Minimal button sets analysis
Minimal sets of used buttons analysis (for PAL and NTSC, inbounds, without SpaceTime-beam [or GT-Code which already needs Dash and Cancel]) [as a generalization of the "No-Dash-Button" category]: (unfinished)
The set of all (2) button-sets which (theoretically) allow for beating the game and that are minimal with respect to subsets is given by {(Left, Right, Down, Up, Jump, Shot, Select)}*{(Dash), (L, R)}= {(Left, Right, Down, Up, Jump, Shot, Select, Dash), (Left, Right, Down, Up, Jump, Shot, Select, L, R)}.
One can easily check that TAS can get across the so-called "Noob-Bridge" even without the use of Dash, by ledge-grabbing onto one crumble-block after another. The Ice-beam though cannot be collected if neither L nor R nor the Dash button is allowed to be used at any time. And without Ice, one cannot use the Botwoon-skip route and one cannot get past the pre-Botwoon room since that would need either a Ceiling-CF., or an Ice-ceiling-clip, or X-Ray (for R.-Mode), or speed echoes, or a shinespark. Thus, the above mentioned button combinations are indeed the only minimal options.
In both cases, Max% is 100% (which is even humanly doable).
TODO: Provide visualization videos for the Max% options.
Set of all Low% options for the case that L and R are added:
[Core = (Interior, Varia, Charge) = (E2, 1*E-Tank, Varia, Charge)]
[Interior = (E2, 1*E-Tank)]
[E2 = (Ball, 1*M, Bomb, 1*SM, 1*PB)]
Gravity-Powerbomb:
(Core+1*M+1*SM+1*PB, Gravity, 2*E-Tank) ;
(Core+1*M+1*SM+1*PB, Gravity, 1*E-Tank, 1*R-Tank) ;
(Core+1*M+1*SM+1*PB, Gravity, 2*R-Tank)
And this option (with all its sub-categories) is the only one, since
(i) all 14% categories that use Speedbooster need Dash to start running for Echoes.
(ii) all 14% categories that use X-Ray need Dash to use it.
(iii) One cannot enter the temporary Blue-Suit state without Speedbooster, Blue-Suit needs Shinespark-Suit if one does not have Speedbooster, Shinespark-Suit needs a Crystal Flash, and for this, one needs at least 10 powerbombs.
(iv) Hypothesis: One cannot collect Ice if one neither can use Dash nor a Shinespark can be used (without major-glitches).
Thus, only 14%Gravity-PB and 14%Ice-PB would remain, but in the latter case, due to the hypothesis, one would have to obtain Shinespark-Suit in order to get to Ice, and in this case, the Shinespark-Suit could only be gotten at Draygon to whom one can only get using Ice in this category, which leaves us only with 14%Gravity-PB, which is a valid option for TAS.
Set of all Low% options for the case that Dash is added:
[Core = (Interior, Varia, Charge) = (E2, 1*E-Tank, Varia, Charge)]
[Interior = (E2, 1*E-Tank)]
[E2 = (Ball, 1*M, Bomb, 1*SM, 1*PB)]
Gravity-Ice:
(Core+1*M+1*SM, Gravity, Ice, 2*E-Tank) ;
(Core+1*M+1*SM, Gravity, Ice, 1*E-Tank, 1*R-Tank) ;
(Core+1*M+1*SM, Gravity, Ice, 2*R-Tank) ;
(Core+2*SM, Gravity, Ice, 2*E-Tank) ;
(Core+2*SM, Gravity, Ice, 1*E-Tank, 1*R-Tank) ;
(Core+2*SM, Gravity, Ice, 2*R-Tank)
X-Ice:
(Core+1*M+1*SM, X-Ray, Ice, 2*E-Tank) ;
(Core+1*M+1*SM, X-Ray, Ice, 1*E-Tank, 1*R-Tank) ;
(Core+1*M+1*SM, X-Ray, Ice, 2*R-Tank) ;
(Core+2*SM, X-Ray, Ice, 2*E-Tank) ;
(Core+2*SM, X-Ray, Ice, 1*E-Tank, 1*R-Tank) ;
(Core+2*SM, X-Ray, Ice, 2*R-Tank)
HighJump-Ice-PAL:
(Core+1*M+1*SM, HighJump, Ice, 2*E-Tank; PAL) ;
(Core+1*M+1*SM, HighJump, Ice, 1*E-Tank, 1*R-Tank; PAL) ;
(Core+1*M+1*SM, HighJump, Ice, 2*R-Tank; PAL) ;
(Core+2*SM, HighJump, Ice, 2*E-Tank; PAL) ;
(Core+2*SM, HighJump, Ice, 1*E-Tank, 1*R-Tank; PAL) ;
(Core+2*SM, HighJump, Ice, 2*R-Tank; PAL)
Ice-Speed:
(Core+1*M+1*SM, Speed, Ice, 2*E-Tank) ;
(Core+2*SM, Speed, Ice, 2*E-Tank) ;
(Core+1*M+1*SM, Speed, Ice, 1*E-Tank, R-Tank) ;
(Core+2*SM, Speed, Ice, 1*E-Tank, R-Tank) ;
(Core+1*M+1*SM, Speed, Ice, 2*R-Tank) ;
(Core+2*SM, Speed, Ice, 2*R-Tank)
In all 14% categories that do not use Ice, a diagonal shinespark for the Zebetite-Skip is necessary, which requires the R button, and all categories that include "PB" require a Crystal Flash and hence L and R. This leaves us with 14%X-Ice, 14%HighJump-Ice(PAL), 14%Gravity-Ice, 14%Ice-Speed, which are all valid options.
