Rank-3 scale theorems: Difference between revisions

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 * Assume ''S'' is a 2-step scale. Then ''S'' is ''slope-LQ'' if the slope between any two pair of points (representing a ''k''-mosstep) is one of the two nearest possible slopes (in the set {k/0,...,0/k}) to b/a.
 * Say that a 2-step scale ''S'' is ''floor-LQ'' if some mode ''M'' of ''S'' satisfies that γ(''M'') = the graph of floor(b/a*x).
-* Say that a k-step scale ''S'' is ''LQ'' if the set of lattice points on γ(''S'') is a translate of floor({(a,b,c)t : 0 <= t <= 1}) (where floor means take the floor coordinate wise) (?)
+* Say that a k-step scale ''S'' is ''LQ'' if the correspomding line in generic position has intersections with coordinate level planes x = k, y = k or z = k that spell out the scale.
 ===== MV2 is equivalent to floor-LQ in 2-step scales (WIP) =====
 Assume wlog there are more L's than s's.