what does the "h" mean next to the Vh, IIh, and Ih scale degrees? I understand that they are Alternate Modal Tonic Degrees, but I haven't found anywhere in the book that clearly explains it.
The letter "h" following these roman numerals (as in Vh, IIh, IIIh and VIIh) indicates their status as conceptual modal tonic degrees of the Lydian Scale.1
1 h = Horizontal state of the LC Scale: duality of non-final to final. v = Vertical state of the LC Scale: unity of chord and scale.
George Russell, The Lydian Chromatic Concept of Tonal Organization, 4th edition (Brookline, MA: Concept Publishing Company, 2001), page 116.