The tritone is spelled as an augmented fourth or a diminished fifth depending on its resolution direction

A tritone resolving OUTWARD (diverging toward a sixth) is spelled as an augmented fourth; one resolving INWARD (converging toward a third) is spelled as a diminished fifth -- reflecting each tone's independent voice-leading tendency. This is the specific spelling concern the commissioning brief names as needing a rigorous, implementable algorithm.

A V7-to-I resolution's tritone (B4-F5 in G7, resolving outward to C5-E5) is correctly an augmented fourth (B-F, letter-distance a 4th) but the upper voice is instead spelled Gb5, turning an outward-resolving augmented fourth into a diminished-fifth spelling that implies the wrong resolution direction on the page.

Foundational species-counterpoint/tonal-harmony pedagogy (Fux-tradition, directly relevant to Gradus's species-counterpoint curriculum and standard dominant/diminished-seventh resolution teaching); universal agreement on the resolution-direction criterion among theory-pedagogy sources, though Gould/Read/Ross (engraving manuals proper) do not themselves adjudicate this -- it is a theory-pedagogy convention, not an engraving-manual rule, and should be cited as such rather than attributed to the engraving authorities.

This rule can be decided from pitches, durations and voices — no layout required. A validator can check it before anything is drawn.