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I have seen tests with Jnats that clearly show acidity of the slurry. The test was from a blog in Japanese.

It is by nature acidic, that is what etches the blade, and what makes the metal in the slurry to rust. Not all stones are equally acidic, some are more than others.

the ones that stick all the time do they leave hazy finish?

In my experience you are correct, that is exactly how it is with other stones too.

the questions if if the shave was good?
If the stone was giving you mate finish with water only then that means it is a prepolisher, using lather will improve the edge but does it improvet it enough...