Item 1 (0C8M)—The Stacks project

are given by

$\left( \begin{matrix} m_1 \\ m_2 \\ m_3 \\ m_4 \\ m_5 \\ m_6 \\ m_7 \\ m_8 \end{matrix} \right), \quad \left( \begin{matrix} -2w & w & 0 & 0 & 0 & 0 & 0 & 0 \\ w & -2w & w & 0 & 0 & 0 & 0 & 0 \\ 0 & w & -2w & w & 0 & 0 & 0 & 0 \\ 0 & 0 & w & -2w & w & 0 & 0 & 0 \\ 0 & 0 & 0 & w & -2w & w & 0 & w \\ 0 & 0 & 0 & 0 & w & -2w & w & 0 \\ 0 & 0 & 0 & 0 & 0 & w & -2w & 0 \\ 0 & 0 & 0 & 0 & w & 0 & 0 & -2w \end{matrix} \right), \quad \left( \begin{matrix} w \\ w \\ w \\ w \\ w \\ w \\ w \\ w \end{matrix} \right)$

with $2m_1 \geq m_2$ , $2m_2 \geq m_1 + m_3$ , $2m_3 \geq m_2 + m_4$ , $2m_4 \geq m_3 + m_5$ , $2m_5 \geq m_4 + m_6 + m_8$ , $2m_6 \geq m_5 + m_7$ , $2m_7 \geq m_6$ , and $2m_8 \geq m_5$ .

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