We give an evaluation for the stuffle-regularised \( t^{*,V}(\{2\}^a,1,\{2\}^b) \) as a polynomial in single-zeta values, \( \log (2) \) and \( V \) . We then apply this to establish some linear independence results of certain sets of motivic multiple \( t \) values. In particular, we prove the elements of Saha’s conjectural basis are linearly independent, on the motivic level, and that the (suitably regularised) elements \( t^\mathfrak {m}(\{1,2\}^\times ) \) form a basis for both the (extended) motivic MtV’s and the alternating MZV’s.
