To repeat the thinnest wire hook "without compromising strength". If you're fishin' wolf fish, the thinnest acceptable is a pretty darn thick wire. If it opens up well then it's clearly too thin.
Any of those hooks I listed above come razor chemically sharpened out of the package and never need sharpening until dulled thru use as JR noted. Also the barb size is so tiny it's easy to get rid of. The metal alloy is superior and rarely opens up.
An example of what I mean by "thin enough" is the TMC 811s in 1/0 or bigger for saltwater fish. The 800s may be more suitable for tarpon.
Just my .02