It depends to some extent who your tire supplier is but the requirements are pretty generic.
Here's a link to some care and maintenance manuals:
Goodyear Aviation Tires - Technical Resources - Tire Care and Maintenance Manual
Note these are not definitive controlled manuals and are not subject to revision service. Use for guidance only. Your NAA may also have some reference material (in UK this is CAP562).
To your specific question, normally the "width" of the rib (between grooves) is the most critical as cuts
across there can start a tread peel between the grooves. Cuts in the same direction as the grooves are not so important (subject to depth as you say).
Hope this helps!