100%Map-Low%Items analysis
100%Map-Low% analysis (without OoB, activating Spazer+Plasma simultaneously, and GT-Code): (unfinished)
This section here is so far completely solved, except of a demonstration video for the 15% TAS option.
1. Certain squares that are not that easy to enter and will add important constraints in order to find all low% categories that allow to beat the game with 100%Map:
(i) map-squares at the bottom of LNF-SpaceJump-statue room
(ii) Springball´s map-square
(iii) area on the left side of the Craterian SuperMissile
(iv) Plasma´s room
(v) Dachora´s area (aswell as 1 specific map-square that is completely within speed-blocks in the room above Crocomire)
2. None of the 9 different 14% categories (including sub-categories) include at least either SpaceJump or Grapple [for a Ceiling-CF in order to get to (i)] except 14%Grapple-Speedbooster which does not have 10 powerbombs.
Therefore, 100%Map-Low% is at least 15% (using (H1)). (Using that certain hypotheses hold), it will be "proven" that the following options are (item-minimal) optimal solutions for 100%Map-Low%:
[Core = (Interior, Varia, Charge) = (E2, 1*E-Tank, Varia, Charge) ]
[Interior = (E2, 1*E-Tank) ]
[E2 = (Ball, 1*M, Bomb, 1*SM, 1*PB) ]
15%Gravity-Powerbomb-Grapple:
(Core+1*M+1*SM+1*PB, Gravity, Grapple, 2*E-Tank) ;
(Core+1*M+1*SM+1*PB, Gravity, Grapple, 1*E-Tank, 1*R-Tank) ;
(Core+1*M+1*SM+1*PB, Gravity, Grapple, 2*R-Tank).
Hypotheses:
(H1) In order to get to (i), at least either SpaceJump or (at least) Grapple (for Ceiling-CF with vertical Grapple-push) is necessary.
(H2) In order to get to (ii) and out of that area, at least either Gravity or (at least) Springball (and X-Ray) is necessary.
(H3) In order to get to (iii), at least either X-Ray, or (at least) 15Powerbombs, or Speedbooster, or Shinespark-Suit is necessary (neglecting that Blue-Suit can be obtained via Shinespark-Suit without Speedbooster, too).
(H4) The person who does the reasoning in order to tell if relevant maneuvers are possible (for TAS) or not possible has sufficient knowledge about the currently known SM-physics.
Combining (H2) and (H3) [or (ii) and (iii) respectively], we get the full set of only those theoretical 15% options:
(I) Gravity,X-Ray
(II) Gravity,15PBs
(III) Gravity,Speedbooster
(IV) Gravity,Shinespark-Suit
(V) X-Ray,Springball
Adding constraints given by (iii), we can conclude the following:
For (I), one would have to add either SpaceJump or Grapple which leads to options with at least 15% that are in both cases not sufficient to beat the game (using (H4)).[Contradiction]
For (II) and (V) adding SpaceJump or Grapple leads to options with at least 16% already.[C.]
For (III), adding Grapple and the for the CF needed 10PBs lead already to 16% options, too, and in the case of adding SpaceJump, there is no way to get to (ii) because of a certain previous room.[C.]
For (IV), one can obtain the Shinespark-Suit using a CF in Draygon´s room, and in the case of adding Grapple, the game can be beaten with 15% and 100%Map ("proof" uses (H4)).
There is also no further restriction than those given by MB2´s Rainbow-beam, regarding the choice of Tanks.
Also, the Plasma-Pirates can be killed with echoes. "q.e.d."
Humanly doable minimal options:
One will at least need 16% since in the above mentioned 15% option a ceiling-CF followed by pushing Samus through the respawn-crumble-blocks via Grapple in GT´s room and a setup to obtain Shinespark-Suit in Draygons room with a cap of 10 powerbombs would be needed which is both infeasible for humans.
On the other hand there exist doable 16% options:
[Core = (Interior, Varia, Charge) = (E2, 1*E-Tank, Varia, Charge) ]
[Interior = (E2, 1*E-Tank) ]
[E2 = (Ball, 1*M, Bomb, 1*SM, 1*PB) ]
16%Gravity-Speed-X-Ray-SpaceJump:
(Core+1*M+1*SM, Gravity, Speed, X-Ray, SpaceJump, 2*E-Tank) ;
(Core+1*M+1*SM, Gravity, Speed, X-Ray, SpaceJump, 1*E-Tank, 1*R-Tank) ;
(Core+1*M+1*SM, Gravity, Speed, X-Ray, SpaceJump, 2*R-Tank) ;
(Core+2*SM, Gravity, Speed, X-Ray, SpaceJump, 2*E-Tank) ;
(Core+2*SM, Gravity, Speed, X-Ray, SpaceJump, 1*E-Tank, 1*R-Tank) ;
(Core+2*SM, Gravity, Speed, X-Ray, SpaceJump, 2*R-Tank)
16%Gravity-Speed-Grapple-SpaceJump:
(Core+1*M+1*SM, Gravity, Speed, Grapple, SpaceJump, 2*E-Tank) ;
(Core+1*M+1*SM, Gravity, Speed, Grapple, SpaceJump, 1*E-Tank, 1*R-Tank) ;
(Core+1*M+1*SM, Gravity, Speed, Grapple, SpaceJump, 2*R-Tank) ;
(Core+2*SM, Gravity, Speed, Grapple, SpaceJump, 2*E-Tank) ;
(Core+2*SM, Gravity, Speed, Grapple, SpaceJump, 1*E-Tank, 1*R-Tank) ;
(Core+2*SM, Gravity, Speed, Grapple, SpaceJump, 2*R-Tank).
Hence, we only need to look for other potential 16% options in order to get the complete set of (humanly doable) solutions:
Necessary constraints/items:
Ball; Bombs; at least either (2*M, 2*SM) or (M, 3*SM) [and at least (M, SM) ]; PB; at least 3 Tanks [at least one of those needs to be an E-Tank]; Charge; SpaceJump (which is for humans needed to get to the lower screens in the SpaceJump-statue room near GT in Lower Norfair); at least either Varia or Gravity (since otherwise a human could not survive Lower Norfair, given a cap of 16 items); at least either X-Ray or Grapple (in order to enter the screens at the top of pre-Shaktool room) [note that a strictly smaller part of this room exists twice due to a copy of this room].
(Ball, Bomb, 3 M/SM, SM, PB, 3 Tanks, Charge, SpaceJump) are already 12 items, and necessarily adding either X-Ray or Grapple makes it 13%. This means that one would need to add 3 more Tanks if Varia was skipped, which gives already 16%. But since at least 1 suit is needed, one would have to add at least 1 item and obtains 17% > 16% which cannot be a minimal humanly doable option anymore due to the above mentioned 16% options [contradiction]. Therefore Varia needs to be used in all cases.
In order to break/get past Speed-blocks [which is needed in various places like Dachora area, near Crocomire and in the E-Tank room to the left of Charge room], either Echoes/temp. Blue-Suit, a Shinespark, Blue-Suit or Shinespark-Suit is needed, and for those at least either Speedbooster or an additional PB-pack [for a Crystal Flash] is needed, which leaves us with the following setup of constraints that contains already 15%:
(Ball, Bomb, 3 M/SM, SM, PB, 3 Tanks, Charge, SpaceJump, Varia) + [X-Ray or Grapple] + [1*PB or Speedbooster]. [These 4 cases are to be distinguished: (i) X-Ray+1*PB (ii) X-Ray+Speedbooster (iii) Grapple+1*PB (iv) Grapple+Speedbooster.] Now, all that is left to do is going through all cases that are generated by adding 1 item, and then decide if the resulting options are doable or not. The remaining types of items that one could potentially add are:
1*M, 1*SM, 1*PB, Grapple, X-Ray, Speedbooster, HighJump, Ice, Spazer, Plasma, Wave, Gravity, ScrewAttack, Springball, E-Tank, R-Tank.
In the cases (i) and (ii) statement A holds, and in the cases (iii) and (iv) statement B holds for adding anyone of the following items, which causes all of those items to be negligible (in PAL and NTSC):
1*M, 1*SM, Speedbooster, Spazer, Plasma, Wave, ScrewAttack, Springball, E-Tank, R-Tank.
A: One cannot get to the upper right door in pre-Coloseum room.
B: One cannot escape pre-Draygon room/get to the upper door from below.
This leaves us with the rest: 1*PB, Grapple, X-Ray, HighJump, Ice, Gravity.
C: For humans, in PAL and NTSC, even with all of the following items (Ball, Bomb, 3 M/SM, SM, 3*PB, 3 Tanks, Charge, SpaceJump, Varia, X-Ray, Grapple, Speedbooster, Ice, HighJump) it is impossible to leave the Springball room back through the vertical entrance-shaft leading into the water (which one has to enter e.g. via R-Jumps in order to activate the map square in which Springball is contained).
Hence due to statement C, the only item remaining that can be added to either i), ii), iii) or iv) in order to potentially end up with another humanly doable option of this category is Gravity. The cases ii) and iv) are given above already and the option iii) is impossible since one would have to obtain Shinespark-Suit at Draygon with a cap of 10 powerbombs since BlueSuit cannot be gotten in this option directly (i.e. without previously obtaining Shinespark-Suit) and since due to lack of X-Ray, the R-Mode Shinespark-Suit method is not an available option.
Therefore the only remaining case that needs to be checked is i) which adds 1*PB, X-Ray and Gravity to (Ball, Bomb, 3 M/SM, SM, PB, 3 Tanks, Charge, SpaceJump, Varia), and [as long as there is no humanly doable way found to generate Shinespark-Suit via Reserve-Mode or via Draygon in this item-setup (with a cap of 10 powerbombs)] this option is not doable aswell.
Demonstration videos for the 16%Gravity-Speed-X-Ray-SpaceJump option:
https://www.youtube.com/watch?v=9wc78qlOwg0]https://www.youtube.com/watch?v=9wc78qlOwg0
https://www.youtube.com/watch?v=2RAoZVEMwZY]https://www.youtube.com/watch?v=2RAoZVEMwZY
Demonstration videos for the 16%Gravity-Speed-Grapple-SpaceJump option:
https://www.youtube.com/watch?v=eGmZIUWWppM]https://www.youtube.com/watch?v=eGmZIUWWppM[/url]
https://www.youtube.com/watch?v=Q0OcOFnbI1E]https://www.youtube.com/watch?v=Q0OcOFnbI1E[/url]
https://www.youtube.com/watch?v=NHG1qBHUN-8]https://www.youtube.com/watch?v=NHG1qBHUN-8[/url]
100%Items-Low%Map analysis, approximation for TAS, without GT-Code, for PAL and NTSC (simultaneously):
This approximation here is outdated:
http://i.imgur.com/ZlGMS7T.png
Currently best approximation, using God-Mode, which improves the previous route by 14 squares:
http://i.imgur.com/MuBAVrE.png
This should be super optimized now, I cannot prove that(/am not sure if) it is an optimal solution though.
There are also two spots in Lower Norfair (the spots with question marks) regarding which I am not sure if
i) an IBJ. (directly) into Ceiling-CF in GT´s room can be executed without entering the lower left map-square in order to get GT´s Missile pack
ii) both lower map-squares in the fireflea room can be skipped simultaneously (and not just one of them by entering the other square).
The blue squares are always necessary and the violet squares need to be entered but do not need to be activated in the map, the pink squares in Terminator room in Crateria will automatically be activated if one enteres the map-squares beneath those and the orange squares are those that I chose in order to construct an approximation for an optimal route.
