Component-wise minimality conjecture for simplicial complexes with torsion

For $p\geq 3$, consider the simplicial $2$-complexes d2_n8_3torsion and d2_n8_4torsion, which have $3$-torsion and $4$-torsion, respectively. Their $f$-vectors record the numbers of faces in each dimension. Component-wise minimality conjecture. The examples d2_n8_3torsion and d2_n8_4torsion have component-wise minimal $f$-vectors among complexes with $3$- and $4$-torsion, respectively. The claim concerns the minimality of the computationally exhibited examples; the source does not state a resolution.