Todd's relation conjecture and binary relations for multiple zeta values in positive characteristic

We prove Todd's relation conjecture: all $\mathbb{F}_q(θ)$-linear relations of Thakur's multiple zeta values are generated from the fundamental binary relation by the operators $\mathcal{B}^{\mathrm{S}}$, $\mathcal{C}^{\mathrm{S}}$, $\mathcal{B}^{\mathrm{S}}\circ \mathcal{C}^{\mathrm{S}}$; moreover