I'm happy that the puzzle is being enjoyed! For anyone getting stuck, here are a few general solving-tips ...

(1) Since this kind of puzzle requires an ordinary mortal to pencil-mark all the candidates, do this right away: For each cell, count how many of its neighbors it's greater-than (call this count G) and how many it's less-than (call this count L) -- then the candidates for that cell can be reduced to the range [G+1,...,9-L].

(2) Apply the inequalities to further reduce the candidate-ranges in each unit (row/column/box): If two neighboring cells have ranges like [min1,...,max1]

> [min2,...,max2], then the inequality requires min1

> min2 and max1

> max2 -- so look for violations to correct, which will eliminate the offending candidates (thus shrinking a range each time). Certain easily-recognised "inequality flow" patterns will become apparent.

(3) In each unit, look at the mins that equal 1 (that is, currently the least candidate in the unit) ... If there is only one of those, that cell is solved as a 1, eliminating any other 1's in the unit -- each elimination possibly producing new inequality violations that would eliminate still more candidates. Likewise for the maxs that equal 9 (that is, currently the greatest candidate in the unit) ... If there is only one of those, that cell is solved as a 9. And so on. Every time a candidate is eliminated, be sure to check its neighbors for inequality violations whose correction will eliminate additional candidates.

(4) Use the least- and greatest-candidates in a unit to make eliminations in other units (e.g. line-line and line-box intersections). Eventually, of course, candidates other than mins/maxs may be eliminated. Apply the

Law of Leftovers and other sudoku strategies as usual.