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This paper establishes uniform bounds on the nonvanishing of the canonical divisor $K_X$ for $K_X$-trivial regular projective surfaces $X$ over imperfect fields of positive characteristic $p$. Specifically, it proves $60K_X \sim 0$ for all such surfaces, demonstrating this bound is sharp with an example in characteristic 5. Further refined bounds are derived for geometrically normal and non-normal cases, with the latter depending on the Albanese morphism, yielding results like $12K_X \sim 0$ for $p=2,3$ and $K_X \sim 0$ for $p \ge 7$ when the Albanese is trivial.
A uniform $60K_X \sim 0$ bound is established for $K_X$-trivial regular surfaces over imperfect fields, with optimality demonstrated and tighter bounds derived based on the Albanese morphism's structure.
For any regular projective surface $X$ over an arbitrary field $k$ of characteristic $p>0$ with $K_X\equiv0$, we prove that \[ 60K_X\sim0 . \] This uniform bound is optimal. To show that the factor $5$ is necessary, we construct an example in characteristic $5$ for which $K_X$ has exact order five. If $X$ is geometrically normal, then $12K_X\sim0$. Our main focus is the geometrically non-normal case, where we obtain more precise bounds according to the Albanese morphism. If it is nontrivial, then $p=2$ or $3$, and we prove $12K_X\sim0$ and $6K_X\sim0$, respectively; both bounds are optimal. If it is trivial, then $K_X\sim0$ for $p\ge7$, while $5K_X\sim0$, $3K_X\sim0$, and $4K_X\sim0$ for $p=5,3,2$, respectively.