See below the basic introduction of Dr. Hayashi´s taxonomy. Following information are from private communication.
Dr Hayashi wrote:
"As for my taxonomic system, I'm still busy to revise it. Harry Mays asked me to present my whole system with all new species ever published by me including n.n.. However, the system needs to solve the position of many new species including unpublished yet. And it will be more than 100. I presume there may be more than 500 species in Haworthia.
Very short introduction of my system;
Genus Haworthia includes Chortolirion and Astroloba, but excludes Poellnitzia. Closest ally of Poellnitzia is Gasteria. There are 3 major groups in the family Aloaceae, namely Aloe, GasteroidGasteria & Poellnitzia) and Haworthioid (Haworthia, Chortolirion and Astroloba). The basic and conclusive difference (without any exceptions) of these 3 groups, are inner floral structure. (
Genus Haworthia is divided into 3 subgenera, Haworthia (not in Bayer's sense), Longifolia (H. graminifolia group, H. wittebergensis and Chortolirion) and Oligonodes (including Astroloba) (cf. Haworthiad 13: 15-20 (1999), Alsterworthia Int. 2: 8-14 (2002)).
Subgenus Haworthia is subdivided into 4 waves (supersection); namely Asperdermis (rough epidermis group consists of former Loratae section and Truncata series), Eriodermis (group with soft, fine setate projections consists of sections Marumiana (-Nortieri), IsabellaeGracilis-Tenera) and Bolusii (-Rooibergensis-Gordonia
Subgenus Oligonodes is subdivided into 2 waves, namely wave Rectofolia consists of sections Venosa and Attenuata, and wave Spirofolia consists of sections Longiflora (Scabra, Limifolia and Bruynsii) and Breviflora (Bilabiloba complex (Maxima group) and Astroloba complex). You can easily see the difference of flower between 2 waves (very large and reddish flower of Rectofolia vs. small and yellowish flower of Spirofolia).
So, my system consists of genus, subgenus, wave (supersection), section, complex (superseries) and series. There are 18 sections at moment. Bayer's "species" roughly corresponds to my series."