[Retros] Schnoebelen promotions / the Pawn case / Singular PGs

[raosorio at fibertel.com.ar]

Hi Joost,

You wrote,

1) "By the way, with SingleBox, Schnoebelen promotions are trivial (and even 
simpler than that)". 


2) "SB doesn't work that way. A pawn stays a pawn until a piece X is 
captured. Only then it's replaced by X. There's no 'looking back' to see 
if the black king would've been in a selfcheck were that pawn piece X". 

commenting the following PG that I presented,

Roberto Osorio - RML february 16th 2006 
rnb2bnk/pppp1p2/1q1p4/8/7p/2N5/PQP1P1PP/R1B1KBNR 
PG in 22 single moves Singular on GOS>> 
---------------------------------------------------------------------------------- 
Solution, 
a) Stipulation: single box type II 
b)sequence: 
1.- d4,h5 2.- d5,h4 3.- d6,exd6 4.- f4,Qf6 5.- f5,Qxb2 6.- f6,Qb6 
7.- f6xg7,ke7 8.- g7xh8,Kf6(h8 can't be bishop or queen) 
9.- Qd4+,Kg6(h8 can't be a knight) 10.- Qb2,Kh7(h8 can't be a rook) 
11.- Nc8,Kxh8 (Schoenebelen pawn). 

I think that the following will clarify both points:

1) I agree that with SingleBox (SB) Schnoebelen promotions are trivial; but this PG is not
just SB but a "Singular PG on GOS". Perhaps I should discussed the concept a bit more, 
since it was lightly presented two years ago. The basic definitions are,

- Geometrically Orthodox Stipulations (GOS): the chess stipulations where the pieces' movements
(from square to square) follows the FIDE rules in terms of its geometry (Orhodox, Madrasi,
Koko, Single Box Type II,Lortap, Patrol, Multicapture, etc), but not necesarily in terms of 
oportunity (related to check situations). Two aspects could be identified in these stipulations 
compared to the orthodox one,

a) Restriction: moves that are not feasible in the involved stipulation (for instance, 
under Madrasi paralysis) but they would be legal in orthodox chess.

b) Potentiation: the opposal to a), i.e., moves that are legal in the stipulation but 
illegal in orthodox chess (this is always related to the King path as a result of the
check power vanishing; for instance, a King moving to be in contact with an other side's queen
wich is paralyzed in Madrasi).

- GOS as an extended space: let's say that when we establish in orthodox chess "PG in
22 single moves", we are referring to the math space that includes all the legal sequences showing
22 single moves, asking to find within this space the "unique" sequence that reaches the position.
To simplify the things, let's close the set and define GOS=(Orhodox, Madrasi, Koko, Single Box Type II, 
Lortap, Patrol, Multicapture), i.e., all these stipulations as part of the same space. Then,  
"PG in 22 single moves Singular on GOS" means that there is just one sequence PERTAINING TO A JUST
ONE OF THESE STIPULATIONS that reaches the position in 22 single moves. Then, the solver has to find
first which is the necesary stipulation and secondly the sequence.

2) After this explanation, it could be appreciated that the above PG HAS NO ORTHODOX SOLUTION (and no
solution in any  GOS stipulation other than SB type II); for this reason, it's "Singular".
The comments in the solution ("h8 can't be bishop or queen", etc) are to explain "why" SB type II is
indispensable to reach the position in 22 single moves.

I see two interesting compositional lines based on "Singular PGs": a) paradoxical tries, as it was
pointed out by Andrey Frolkin in 2006; b) stipulation twins / two solutions, a strong field.
I have no example. It would be nice to see one.

Best,
Roberto