AI 中文总结
研究n×n幺模矩阵离奇异性的距离，固定n = 4，通过评估(2k + 1)元及(k + 1)元情形取得显著进展，为研究幺模矩阵性质提供新视角。
AI 中文摘要
对于n×n幺模矩阵，其离奇异性能有多近？随着n增加，三元情形难以有精确表达式。但固定n = 4，随着k增加评估(2k + 1)元情形有显著进展；4×4非负幺模矩阵的(k + 1)元情形同理。
英文摘要
How close to singularity can an $n \times n$ unimodular matrix be? For ternary cases as $n$ increases, exact expressions are unlikely, but upon fixing $n=4$ and assessing $(2k+1)$-ary cases as $k$ increases, we make significant progress; similarly for $(k+1)$-ary cases of $4\times 4$ nonnegative unimodular matrices.
Comments21 pages; $5\times 5$ conjectures appear at end; $6\times 6$ and $7\times 7$ signed conjectures likewise
