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The book "Understanding Wood" will teach you how wood moves with changes in relative humidity in the room. I assume your walnut would be plain sliced which moves a lot more than quarter sawn. You can look up the movement factors online too. I would guess for most parts of the country the humidity would be a low of 5-10% in the winter and maybe 50% in the summer. So assume a 40% swing and look up. I'd bet walnut will move 1/4" to 3/8" between the seasons. You will read a lot about sealing with finish on all sides to prevent this but it does not work. Wood finish is not hermetic (means it is not vapor proof). You need to plan for the movement. Something like fasten solidly at the back splash and use slots in the substrate so the counter top can move. Your other issue is the wood moves differently with the grain (radially) or across the grain (Tangentially). The makes the wood cup when the humidity changes. To mitigate the engineering says to never have any piece more than 3X wider than the thickness. But that means ugly narrow strips. You also need to alternate the way the growth rings angle when looking at end grain. Some will say if you fasten well enough you can keep the wood from cupping, but if fastened tightly enough and the wood wants to cup it will crack. These are the reasons why you rarely see countertops made this way. 8/4 would be much more stable.
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This is 6/4 walnut edge grain counter top in my laundry room. It has a coat or two of garnet shellac and Waterlox topcoat. The garnet shellac was advice from someone on the forum and really makes a difference in the visual depth of the walnut.
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If the cabinets are wood then wood countertops may be too much wood. Dark Corian may provide some balance. It has a better feel than stone.
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Is resawing possible?
A thinner "face cut" applied to 3/4 Birch plywood - fastened to cabinetry should resist warp.
If you're in a home with high swings in humidity, the plywood could be press fit or pin nailed to allow some flex.
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