[Retros] (59,23,0)/9.0/# is sound (Re: FW: FW: distance-PG-)

[Noam Elkies]

I wrote:

> Nicolas Dupont <Nicolas.Dupont at univ-lille1.fr> writes:

> > Without ep (nor final checkmate), my best bound is reached via the  
> > following sequence:

> > 1. Pe2-e4   Ph7-h5     2. Dd1xh5   Pa7-a5     3. Dh5xa5   Th8xh2
> > 4. Da5xc7   Th2-h8     5. Th1xh8   Ta8xa2     6. Dc7-h2   Ta2-a8
> > 7. Ta1-a6   Dd8-a5     8. Ta6-h6   Da5-h5     9. Ff1-a6   Dh5-d1

> > (63,23,0) in 9.0 => move-length average a bit over 5.30.

I replies:

> This fine record is also tantalizingly close to checkmate.
> Does it remain sound if the final three moves are changed to

> 7. Ta1-a7   Dd8-a5     8. Ff1-a6   Da5-h5     9. Re1-f1   Dh5-d1#

> ?  This loses 5 units (last three White moves are (7,5,0) instaead of
> (12,5,0) but still comes to (58,23,0) = 90.52691... which makes the
> per-(half-)move average 5.02927...  One might even try to make the
> 7th move Ta1xa8, raising the orthogonal count from 58 to 59 and the
> average to 5.084828..

Update: it's sound (C+ Popeye in about 2 minutes).

::::::::::::::::::::::::::::::::::::::::

Popeye C-Version 3.41 (1024 KB)

  NDE 9/2016, after Nicolas Dupont

+---a---b---c---d---e---f---g---h---+
|                                   |
8   R  -S  -B   .  -K  -B  -S   R   8
|                                   |
7   .  -P   .  -P  -P  -P  -P   .   7
|                                   |
6   B   .   .   .   .   .   .   .   6
|                                   |
5   .   .   .   .   .   .   .   .   5
|                                   |
4   .   .   .   .   P   .   .   .   4
|                                   |
3   .   .   .   .   .   .   .   .   3
|                                   |
2   .   P   P   P   .   P   P   Q   2
|                                   |
1   .   S   B  -Q   .   K   S   .   1
|                                   |
+---a---b---c---d---e---f---g---h---+
  dia9.0                    14 + 11

  1.e2-e4 h7-h5   2.Qd1*h5 a7-a5   3.Qh5*a5 Rh8*h2   4.Qa5*c7 Rh2-h8   5.Rh1*h8 Ra8*a2   6.Qc7-h2 Ra2-a8   7.Ra1*a8 Qd8-a5   8.Bf1-a6 Qa5-h5   9.Ke1-f1 Qh5-d1 dia 

solution finished. Time = 2:07.279 m:s

::::::::::::::::::::::::::::::::::::::::

Popeye reports that The 1-unit-shorter version (7.Ra1-a7 instead of Ra1xa8)
is also sound, though after considerably more calculation (12:51.400 m:s).
So we have the first sound PGs ending in mate with moves of average length
greater than 5.

NDE