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You can get a knife so sharp it hardly cuts paper. To cut it it needs micro serrations, the finer the stone the smaller the serrations.
On some of my woodcarving knives I use a translucent arkansas stone.
The sharpened blade will hardly cut paper and definitely won’t cut rope but if you cut yourself with it you won’t feel it. It leaves a shiny finish on the wood it cuts though.
The best edge for paper if that’s your thing is around 1000 grit, but use the stone very gently as you sharpen.
Should be able to get scary sharp with that. Tried permanent marker on the cutting surface to make sure your removing material where you think you are?