references:

1) To make a truly flat surface you mutually refernce 3 surfaces. This can be done either by marking-and-scraping, or mutual lapping.

2) "ordinary" lapping involves embedding abrasive particles into a soft-but-flat surface, thus making a flat abrasive tool. The harder workpiece is then (paradoxically) abraded.

3) Woodworkers common use a variant of (2) were normal sheet abrasive is fixed to a "flat-enough" reference surface, and the workpiece (a wood plane) rubbed over it.

My query is: When using (2) or (3) what prevents the workpiece becoming CONVEX. It (obviously?) can't become concave.

I have had a practical problem when trying to flatten a 1" wide chisel using this technique. The tool definitely became (slightly) convex over its width.

Am I doing lapping wrong, or is lapping (or whatever (3) is called) the wrong technique?

It works best if the force moving the item is directed near its center. Also the item has to be inflexible, and the material under the grit paper also should be quite rigid.

The 3 surface method doesn't work on rectangles.

A magnetic steel chisel can be strongly held to a grit paper with magnetic force. That keeps things nicely in line. The usual mistake is to apply too much force, and not keep it concentrate at the center.

All methods of hand work using self guiding material removal techniques have the potential to go too far and damage the accuracy of a surface. Usually 90 percent coverage of the existing surface is enough. High spot contact. The remaining 10 percent takes a lot of work, and by hand, the error is roughly proportional to the amount of work.