii) For all $w\geq1$,

$$\displaystyle\!\frac{\mathsf {FMZV}^{(2)}_w}{\zeta^{(2)}_\mathcal{A}(\{1\}^w)\mathbb{Q}}=\displaystyle\!\frac{\mathsf {FMMVe}_w}{\zeta^{(2)}_\mathcal{A}(\{1\}^w)\mathbb{Q}}=\displaystyle\!\frac{\mathsf {FES}_w}{\zeta_\mathcal{A}(\{\bar1\}^w)\mathbb{Q}}=\displaystyle\!\frac{\mathsf {FMMVo}_w}{t_\mathcal{A}(\{1\}^w)\mathbb{Q}}=\displaystyle\!\frac{\mathsf {FMtV}_w}{t_\mathcal{A}(\{1\}^w)\mathbb{Q}}$$

all have dimension $F_w-1$. (iii) For all $k\geq1$,

$$\dim_\mathbb{Q}\mathsf {FMTV}_{2k+1}=\dim_\mathbb{Q}\mathsf {FMTV}_{2k}+\dim_\mathbb{Q}\mathsf {FMTV}_{2k-1}.$$

These are numerical dimension conjectures for finite multiple mixed-value subspaces. The table and surrounding text present them as conjectural and provide no formal proof.