The secret was torsion-box construction. A torsion box is a simple grid of slender ribs glued between thin plywood skins. It makes these shelves stiff and flat, yet incredibly light. This rigid architecture means torsion-box shelves won’t sag or twist, and they can be mounted without any external support.
11. Clamp the three shelf components together without glue, so you can check the fit of the miter joints. Use plywood braces to support the upper shelf and hold everything square.
6. Rout the edges flush. Use a second shelf to support the router and a piece of scrap plywood as a spacer.
I tried this, even though you told me it wouldn't work very well. You were right; it didn't work very well. I rounded the miter a bit and made it worse.
I was afraid of that. We have to remember that the normal wood glue we use is water soluble. That's why for cutting boards or outside projects we have to use a different type of glue.