Life-like p1 photon project

[Sokwe]

It's enough for me to think there are likely p1 photons here.

There are (in B268/S02568):

Code: Select all

#C [[ TRACK 0 -1 ]]
x = 127, y = 65, rule = B268/S02568
21b2o$25b2o9b2o66b2o$20bo2bobobo4b2o55b2o9b2o$16b2o3bob4obo2bobobo2bo
54b2o4bobobo2bo$15bobobobo2b2o2bobob4obo3b2o45bo2bobobo2bob4obo3b2o$
14bob4o4b2o4bo2b2o2bobobobo40b2o3bob4obobo2b2o2bobobobo$16b3o5b2o7b2o
4b4obo38bobobobo2b2o2bo4b2o4b4obo$16b3o5b2o7b2o5b3o39bob4o4b2o7b2o5b3o
$16b3o5b2o3b2o2b2o5b3o41b3o5b2o7b2o5b3o$16b3o5b2o7b2o2b2ob3o2b2o37b3o
5b2o2b2o3b2o5b3o$16b3o5b2o2bo2bob2obobob3o37b2o2b3ob2o2b2o7b2o5b3o$12b
2o2b3ob2o2b2o3bob3o2bo2b4obo2bo36b3obobob2obo2bo2b2o5b3o$16b3obobob2ob
obo2bo6b2ob3obo32bo2bob4o2bo2b3obo3b2o2b2ob3o2b2o$11bo2bob4o2bo2b3obo
9b2ob2o2bo33bob3ob2o6bo2bobob2obobob3o$12bob3ob2o6bo2bo6b2ob3o6b2o30bo
2b2ob2o9bob3o2bo2b4obo2bo$12bo2b2ob2o9bo5bobo2b2o2bobobobo26b2o6b3ob2o
6bo2bo6b2ob3obo$9b2o6b3ob2o6bo4bob5o2bo2b4obo24bobobobo2b2o2bobo5bo9b
2ob2o2bo$8bobobobo2b2o2bobo5bo6b4o3bo3b3o25bob4o2bo2b5obo4bo6b2ob3o6b
2o$7bob4o2bo2b5obo4bo6b4obobobob3obob2o22b3o3bo3b4o6bo5bobo2b2o2bobobo
bo$9b3o3bo3b4o6bo3b2ob6obob7obobo16b2obob3obobobob4o6bo4bob5o2bo2b4obo
$4b2obob3obobobob4o6bo2bobo2bob2o5b2ob2ob3obo14bobob7obob6ob2o3bo6b4o
3bo3b3o$3bobob7o3b6ob2o3bobob5ob2o2bo2b2ob2o2b2o15bob3ob2ob2o5b2obo2bo
bo2bo6b4obobobob3obob2o$2bob3ob2ob2o5b2obo2bobo2bo3b3o2b3o3bob2o2b4o
18b2o2b2ob2o2bo2b2ob5obobo3b2ob6o3b7obobo$4b2o2b2ob2o5b2ob5obobobob3o
3b2obo3b2o4b2o19b4o2b2obo3b3o2b3o3bo2bobo2bob2o5b2ob2ob3obo$5b4o2b2o5b
3o2b3obobob5obob4obob2obo2b2o2b2o15b2o4b2o3bob2o3b3obobobob5ob2o5b2ob
2o2b2o$6b2o3b2o5b2o3b3o6b2ob3o2b2o2b4o2bob2o15b2o2b2o2bob2obob4obob5ob
obob3o2b3o5b2o2b4o$6b2obob2o2b2ob2obob3obobo2b2ob2o3b2o3b2o3bob2obo2bo
14b2obo2b4o2b2o2b3ob2o6b3o3b2o5b2o3b2o$3b2ob2ob4obobob2ob7o2bob2o2bobo
b2obob2obobo2b3obo10bo2bob2obo3b2o3b2o3b2ob2o2bobob3obob2ob2o2b2obob2o
$2bobob2o2b2o5b3o2b2ob2o3bob7o2b3o2b3o5bo2bo11bob3o2bobob2obob2obobo2b
2obo2b7ob2obobob4ob2ob2o$bob3o4b2o2bo2b2o3b2ob2obobo2bo3bo4bo4bo9bo11b
o2bo5b3o2b3o2b7obo3b2ob2o2b3o5b2o2b2obobo$3b3o2bob2o3bob2obob2o2b3o28b
o11bo9bo4bo4bo3bo2bobob2ob2o3b2o2bo2b2o4b3obo$4bo2bo2b2obobob2ob3o4bo
26b2obob2o8bo28b3o2b2obob2obo3b2obo2b3o$7bo3b3o3b2o2bo31bobobobobo4b2o
bob2o26bo4b3ob2obobob2o2bo2bo$7bo4bo4b2o33bob3ob3obo2bobobobobo31bo2b
2o3b3o3bo$7bo9b2o35b3ob3obobob3ob3obo33b2o4bo4bo$7bo9b2o36bo2b3o3bob3o
b3o35b2o9bo$4b2obob2o6b2o40bo6b3o2bo36b2o9bo$3bobobobobo5b2o48bo40b2o
6b2obob2o$2bob3ob3obo4b2o89b2o5bobobobobo$4b3o2b2o6b2o89b2o4bob3ob3obo
$5bo3b2o6b2o89b2o6b2o2b3o$9b2o6b2o89b2o6b2o3bo$9b2o6b2o89b2o6b2o$9b2o
3b2ob2ob2o86b2o6b2o$9b2o2bobob2obobo82b2ob2ob2o3b2o$9b2obob3o2b3obo80b
obob2obobo2b2o$9b2o3b3o3b2o81bob3o2b3obob2o$9b2obob3obob2obob2o78b2o3b
3o3b2o$9b2ob3ob3o2b3obobo72b2obob2obob3obob2o$9b3ob2ob2o4bob3obo70bobo
b3o2b3ob3ob2o$5b2o2b2o2b3o8b3o71bob3obo4b2ob2ob3o$9b2o3b2o2bo6bo74b3o
8b3o2b2o2b2o$4bo2bob2obob2obo83bo6bo2b2o3b2o$5bob3o2b3o2bo91bob2obob2o
bo2bo$5bo2bo4bo3bo91bo2b3o2b3obo$5bo11bo91bo3bo4bo2bo$5bo11bo91bo11bo$
2b2obob2o8bo91bo11bo$bobobobobo4b2obob2o88bo8b2obob2o$ob3ob3obo2bobobo
bobo84b2obob2o4bobobobobo$2b3ob3obobob3ob3obo82bobobobobo2bob3ob3obo$
3bo2b3o3bob3ob3o83bob3ob3obobob3ob3o$7bo6b3o2bo86b3ob3obo3b3o2bo$15bo
91bo2b3o6bo$111bo!

That ship also works in B26/S02568. This leaves B267/S02568 and B2678/S02568 as the only unsolved rules without B4 or B5.

Edit: I used a basic LLSSS search to shorten the sides a bit:

Code: Select all

x = 125, y = 50, rule = B26/S02568
20b2o81b2o$24b2o9b2o51b2o9b2o$19bo2bobobo4b2o59b2o4bobobo2bo$15b2o3bob
4obo2bobobo2bo49bo2bobobo2bob4obo3b2o$14bobobobo2b2o2bobob4obo3b2o41b
2o3bob4obobo2b2o2bobobobo$13bob4o4b2o4bo2b2o2bobobobo39bobobobo2b2o2bo
4b2o4b4obo$15b3o5b2o7b2o4b4obo37bob4o4b2o7b2o5b3o$15b3o5b2o7b2o5b3o41b
3o5b2o7b2o5b3o$15b3o5b2o3b2o2b2o5b3o41b3o5b2o2b2o3b2o5b3o$15b3o5b2o7b
2o2b2ob3o2b2o33b2o2b3ob2o2b2o7b2o5b3o$15b3o5b2o2bo2bob2obobob3o41b3obo
bob2obo2bo2b2o5b3o$11b2o2b3ob2o2b2o3bob3o2bo2b4obo2bo31bo2bob4o2bo2b3o
bo3b2o2b2ob3o2b2o$15b3obobob2obobo2bo6b2ob3obo33bob3ob2o6bo2bobob2obob
ob3o$10bo2bob4o2bo2b3obo9b2ob2o2bo33bo2b2ob2o9bob3o2bo2b4obo2bo$11bob
3ob2o6bo2bo6b2ob3o6b2o27b2o6b3ob2o6bo2bo6b2ob3obo$11bo2b2ob2o9bo5bobo
2b2o2bobobobo25bobobobo2b2o2bobo5bo9b2ob2o2bo$8b2o6b3ob2o6bo4bob5o2bo
2b4obo23bob4o2bo2b5obo4bo6b2ob3o6b2o$7bobobobo2b2o2bobo5bo6b4o3bo3b3o
27b3o3bo3b4o6bo5bobo2b2o2bobobobo$6bob4o2bo2b5obo4bo6b4obobobob3obob2o
17b2obob3obobobob4o6bo4bob5o2bo2b4obo$8b3o3bo3b4o6bo3b2ob6obob7obobo
15bobob7obob6ob2o3bo6b4o3bo3b3o$3b2obob3obobobob4o6bo2bobo2bob2o5b2ob
2ob3obo13bob3ob2ob2o5b2obo2bobo2bo6b4obobobob3obob2o$2bobob7o3b6ob2o3b
obob5ob2o2bo2b2ob2o2b2o17b2o2b2ob2o2bo2b2ob5obobo3b2ob6o3b7obobo$bob3o
b2ob2o5b2obo2bobo2bo3b3o2b3o3bob2o2b4o19b4o2b2obo3b3o2b3o3bo2bobo2bob
2o5b2ob2ob3obo$3b2o2b2ob2o5b2ob5obobobob3o3b2obo3b2o4b2o19b2o4b2o3bob
2o3b3obobobob5ob2o5b2ob2o2b2o$4b4o2b2o5b3o2b3obobob5obob4obob2obo2b2o
2b2o11b2o2b2o2bob2obob4obob5obobob3o2b3o5b2o2b4o$5b2o3b2o5b2o3b3o6b2ob
3o2b2o2b4o2bob2o19b2obo2b4o2b2o2b3ob2o6b3o3b2o5b2o3b2o$5b2obob2o2b2ob
2obob3obobo2b2ob2o3b2o3b2o3bob2obo2bo9bo2bob2obo3b2o3b2o3b2ob2o2bobob
3obob2ob2o2b2obob2o$2b2ob2ob4obobob2ob3ob3o2bob2o2bobob2obob2obobo2b3o
bo11bob3o2bobob2obob2obobo2b2obo2b3ob3ob2obobob4ob2ob2o$bobob2o2b2o5b
3o2b2ob2o3bob7o2b3o2b3o5bo2bo11bo2bo5b3o2b3o2b7obo3b2ob2o2b3o5b2o2b2ob
obo$ob3o4b2o2bo2b2o3b2o2bobobo2bo3bo4bo4bo9bo11bo9bo4bo4bo3bo2bobobo2b
2o3b2o2bo2b2o4b3obo$2b3o2bob2o3bob2obob7obo26bo11bo26bob7obob2obo3b2ob
o2b3o$3bo2bo2b2obobo2b3ob2o3bo2bo23b2obob2o8bo26bo2bo3b2ob3o2bobob2o2b
o2bo$6bo3b3o5bo2b2o6bo22bobobobobo4b2obob2o23bo6b2o2bo5b3o3bo$6bo4bo9b
2o6bo21bob3ob3obo2bobobobobo22bo6b2o9bo4bo$6bo14b2o3b2obob2o20b3ob3obo
bob3ob3obo18b2obob2o3b2o14bo$6bo14b2o2bobobobobo20bo2b3o3bob3ob3o19bob
obobobo2b2o14bo$6bo14b2obob3ob3obo23bo6b3o2bo19bob3ob3obob2o14bo$6bo
11b2ob2obob3o2b2o33bo25b2o2b3obob2ob2o11bo$6bo10bobo2b2ob2ob4o61b4ob2o
b2o2bobo10bo$6bo9bob9ob2o65b2ob9obo9bo$6bo11b2o7b3o2bo59bo2b3o7b2o11bo
$6bo11b2o8bo2bo61bo2bo8b2o11bo$3b2obob2o8b2o11bo61bo11b2o8b2obob2o$2bo
bobobobo4b2ob2ob2o8bo61bo8b2ob2ob2o4bobobobobo$bob3ob3obo2bobob2obobo
4b2obob2o55b2obob2o4bobob2obobo2bob3ob3obo$3b3ob3obobob3o2b3obo2bobobo
bobo53bobobobobo2bob3o2b3obobob3ob3o$4bo2b3o3bob3o3b2obobob3ob3obo51bo
b3ob3obobob2o3b3obo3b3o2bo$8bo6b3obob2o3bob3ob3o55b3ob3obo3b2obob3o6bo
$16bo2b3o6b3o2bo57bo2b3o6b3o2bo$20bo8bo65bo8bo!

[amling]

Using proj002 in B268/S0256 with raw:1:0:0:1:0:1:0:1:0, AF2=6, and W-height 3 I got the following self-forcing edge set of 45 blocks:

Code: Select all

| LLLLL!LLLLLL!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!RRRRRR |
| .....!WWWWWW!WWWWW...........!WWWWW...........!WWWWW...*.......!WWWWW...........!WWWWW....*......!WWWWW..**.*.....!WWWWW...........!WWWWW..**.*.....!WWWWW.*.........!WWWWW.*.........!WWWWW...........!WWWWW..*........!WWWWW..**.*.....!WWWWW...........!WWWWW...*.......!WWWWW....*......!WWWWW..**.*.....!WWWWW...*.......!WWWWW...........!WWWWW...*.......!WWWWW.*.........!WWWWW.*.........!WWWWW...........!WWWWW...........!WWWWW....*......!WWWWW..**.*.....!WWWWW.*.........!WWWWW*..........!WWWWW*...*......!WWWWW*...*......!WWWWW*..........!WWWWW****.......!WWWWW*..........!WWWWW*..*.......!WWWWW*...*......!WWWWW*..........!WWWWW*..........!WWWWW*..........!WWWWW*..........!WWWWW*...*......!WWWWW****.......!WWWWW****.*.....!WWWWW*...*......!WWWWW**.*.......!WWWWW****.*.....!...... |
| .....!WWWWWW!WWWWW...........!WWWWW....*......!WWWWW....*......!WWWWW....*......!WWWWW..**.*.....!WWWWW.*****.....!WWWWW.*.........!WWWWW.*****.....!WWWWW....*......!WWWWW.*.........!WWWWW...........!WWWWW..*........!WWWWW..****.....!WWWWW...*.......!WWWWW....*......!WWWWW..**.*.....!WWWWW.*****.....!WWWWW*...*......!WWWWW*..........!WWWWW***..*.....!WWWWW**.........!WWWWW**..*......!WWWWW*..........!WWWWW*...*......!WWWWW****.*.....!WWWWW******.....!WWWWW*.*........!WWWWW....*......!WWWWW..**.*.....!WWWWW..**.*.....!WWWWW.**.*......!WWWWW.*.........!WWWWW....*......!WWWWW....*......!WWWWW..**.*.....!WWWWW.*.........!WWWWW.**.*......!WWWWW*..........!WWWWW*...*......!WWWWW****.*.....!WWWWW**.........!WWWWW******.....!WWWWW****.*.....!WWWWW*...*......!WWWWW******.....!...... |
| .....!WWWWWW!WWWWW.....*.....!WWWWW.....*.....!WWWWW..**.*.....!WWWWW.*...*.....!WWWWW.*****.....!WWWWW..**.......!WWWWW.*...*.....!WWWWW.*.*.......!WWWWW.....*.....!WWWWW.....*.....!WWWWW*....*.....!WWWWW*....*.....!WWWWW*..*.......!WWWWW***..*.....!WWWWW****.*.....!WWWWW******.....!WWWWW**.*.......!WWWWW..**.*.....!WWWWW.*...*.....!WWWWW.....*.....!WWWWW.....*.....!WWWWW.....*.....!WWWWW*....*.....!WWWWW*....*.....!WWWWW******.....!WWWWW**.*.......!WWWWW***..*.....!WWWWW.....*.....!WWWWW..****.....!WWWWW.*****.....!WWWWW.*...*.....!WWWWW..**.*.....!WWWWW**...*.....!WWWWW****.*.....!WWWWW******.....!WWWWW**...*.....!WWWWW**...*.....!WWWWW.....*.....!WWWWW.....*.....!WWWWW.*****.....!WWWWW..**.*.....!WWWWW...*.......!WWWWW******.....!WWWWW****.*.....!WWWWW*..*.......!...... |

Using the same settings for B2678/S0256, I got the following self-forcing edge set of 43 blocks:

Code: Select all

| LLLLL!LLLLLL!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!LLLLLuuuuuuRRRRR!RRRRRR |
| .....!WWWWWW!WWWWW...........!WWWWW...........!WWWWW...*.......!WWWWW...........!WWWWW....*......!WWWWW..**.*.....!WWWWW...........!WWWWW..**.*.....!WWWWW.*.........!WWWWW.*.........!WWWWW...........!WWWWW..*........!WWWWW..**.*.....!WWWWW...........!WWWWW...*.......!WWWWW....*......!WWWWW..**.*.....!WWWWW...*.......!WWWWW...........!WWWWW...*.......!WWWWW.*.........!WWWWW...........!WWWWW...........!WWWWW....*......!WWWWW..**.*.....!WWWWW.*.........!WWWWW*..........!WWWWW*...*......!WWWWW*...*......!WWWWW*..........!WWWWW****.......!WWWWW*..*.......!WWWWW*...*......!WWWWW*..........!WWWWW*..........!WWWWW*..........!WWWWW*..........!WWWWW*...*......!WWWWW****.......!WWWWW****.*.....!WWWWW*...*......!WWWWW**.*.......!WWWWW****.*.....!...... |
| .....!WWWWWW!WWWWW...........!WWWWW....*......!WWWWW....*......!WWWWW....*......!WWWWW..**.*.....!WWWWW.*****.....!WWWWW.*.........!WWWWW.*****.....!WWWWW....*......!WWWWW.*.........!WWWWW...........!WWWWW..*........!WWWWW..****.....!WWWWW...*.......!WWWWW....*......!WWWWW..**.*.....!WWWWW.*****.....!WWWWW*...*......!WWWWW*..........!WWWWW***..*.....!WWWWW**..*......!WWWWW*..........!WWWWW*...*......!WWWWW****.*.....!WWWWW******.....!WWWWW*.*........!WWWWW....*......!WWWWW..**.*.....!WWWWW..**.*.....!WWWWW.**.*......!WWWWW.*.........!WWWWW....*......!WWWWW..**.*.....!WWWWW.*.........!WWWWW.**.*......!WWWWW*..........!WWWWW*...*......!WWWWW****.*.....!WWWWW**.........!WWWWW******.....!WWWWW****.*.....!WWWWW*...*......!WWWWW******.....!...... |
| .....!WWWWWW!WWWWW.....*.....!WWWWW.....*.....!WWWWW..**.*.....!WWWWW.*...*.....!WWWWW.*****.....!WWWWW..**.......!WWWWW.*...*.....!WWWWW.*.*.......!WWWWW.....*.....!WWWWW.....*.....!WWWWW*....*.....!WWWWW*....*.....!WWWWW*..*.......!WWWWW***..*.....!WWWWW****.*.....!WWWWW******.....!WWWWW**.*.......!WWWWW..**.*.....!WWWWW.*...*.....!WWWWW.....*.....!WWWWW.....*.....!WWWWW*....*.....!WWWWW*....*.....!WWWWW******.....!WWWWW**.*.......!WWWWW***..*.....!WWWWW.....*.....!WWWWW..****.....!WWWWW.*****.....!WWWWW.*...*.....!WWWWW..**.*.....!WWWWW****.*.....!WWWWW******.....!WWWWW**...*.....!WWWWW**...*.....!WWWWW.....*.....!WWWWW.....*.....!WWWWW.*****.....!WWWWW..**.*.....!WWWWW...*.......!WWWWW******.....!WWWWW****.*.....!WWWWW*..*.......!...... |

You may want to check my work here, as I would hate to make a claim after incorrectly applying your method.

For rules B267/S02568 and B2678/S02568 the situation seems less clear to me. My rudimentary c1-s2s tests were unable to find a front edge whose slope reversed at some point, which seemed to be the main cause of the difficulty in B26(8)/S02568. However, my limited memory may be at fault there. I don't know how much trouble it is, but could you try B267/S02568? I don't particularly think it will work, but it might give insight into whether these rules have p1 photons.

For B268/S0256 I perhaps waited longer, as I got a smaller set of 42 blocks. I decided the initial search had probably stabilized at depth 10 and 39 blocks. Restarted with those 39 blocks, it updated to 42 blocks as it completed w_pos 11. Restarted with those 42 blocks, it updated to those same 42 blocks as it completed w_pos 11.

I have verified your 45 are a superset of the 42 and verified they they are also self-forcing so it's still quite likely you've using the tools correctly.

For B2678/S0256 similarly I bet I just waited longer. Ditto initial search depth 10, 39 blocks. Ditto 39 blocks -> 42 blocks at w_pos 11. Ditto 42 blocks -> 42 blocks at w_pos 11. Ditto verified your 43 are a superset of the 42 and ditto verified they are self-forcing.

What parameters were you hoping for for B267/S02568? I've started the same front edge s2s with 3x6 blocks under the assumption/hope it's most likely to be similar to these others, but haven't personally looked at the rule. EDIT: I will leave it running, but this seems hopeless, right? The photon from B26(8)/S02568 has very few B7s and they're all sort of in the middle.

[Sokwe]

Thanks for independently verifying those results. The reason I stopped where I did was that I was reaching my memory limit, and rather than have it run slowly with swap memory, I figured the sets would probably be small enough as they were.

What parameters were you hoping for for B267/S02568? I've started the same front edge s2s with 3x6 blocks under the assumption/hope it's most likely to be similar to these others, but haven't personally looked at the rule. EDIT: I will leave it running, but this seems hopeless, right? The photon from B26(8)/S02568 has very few B7s and they're all sort of in the middle.

It's probably hopeless, as you said. 3x6 seems fine. I was just hoping to get some more insight on those rules. You don't need to bother with the searches I suggest if you think there are better uses of your time and resources.

Edit: actually, if the proj002 B267/S02568 were to work, I would think it would need 4x6 or 5x6 blocks. This is all well beyond my laptop's ability.

Edit 2: with 3x6 you will get these two edges, which are the same, except being flipped over a horizontal axis:

Code: Select all

...*..
.**..*
.....*

.....*
.**..*
...*..

Here are example partial results for these edges:

Code: Select all

x = 181, y = 49, rule = B267/S02568History
3.A115.A$4.A115.A$2.2A.A9.A102.2A.A$.5A10.A6.A93.5A8.A$2.2A7.A2.2A.A
6.A8.A84.2A7.A3.A$4.7A2.5A4.2A.A8.A5.A79.7A2.2A.A$.3A9.A.A5.5A6.2A.A
5.A75.3A9.4A$6A5.3A.A.4A.2A7.5A3.2A.A73.6A4.2A2.A$.3A.A4.14A.7A.A4.5A
5.A68.3A.A3.2A4.2A.A$4.A4.2A3.3A2.A.A.9A.A.3A.2A8.A70.A5.6A3.A$2.2A6.
2A4.2A3.A.A.16A.7A.A67.2A7.8A.A$13.2A6.3A4.A3.3A3.A.11A2.A77.6A4.A$3.
2A6.3A3.4A.4A3.2A3.2A.A2.A.7A5.A64.10A5.A7.A$5.A4.14A.A3.A3.A6.A7.A.
4A.A73.A.A2.A.6A.A$2.3A.A2.2A2.5A2.2A2.A4.14A5.8A62.2A5.2A5.A.10A$.6A
3.2A5.2A3.2A5.12A.A2.A2.A.4A66.A3.2A2.7A.6A$2.3A9.A6.A6.A12.A4.A.A4.
2A62.3A.A3.7A.2A6.2A$5.9A2.15A8.2A5.5A2.3DC2D57.6A4.2A4.5A2.5DC$3.2A
11.13A.A13.A2.2A.A2.D2C2DC58.3A8.2A3.2A.A2.D2C2DC$2.5A7.2A13.A10.4A5.
A3.5DC61.6A3.A5.A3.3DC2D$3.2A.A6.5A10.A19.A6.2A10.A50.2A6.A.A5.A4.2A
6.A$5.A8.2A.A23.2A11.2A12.A48.5A16.2A8.A$4.A11.A26.A11.13A.A48.2A.A6.
2A9.9A.A$15.A24.3A.A11.14A2.A47.A9.A9.10A$39.6A22.A5.A45.A7.3A.A15.A$
40.3A14.A.A7.A.4A.A51.6A9.A6.2A.A$43.14A3.A3.A2.8A2.A49.3A8.A3.A5.A3.
A$41.2A16.2A4.A.A.4A5.A51.8A2.2A.A4.4A.A$40.5A4.2A6.2A6.3A4.6A.A48.2A
10.4A3.A.5A2.A$41.2A.A6.A4.9A.4A3.7A47.5A5.2A2.A4.6A5.A$43.A4.3A.A2.
2A2.9A.A7.A50.2A.A4.2A3.A.4A.A.A.5A.A$42.A4.6A3.2A5.A.A2.A3.2A4.2A.A
48.A6.10A.A.A.7A2.A$48.3A9.A2.A2.2A6.A3.A3.A46.A8.4A.4A.4A4.A5.A$51.
9A2.4A7.2A3.4A.A58.6A.5A3.5A.A$49.2A11.11A4.A.5A55.2A2.A3.5A.A3.7A4.A
$48.5A7.2A4.16A56.2A4.2A2.2A2.A4.A3.A7.A$49.2A.A6.5A8.5A.A.A.2A.A53.
6A5.2A5.2A2.A.6A.A$51.A8.2A.A3.2A7.A.A.A.A3.A53.10A6.A3.11A3.A$50.A
11.A6.A3.A2.A.3A.4A.A57.16A.A5.A6.A$61.A4.3A.A3.A.2A.3A.5A53.2A7.11A.
A.2A2.A.5A.A$65.6A3.3A.3A.4A57.A.A14.5A2.10A$64.2A2.A4.A.2A.A.A.A.A.
2A.A50.2A4.A2.2A10.A.5A.A4.A$65.2A2.8A.A.A.A.A.A3.A48.2A4.2A4.A10.3A.
2A2.2A3.2A.A$69.5A2.5A.3A.4A.A48.5A5.A.A9.A2.6A2.3A3.A$64.5A4.2A2.A.
3A.3A.5A49.12A9.2A.A.12A.A$63.8A6.A3.4A.4A54.7A11.4A4.3A3.5A$64.5A.A
3.6A2.A.A.A2.2A49.2A8.2A10.A.4A4.2A4.A$69.A3.6A5.A.2A4.A$65.A2.A5.A3.
5A.2A4.A.A!

At 4x6 these partial results at least would not give the same (up to reflection) edges.

Edit 3: am I right to think that this is doomed even at 5x7? Consider the partial results below:

Code: Select all

x = 185, y = 59, rule = B267/S02568History
144.2A8.2A10.A.4A4.2A4.A$148.7A11.4A4.3A3.5A$145.12A9.2A.A.12A.A$144.
5A5.A.A9.A2.6A2.3A3.A$143.2A4.2A4.A10.3A.2A2.2A3.2A.A$144.2A4.A2.2A
10.A.5A.A4.A$147.A.A14.5A2.10A$145.2A7.11A.A.2A2.A.5A.A$149.16A.A5.A
6.A$144.10A6.A3.11A3.A$3.A139.6A5.2A5.2A2.A.6A.A$4.A137.2A4.2A2.2A2.A
4.A3.A7.A$2.2A.A9.A127.2A2.A3.5A.A3.7A4.A$.5A10.A6.A122.6A.5A3.5A.A$
2.2A7.A2.2A.A6.A8.A99.A8.4A.4A.4A4.A5.A$4.7A2.5A4.2A.A8.A5.A93.A6.10A
.A.A.7A2.A$.3A9.A.A5.5A6.2A.A5.A90.2A.A4.2A3.A.4A.A.A.5A.A$6A5.3A.A.
4A.2A7.5A3.2A.A88.5A5.2A2.A4.6A5.A$.3A.A4.14A.7A.A4.5A5.A83.2A10.4A3.
A.5A2.A$4.A4.2A3.3A2.A.A.9A.A.3A.2A8.A84.8A2.2A.A4.4A.A$2.2A6.2A4.2A
3.A.A.16A.7A.A80.3A8.A3.A5.A3.A$13.2A6.3A4.A3.3A3.A.11A2.A76.6A9.A6.
2A.A$3.2A6.3A3.4A.4A3.2A3.2A.A2.A.7A5.A68.A7.3A.A15.A$5.A4.14A.A3.A3.
A6.A7.A.4A.A68.A9.A9.10A$2.3A.A2.2A2.5A2.2A2.A4.14A5.8A66.2A.A6.2A9.
9A.A$.6A3.2A5.2A3.2A5.12A.A2.A2.A.2A2C5D62.5A16.2C5D3.A$2.3A9.A6.A6.A
12.A4.A.A3.D2C4D63.2A6.A.A5.A3.D2C4D2.A$5.9A2.15A8.2A5.5A.4DC2D65.6A
3.A5.A2.4DC2D$3.2A11.13A.A13.A2.2A.A.2D2C2DC62.3A8.2A3.2A.A.2D2C2DC$
2.5A7.2A13.A10.4A5.A2.6DC61.6A4.2A4.5A.6DC$3.2A.A6.5A10.A19.A6.2A10.A
53.3A.A3.7A.2A6.2A$5.A8.2A.A23.2A11.2A12.A55.A3.2A2.7A.6A$4.A11.A26.A
11.13A.A52.2A5.2A5.A.10A$15.A24.3A.A11.14A2.A60.A.A2.A.6A.A$39.6A22.A
5.A49.10A5.A7.A$40.3A14.A.A7.A.4A.A60.6A4.A$43.14A3.A3.A2.8A2.A44.2A
7.8A.A$41.2A16.2A4.A.A.4A5.A45.A5.6A3.A$40.5A4.2A6.2A6.3A4.6A.A41.3A.
A3.2A4.2A.A$41.2A.A6.A4.9A.4A3.7A40.6A4.2A2.A$43.A4.3A.A2.2A2.9A.A7.A
43.3A9.4A$42.A4.6A3.2A5.A.A2.A3.2A4.2A.A42.7A2.2A.A$48.3A9.A2.A2.2A6.
A3.A3.A39.2A7.A3.A$51.9A2.4A7.2A3.4A.A37.5A8.A$49.2A11.11A4.A.5A38.2A
.A$48.5A7.2A4.16A42.A$49.2A.A6.5A8.5A.A.A.2A.A37.A$51.A8.2A.A3.2A7.A.
A.A.A3.A$50.A11.A6.A3.A2.A.3A.4A.A$61.A4.3A.A3.A.2A.3A.5A$65.6A3.3A.
3A.4A$64.2A2.A4.A.2A.A.A.A.A.2A.A$65.2A2.8A.A.A.A.A.A3.A$69.5A2.5A.3A
.4A.A$64.5A4.2A2.A.3A.3A.5A$63.8A6.A3.4A.4A$64.5A.A3.6A2.A.A.A2.2A$
69.A3.6A5.A.2A4.A$65.A2.A5.A3.5A.2A4.A.A!

On the left, I have a 5x7 edge highlighted. On the right I have flipped the partial result, and the same "edge" is highlighted. In this case it's not an edge, but I don't think the secondary steps in proj002 will be able to notice that. That is, I imagine the secondary step would find the following zero end:

Code: Select all

x = 29, y = 22, rule = B267/S02568History
.5A16.2C5D$2.2A6.A.A5.A3.D2C4D$4.6A3.A5.A2.4DC2D$.3A8.2A3.2A.A.2D2C2D
C$6A4.2A4.5A.6DC$.3A.A3.7A.2A6.2A$4.A3.2A2.7A.6A$2.2A5.2A5.A.10A$13.A
.A2.A.6A.A$3.10A5.A7.A$15.6A4.A$2.2A7.8A.A$4.A5.6A3.A$.3A.A3.2A4.2A.A
$6A4.2A2.A$.3A9.4A$4.7A2.2A.A$2.2A7.A3.A$.5A8.A$2.2A.A$4.A$3.A!

At 5x8 or 6x7 (edit: or 6x6 or 6x5 or 6x4 or 6x3?) these will differ, but I'm not sure if the search is feasible with such high values. Certainly not with my laptop.

[amling]

I have made a terrible mistake in implementing the forbidden block filter. For geometries with tiles bigger than one bit it can remove valid partials (it matches the pattern it has against the trailing bits of a partial even if they're not at a tile boundary). The bottom line is that I must withdraw my proof of B2478/S134568 and return it (and possibly the no-B8/S8 versions of it) to the todo list.

EDIT: And I've pushed the fixed version to codeberg just now as 1f6c731f8b1b. If you're filtering forbidden blocks in more interesting geometries make sure to update.

Digging through my post history with the word "forbid" I believe the only places where I have used such a thing are:

(*) B2467/S134568

Completes when redone, although with a somewhat longer partial:

Code: Select all

| .......................................................................................................................................... |
| .......................................................................................................................................... |
| .....................................................**........**........**........**..................................................... |
| ....................................................*..*......*..*......*..*......*..*.................................................... |
| ...................................................*....*....*....*....*....*....*....*................................................... |
| ....................................................****......****......****......****.................................................... |
| ..................................................*......*..*......*..*......*..*......*.................................................. |
| ......................**........**..................****......****......****......****..................**........**...................... |
| .....................*..*......*..*.............****....******....******....******....****.............*..*......*..*..................... |
| ....................*....*....*....*...........*..........................................*...........*....*....*....*.................... |
| .....................****......****...........*.....*..*......*..*......*..*......*..*.....*...........****......****..................... |
| ...................*......*..*......*........*..*........................................*..*........*......*..*......*................... |
| .....................****......****........****............................................****........****......****..................... |
| .................****....******....****.....***............................................***.....****....******....****................. |
| ................*......................*..*.***............................................***.*..*......................*................ |
| ...............*.....*..*......*..*.....*.*.***............................................***.*.*.....*..*......*..*.....*............... |
| ..............*..*....................*..*..***............................................***..*..*....................*..*.............. |
| ............****........................***.***..**....................................**..***.***........................****............ |
| .............***........................***.*.*...***...**......................**...***...*.*.***........................***............. |
| ...........*.*.*...**...................***.....*.***.***........................***.***.*.....***...................**...*.*.*........... |
| .................***...............**...*.*.*...*.*.*.***.*....................*.***.*.*.*...*.*.*...**...............***................. |
| .............*...***.*..............***........**.....***.*.**..............**.*.***.....**........***..............*.***...*............. |
| ............*.*..***.*.**.........*.***...*.........*.*.*..*..*............*..*..*.*.*.........*...***.*.........**.*.***..*.*............ |
| .............*...***..*..*.....**.*.***......***...........*.*..............*.*...........***......***.*.**.....*..*..***...*............. |
| ........**...*...*.*.**.*.....*..*..*.*.......*....*.***.*..*..*..........*..*..*.***.*....*.......*.*..*..*.....*.**.*.*...*...**........ |
| .........***..**.........***...*.*......**..*.****.*..*..*..*..*.**....**.*..*..*..*..*.****.*..**......*.*...***.........**..***......... |
| .......*.***..*..*...**..***.*..*..*.***..*.*.***...*.*.*..***..*..*..*..*..***..*.*.*...***.*.*..***.*..*..*.***..**...*..*..***.*....... |
| ....**.*.****....*.***...*.*.*..**...***.*...****.**...*..****..*.*....*.*..****..*...**.****...*.***...**..*.*.*...***.*....****.*.**.... |
| .....*****.**....*****.*.....**....*.*.*.**..**.*.***..*..**.*..***....***..*.**..*..***.*.**..**.*.*.*....**.....*.*****....**.*****..... |
| . . . * * . * . . * . . . . . . . . . . . . . * . * . . . * . . . . . . * . . * . . . * . . * . . . . . . . . . . . * * . . . * * * * . .  |

(*) B2478/S134568 and B248/S13456

B2478/S134568 does not seem to complete, producing some more-interesting looking partials like:

Code: Select all

| ................................................................................................................................................ |
| ................................................................................................................................................ |
| .......................................................................**....................................................................... |
| ............................................................**........*..*........**............................................................ |
| .................................................**........*..*......*....*......*..*........**................................................. |
| ......................................**........*..*......*....*...***....***...*....*......*..*........**...................................... |
| ...........................**........*..*......*....*...***....***.***....***.***....***...*....*......*..*........**........................... |
| ..........................*..*......*....*...***....***.***....***.*.*....***.***....***.***....***...*....*......*..*.......................... |
| .........................*....*...***....***.***....***.*.*....*.*...**...***.***....***.***....***.***....***...*....*......................... |
| ..................**...***....***.***....***.*.*....*.*...**..**..........***.***....***.*.*....***.***....***.***....***...**.................. |
| ...................***.***....***.***....*.*...**..**...............*..*..***.***....*.*...**...***.***....***.***....***.***................... |
| .................*.***.***....***.***...**.................****...........***.***....*..........***.***....***.***....***.***.*................. |
| ..............**.*.***.***....***.***...........****......*....*..........***.***..**.....*..*..***.***....***.***....***.***.*.**.............. |
| .............*..*..*.*.***....***.***..*..*......*****...*......*.........***.*.*...*...........***.***....***.***....***.*.*..*..*............. |
| ..............*.*....*.***....***.*.*..........*.*.***.***......***...**..***.....*.*...........***.***....*.*.***....***.*....*.*.............. |
| ............*..*..*.*..***....*.*...*..............***.***......***.***...*.*.*...*.**..........***.***....*...*.*....***..*.*..*..*............ |
| ..............***...**.*.*....*......**..........*.*.*.***......*.*.***.*........**.........**..*.*.***..**......*....*.*.**...***.............. |
| ..............***........*..**.......*.................*.*.....**...*.*.*...*........***...*..*.....*.*...*.......**..*........***.............. |
| .........**...***....**.*..*...*..**...............*.....*..............**........******.***.*..*.....*.....**..*...*..*.**....***...**......... |
| ........*..*..*.*...*..***..*..*.*..****..................**....***.*..............***.*.***.**....*.*..****..*.*..*..***..*...*.*..*..*........ |
| .......*....*...*....*.***..***...*.***...................*......*..*.***........*.*.*...*.*....*.*.***..***.*...***..***.*....*...*....*....... |
| ......*..*.**....**.**.*.*..***..**.*.*.*.................*.*..*.*.*...*......................**.**.****.*.*.**..***..*.*.**.**....**.*..*...... |
| .......**.***....*..****...**.*.....*....................**.*.*.*...**.*.*.........*....*.******.****.**.***.....*.*..*...***...*..***.**....... |
| .. .. .. .* *. .. .. ** .. ** .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ** .* ** ** ** .. .. .. .. .. ** .. .. ** .. .. ..  |

B248/S13456 completes the same:

Code: Select all

|                             .. |
|                           .... |
|                         ...... |
|                       ........ |
|                     .......... |
|                   ............ |
|                 .............. |
|               ................ |
|             .................. |
|           .................... |
|         ...................... |
|       ............**.......... |
|     .......**...***........... |
|   ..........***.***.*......... |
| ..........*.***.*.*.*.**...... |
| .......**.*.*.*...*..*..*...   |
| ......*..*..*......*.....*     |
| .......*.*...*.*...**.*.       |
| .....*..*..*..****....         |
| .......***...****..*           |
| .......***...**.*.             |
| .......*.*..***.               |
| .......*.**.**                 |
| ......**....                   |
| ..........                     |
| .......*                       |
| ......                         |
| ....                           |
| ..                             |

(*) B24678/S134568

Completes the same:

Code: Select all

| .                              |
| ..                             |
| ...                            |
| ....                           |
| .....                          |
| ......                         |
| .......                        |
| ........                       |
| .........                      |
| ..........                     |
| ...........                    |
| ............                   |
| .............                  |
| ..............                 |
| ...............                |
| ................               |
| .................              |
| ..................             |
| .............**....            |
| ............*..*....           |
| ...........*....*....          |
| ............****......         |
| ..........*......*.....        |
| ............****........       |
| ........****....****.....      |
| .......*............*.....     |
|   ....*.....*..*.....*.....    |
|   ...*..*..........*..*.....   |
|     ..**.*...........****....  |
|     *.....*....**....***...... |
|       .**..*..*..*...*.*.*.... |
|       *..**....*.***.......... |
|         ....*.**.***...*...... |
|         **..*....*.*..*.*..... |
|           ..***......*...*.... |
|           ..***.*.***..**..... |
|             *.*.*..**..**..... |
|             ***..*.**..**..... |
|               *.**.**..**..... |
|               .....**..**..... |
|                 **.**..**..... |
|                 **.**..**..... |
|                   .**..**..... |
|                   .**..**..... |
|                     *..**..... |
|                     *..**..... |
|                       .**..... |
|                       .**..... |
|                         *..... |
|                         *..... |
|                           .... |
|                           .... |
|                             .. |
|                             .. |

[Sokwe]

I have made a terrible mistake in implementing the forbidden block filter. For geometries with tiles bigger than one bit it can remove valid partials (it matches the pattern it has against the trailing bits of a partial even if they're not at a tile boundary). The bottom line is that I must withdraw my proof of B2478/S134568 and return it (and possibly the no-B8/S8 versions of it) to the todo list.

EDIT: And I've pushed the fixed version to codeberg just now as 1f6c731f8b1b. If you're filtering forbidden blocks in more interesting geometries make sure to update.

Digging through my post history with the word "forbid" I believe the only places where I have used such a thing are:

According to my notes, the rules B2568/S1348 and B2568/S13478 relied on forbidden blocks as well. Do those need to be rechecked?

[amling]

I have made a terrible mistake in implementing the forbidden block filter. For geometries with tiles bigger than one bit it can remove valid partials (it matches the pattern it has against the trailing bits of a partial even if they're not at a tile boundary). The bottom line is that I must withdraw my proof of B2478/S134568 and return it (and possibly the no-B8/S8 versions of it) to the todo list.

EDIT: And I've pushed the fixed version to codeberg just now as 1f6c731f8b1b. If you're filtering forbidden blocks in more interesting geometries make sure to update.

Digging through my post history with the word "forbid" I believe the only places where I have used such a thing are:

According to my notes, the rules B2568/S1348 and B2568/S13478 relied on forbidden blocks as well. Do those need to be rechecked?

I believe(d) those were done with large AF2 instead of U a non-1 multiple of X which means the bug does not affect them. I have now explicitly dug up my notes for both B2568/S1348 and B2568/S13478 and they are reasonably detailed. Both include commands and are all geometry "c1-f2b" meaning they were single-bit tiles.

[Sokwe]

(*) B2478/S134568

B2478/S134568 does not seem to complete, producing some more-interesting looking partials like...

I downloaded the latest version (I compiled with AF2=5 for some reason), and I tried this rule using raw:2:-1:0:0:-1:1:0:0:1 with the following forbidden blocks:

Code: Select all

|   WW |
| .**. |
| .**. |
| WW   |

|     WW |
|   WWWW |
| W.**.W |
| W.**.W |
| WWWW   |
| WW     |

|     WW |
|   WWWW |
| .****. |
| .****. |
| WWWW   |
| WW     |

|       WW |
|     WWWW |
|   WWWWWW |
| W.****.W |
| W.****.W |
| WWWWWW   |
| WWWW     |
| WW       |

My command line input looked like this:

Code: Select all

./rlife llsss-recentering-wao raw:2:-1:0:0:-1:1:0:0:1 --rule 'B2478/S134568' '@zero' --wao-left-pad 00 --wao-right-pad 00 --wao-idx ALL --filters forbid_block:f1a.block,forbid_block:f1b.block,forbid_block:f2a.block,forbid_block:f2b.block XX

This completed without finding anything. I would assume this means there are no p1 photons in this rule (and thus all of B247(8)/S13456(8)), but I would appreciate independent confirmation.

Edit:

If the proj002 B267/S02568 were to work, I would think it would need... 5x8 or 6x7 blocks

Actually, I think 6x7 and 7x6 also wouldn't work, due to partials like this:

Code: Select all

x = 159, y = 119, rule = B267/S02568History
3.A$4.A$2.2A.A9.A$.5A10.A6.A$2.2A7.A2.2A.A6.A8.A$4.7A2.5A4.2A.A8.A5.A
$.3A9.A.A5.5A6.2A.A5.A$6A5.3A.A.4A.2A7.5A3.2A.A$.3A.A4.14A.7A.A4.5A5.
A$4.A4.2A3.3A2.A.A.9A.A.3A.2A8.A$2.2A6.2A4.2A3.A.A.16A.7A.A$13.2A6.3A
4.A3.3A3.A.11A2.A$3.2A6.3A3.4A.4A3.2A3.2A.A2.A.7A5.A$5.A4.14A.A3.A3.A
6.A7.A.4A.A$2.3A.A2.2A2.5A2.2A2.A4.14A5.4A4C3D55.A33.3A.4C3D$.6A3.2A
5.2A3.2A5.12A.A2.A2.A.2A2C5D47.A8.A14.A15.2A4.2C5D$2.3A9.A6.A6.A12.A
4.A.A3.D2C4D48.A5.2A.A6.A7.A6.A6.5A2.D2C4D$5.9A2.15A8.2A5.5A.4DC2D46.
2A.A3.5A7.A4.2A.A6.A6.2A.A2.4DC2D$3.2A11.13A.A13.A2.2A.A.2D2C2DC45.5A
4.2A7.2A.A2.5A4.2A.A7.A3.2D2C2DC$2.5A7.2A13.A10.4A5.A2.6DC46.2A8.11A
3.2A5.5A6.A4.6DC$3.2A.A6.5A10.A19.A6.2A10.A39.6A2.7A.A7.5A.2A16.2A$5.
A8.2A.A23.2A11.2A12.A35.3A6.A2.A4.A2.5A2.8A.16A$4.A11.A26.A11.13A.A
33.6A8.2A2.3A5.A2.A3.A.20A$15.A24.3A.A11.14A2.A31.3A.A8.A2.A.4A7.2A3.
A.16A.A$39.6A22.A5.A33.A9.7A.A7.A4.A17.A$40.3A14.A.A7.A.4A.A30.2A10.
5A2.A8.8A14.A$43.14A3.A3.A2.8A2.A37.A2.A3.2A9.6A.A$41.2A16.2A4.A.A.4A
5.A27.9A3.A.2A10.A6.A$40.5A4.2A6.2A6.3A4.6A.A38.17A3.A$41.2A.A6.A4.9A
.4A3.7A25.2A6.6A.A.11A.A$43.A4.3A.A2.2A2.9A.A7.A29.A4.7A.A12.A$42.A4.
6A3.2A5.A.A2.A3.2A4.2A.A22.3A.A2.2A5.5A9.A$48.3A9.A2.A2.2A6.A3.A3.A
20.6A3.2A5.2A.A$51.9A2.4A7.2A3.4A.A20.3A8.A5.A$49.2A11.11A4.A.5A23.6A
2.A4.A$48.5A7.2A4.16A23.2A6.A$49.2A.A6.5A8.5A.A.A.2A.A18.5A$51.A8.2A.
A3.2A7.A.A.A.A3.A18.2A.A$50.A11.A6.A3.A2.A.3A.4A.A19.A$61.A4.3A.A3.A.
2A.3A.5A18.A$65.6A3.3A.3A.4A$64.2A2.A4.A.2A.A.A.A.A.2A.A$65.2A2.8A.A.
A.A.A.A3.A$69.5A2.5A.3A.4A.A$64.5A4.2A2.A.3A.3A.5A$63.8A6.A3.4A.4A$
64.5A.A3.6A2.A.A.A2.2A$69.A3.6A5.A.2A4.A$65.A2.A5.A3.5A.2A4.A.A22$3.A
$4.A$2.2A.A9.A$.5A10.A6.A$2.2A7.A2.2A.A6.A8.A$4.7A2.5A4.2A.A8.A5.A$.
3A9.A.A5.5A6.2A.A5.A$6A5.3A.A.4A.2A7.5A3.2A.A$.3A.A4.14A.7A.A4.5A5.A$
4.A4.2A3.3A2.A.A.9A.A.3A.2A8.A$2.2A6.2A4.2A3.A.A.16A.7A.A$13.2A6.3A4.
A3.3A3.A.11A2.A$3.2A6.3A3.4A.4A3.2A3.2A.A2.A.7A5.A$5.A4.14A.A3.A3.A6.
A7.A.3ACDC3D$2.3A.A2.2A2.5A2.2A2.A4.14A5.5A3C3D94.CDC3D$.6A3.2A5.2A3.
2A5.12A.A2.A2.A.3AC5D55.A38.3C3D$2.3A9.A6.A6.A12.A4.A.A4.2C4D47.A8.A
14.A21.AC5D$5.9A2.15A8.2A5.5A2.3DC2D48.A5.2A.A6.A7.A6.A14.2C4D$3.2A
11.13A.A13.A2.2A.A2.D2C2DC46.2A.A3.5A7.A4.2A.A6.A13.3DC2D$2.5A7.2A13.
A10.4A5.A3.5DC45.5A4.2A7.2A.A2.5A4.2A.A12.D2C2DC$3.2A.A6.5A10.A19.A6.
2A10.A37.2A8.11A3.2A5.5A12.5DC$5.A8.2A.A23.2A11.2A12.A38.6A2.7A.A7.5A
.2A16.2A$4.A11.A26.A11.13A.A34.3A6.A2.A4.A2.5A2.8A.16A$15.A24.3A.A11.
14A2.A30.6A8.2A2.3A5.A2.A3.A.20A$39.6A22.A5.A30.3A.A8.A2.A.4A7.2A3.A.
16A.A$40.3A14.A.A7.A.4A.A32.A9.7A.A7.A4.A17.A$43.14A3.A3.A2.8A2.A27.
2A10.5A2.A8.8A14.A$41.2A16.2A4.A.A.4A5.A36.A2.A3.2A9.6A.A$40.5A4.2A6.
2A6.3A4.6A.A26.9A3.A.2A10.A6.A$41.2A.A6.A4.9A.4A3.7A38.17A3.A$43.A4.
3A.A2.2A2.9A.A7.A27.2A6.6A.A.11A.A$42.A4.6A3.2A5.A.A2.A3.2A4.2A.A25.A
4.7A.A12.A$48.3A9.A2.A2.2A6.A3.A3.A21.3A.A2.2A5.5A9.A$51.9A2.4A7.2A3.
4A.A19.6A3.2A5.2A.A$49.2A11.11A4.A.5A20.3A8.A5.A$48.5A7.2A4.16A25.6A
2.A4.A$49.2A.A6.5A8.5A.A.A.2A.A19.2A6.A$51.A8.2A.A3.2A7.A.A.A.A3.A17.
5A$50.A11.A6.A3.A2.A.3A.4A.A17.2A.A$61.A4.3A.A3.A.2A.3A.5A19.A$65.6A
3.3A.3A.4A20.A$64.2A2.A4.A.2A.A.A.A.A.2A.A$65.2A2.8A.A.A.A.A.A3.A$69.
5A2.5A.3A.4A.A$64.5A4.2A2.A.3A.3A.5A$63.8A6.A3.4A.4A$64.5A.A3.6A2.A.A
.A2.2A$69.A3.6A5.A.2A4.A$65.A2.A5.A3.5A.2A4.A.A!

However, 7x7 might work, but I don't know if that's possible, even at 60+ GB.

[amling]

(*) B2478/S134568

B2478/S134568 does not seem to complete, producing some more-interesting looking partials like...

I downloaded the latest version (I compiled with AF2=5 for some reason), and I tried this rule using raw:2:-1:0:0:-1:1:0:0:1 ... I would assume this means there are no p1 photons in this rule (and thus all of B247(8)/S13456(8)), but I would appreciate independent confirmation.

Oh, nice! I verify it, with AF2=4 and final partial:

Code: Select all

|                                                                   .. |
|                                                                 .... |
|                                                               ...... |
|                                                             ........ |
|                                                           .......... |
|                                                         ............ |
|                                                       .............. |
|                                                     ................ |
|                                                   .................. |
|                                                 .................... |
|                                               ...................... |
|                                             ........................ |
|                                           .......................... |
|                                         ............................ |
|                                       .............................. |
|                                     ................................ |
|                                   .................................. |
|                                 ............**...................... |
|                               .......**...***....................... |
|                             ..........***.***.*..**................. |
|                           ..........*.***.***.*.*..*................ |
|                         .........**.*.***.***..*....*....**.......   |
|                       ..........*..*..*.*.***.***.*..*..*..*....     |
|                     .............*.*....*.***.***...**.*....*.       |
|                   .............*..*..*.*..***.*.*.*.....****         |
|                 .................***...**.*.*.......**..**           |
|               ...................***............*...****             |
|             .....................***..*..***.*......**               |
|           ..................**...*.*......*..*.*.*..                 |
|         .....................***...**.*.*.*.*....*                   |
|       .....................*.***......*....*..**                     |
|     ....................**.*.***..*..*....**..                       |
|   .....................*..*..***......***.**                         |
| ........................*.**.*.*......***.                           |
| .....................***.......**.....*.                             |
| ...................*****..**..........                               |
| ............**...*****.*...***.**.**                                 |
| .............***.***.*...*.***..**                                   |
| ...........*.***.*.*.....*.*.*.*                                     |
| ........**.*.***.*......**....                                       |
| .......*..*..*.*..*.*.......                                         |
| ........*.*....*.**......*                                           |
| ......*..*..*.*.........                                             |
| ........***...**..***.                                               |
| ........***........*                                                 |
| ........***....***                                                   |
| ........***.....                                                     |
| ........*.*...                                                       |
| ........***.                                                         |
| ........**                                                           |
| ........                                                             |
| ......                                                               |
| ....                                                                 |
| ..                                                                   |

However, 7x7 might work, but I don't know if that's possible, even at 60+ GB.

These bigger block sizes are just not gonna be possible without a severe reworking of how it operates. In particular the state initializing code, for a field of 7x7 wildcards, would explicitly iterate over the 2^49 possible expansions of them. Maybe the CA checks could be folded in earlier (it's never mattered before and usually CA checks thinner than AF2 are somewhere between trivial and vacuous), but I am not optimistic about getting anywhere near those sorts of block sizes even so.

[amling]

I was thinking a bit more about downward-self-forcing blocks and automatically detecting them when I realized there is a much more powerful (more general) technique very close to what the code already does.

If you think about it, blocks that force themselves downward could not show up at all in a search in the reverse direction (where c1-f2b and c1-b2f are reverses and c1-s2s is a reverse of itself). And the existing proj001/proj002 code can already be used to build significant upper bounds on the blocks that can show up in a search. Coupled with something to reverse the blocks and to use them as a global upper bound on a search (in the other direction), and maybe the computer can do the guessing for us.

I've copied and reworked a bunch of the proj001/proj002 code into a "proj003". The aim here is to prove and manage upper bounds on the blocks reachable in finite patterns, just like in proj001, but now including the ability to flip the upper bound to the reversed geometry and then actually apply it as an upper bound filter to continue the process on the other side. You could even conceivably go back and forth between the two directions, refining the upper bound as many times as you need. The end goal here being that eventually a search with a proven upper bound terminates with no results.

As an example, with the code as prototyped and AF2=7, returning to B258/S134578, I can run:

Code: Select all

rlife llsss-recentering c1-s2s --rule 'B258/S134578' '@zero' --ends 'proj003:01:02:b1.blocks' XX

This dumps the 2x7 blocks possible at depths [1, 3) similar to the first step of proj001. I let it run for a bit and stabilize. At this point b1.blocks contains:

Code: Select all

[0,0,0,0,0,0,0]
[0,0,0,0,0,0,1]
[0,0,0,0,0,1,0]
[0,0,0,0,1,0,0]
[0,0,0,1,0,0,0]
[0,0,1,0,0,0,0]
[0,1,0,0,0,0,0]
[1,0,0,0,0,0,0]

This is a JSON dump of the 8 blocks possible, where the bit-packing details of the format are probably not relevant. At this point we have proven these 8 blocks are the only blocks that can appear in a finite ship by depth 1.

Now I want to run a search starting with any combinations of those blocks. For this there is now another magic grid, "@proj003:...", that will fake up the grid for me. Now running...

Code: Select all

rlife llsss-recentering c1-s2s --rule 'B258/S134578' '@proj003:02:b1.blocks' --ends 'proj003:01:02:b2.blocks' XX

...it will dump an upper bound on the blocks one depth further. This seems to stabilize at:

Code: Select all

[0,0,0,0,0,0,0]
[0,0,0,0,0,0,1]
[0,0,0,0,0,1,0]
[0,0,0,0,1,0,0]
[0,0,0,0,1,0,2]
[0,0,0,1,0,0,0]
[0,0,0,1,0,2,0]
[0,0,1,0,0,0,0]
[0,0,1,0,2,0,0]
[0,1,0,0,0,0,0]
[0,1,0,2,0,0,0]
[0,2,0,0,0,0,0]
[1,0,0,0,0,0,0]
[1,0,2,0,0,0,0]
[2,0,0,0,0,0,0]

At this point we have proven these 15 blocks are the only blocks that can appear in a finite ship by depth 2.

I run several more steps and eventually the 76 blocks in "b12.blocks" produce the same set of 76 in "b13.blocks". At this point we have proven these 76 blocks are the only blocks that can appear in a finite ship, anywhere.

Now I run the "rev-w" tool to reverse them. It takes both the from and the to geometry and checks to make sure such a reversal makes sense, then reorders the bits appropriately. For typical cases and W size of 2, there are 2 bits per column and they're just gonna be flipped but it seemed worth being ready for e.g. geometries with U=2X, etc. After this command...

Code: Select all

rlife proj003 rev-w c1-s2s c1-s2s 2 < b12.blocks > b12r.blocks

..."b12r.blocks" also contains an upper bound on the blocks that could appear in a finite ship. Careful analysis shows that of the 76, 59 do not show up reversed so this is a pretty severe limitation. Now when I run with the "proj003_limit_blocks" filter (and "wcaf" this time so it terminates eventually), I get no ships:

Code: Select all

rlife llsss-recentering c1-s2s --rule 'B258/S134578' '@zero' --filters wcaf,proj003_limit_blocks:02:b12r.blocks XX

In fact, the search dies pretty much immediately because the restriction is so very severe.

It's my hope that this will somewhat automate the process of guessing self-forcing blocks and forbidding them. It's also probably possible to combine several of these techniques more generally but TBD on how to structure the tools (global block bound, right-edge-only block bound, proj001-style end goal of more generic self-forcing, etc.). Also TBD trying this out on a geometry that hasn't already been solved. Perhaps I'll have more later tonight.

[Sokwe]

I would assume this means there are no p1 photons in [B2478/S134568] (and thus all of B247(8)/S13456(8)), but I would appreciate independent confirmation.

Oh, nice! I verify it, with AF2=4

Thanks! That should put us back where we thought we were before the bug discovery. This seems like a good moment to give an update on the project as a whole.

Here is the list of unsolved rules:

Code: Select all

B2458/S13467

B257/S0147
B2578/S0147
B257/S01478
B2578/S01478
B257/S0148
B2578/S0148
B257/S014
B2578/S014

B246/S0134
B2467/S0134
B246/S01348
B2467/S01348
B246/S013478
B2467/S013478
B246/S01347
B2467/S01347

B248/S013467
B248/S013468
B248/S01346

B247/S0136
B2478/S0136
B248/S0136
B24/S0136
B247/S01368
B2478/S01368
B248/S01368
B24/S01368
B247/S013678
B248/S013678
B24/S013678
B247/S01367
B2478/S01367
B248/S01367
B24/S01367
B247/S0137
B2478/S0137
B248/S0137
B24/S0137
B247/S01378
B2478/S01378
B248/S01378
B24/S01378
B247/S0138
B2478/S0138
B248/S0138
B24/S0138
B247/S013
B2478/S013
B248/S013
B24/S013

B246/S0137
B2468/S0137
B246/S01378
B2468/S01378
B246/S0138
B2468/S0138
B246/S013
B2468/S013

B267/S02568
B2678/S02568

B248/S0257
B24/S0257
B248/S02578
B24/S02578
B247/S0258
B2478/S0258
B248/S0258
B24/S0258
B247/S025
B2478/S025
B248/S025
B24/S025

B257/S0247
B2578/S0247
B258/S0247
B25/S0247
B257/S02478
B2578/S02478
B258/S02478
B25/S02478
B257/S0248
B2578/S0248
B258/S0248
B25/S0248
B257/S024
B2578/S024
B258/S024
B25/S024

B2568/S0235
B25678/S0235
B257/S0235
B2578/S0235
B2568/S02358
B25678/S02358
B257/S02358
B2578/S02358

B246/S0235
B2468/S0235
B246/S02358
B2468/S02358

B25678/S023567
B2567/S023567

B2456/S023568
B2456/S02356

Here is the rule map:

Code: Select all

             B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B
             2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
                                             4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
                             5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
                     6 6 6 6 6 6 6 6                 6 6 6 6 6 6 6 6
                 7 7 7 7         7 7 7 7         7 7 7 7         7 7 7 7
               8 8     8 8     8 8     8 8     8 8     8 8     8 8     8 8
            ----------------------------------------------------------------
S          : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S        8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S       78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S       7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S      67  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S      678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S      6 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S      6   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S     56   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S     56 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S     5678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S     567  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S     5 7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S     5 78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S     5  8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S     5    : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    45    : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    45  8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    45 78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    45 7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    4567  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    45678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    456 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    456   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    4 6   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    4 6 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    4 678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    4 67  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    4  7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    4  78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    4   8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S    4     : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   34     : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   34   8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   34  78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   34  7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   34 67  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   34 678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   34 6 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   34 6   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3456   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3456 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   345678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   34567  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   345 7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   345 78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   345  8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   345    : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3 5    : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3 5  8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3 5 78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3 5 7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3 567  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3 5678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3 56 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3 56   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3  6   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3  6 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3  678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3  67  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3   7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3   78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3    8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S   3      : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23      : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23    8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23   78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23   7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23  67  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23  678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23  6 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23  6   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23 56   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23 56 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23 5678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23 567  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23 5 7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23 5 78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23 5  8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23 5    : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2345    : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2345  8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2345 78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2345 7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  234567  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2345678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23456 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  23456   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  234 6   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  234 6 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  234 678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  234 67  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  234  7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  234  78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  234   8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  234     : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 4     : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 4   8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 4  78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 4  7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 4 67  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 4 678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 4 6 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 4 6   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 456   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 456 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 45678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 4567  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 45 7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 45 78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 45  8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2 45    : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2  5    : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2  5  8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2  5 78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2  5 7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2  567  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2  5678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2  56 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2  56   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2   6   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2   6 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2   678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2   67  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2    7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2    78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2     8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S  2       : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 12       :
S 12     8 :
S 12    78 :
S 12    7  :
S 12   67  :
S 12   678 :
S 12   6 8 :
S 12   6   :
S 12  56   :
S 12  56 8 :
S 12  5678 :
S 12  567  :
S 12  5 7  :
S 12  5 78 :
S 12  5  8 :
S 12  5    :
S 12 45    :
S 12 45  8 :
S 12 45 78 :
S 12 45 7  :
S 12 4567  :
S 12 45678 :
S 12 456 8 :
S 12 456   :
S 12 4 6   :
S 12 4 6 8 :
S 12 4 678 :
S 12 4 67  :
S 12 4  7  :
S 12 4  78 :
S 12 4   8 :
S 12 4     :
S 1234     :
S 1234   8 :
S 1234  78 :
S 1234  7  :
S 1234 67  :
S 1234 678 :
S 1234 6 8 :
S 1234 6   :
S 123456   :
S 123456 8 :
S 12345678 :
S 1234567  :
S 12345 7  :
S 12345 78 :
S 12345  8 :
S 12345    :
S 123 5    :
S 123 5  8 :
S 123 5 78 :
S 123 5 7  :
S 123 567  :
S 123 5678 :
S 123 56 8 :
S 123 56   :
S 123  6   :
S 123  6 8 :
S 123  678 :
S 123  67  :
S 123   7  :
S 123   78 :
S 123    8 :
S 123      :
S 1 3      :                                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3    8 :                                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3   78 :                                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3   7  :                                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3  67  :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3  678 :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3  6 8 :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3  6   :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3 56   :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3 56 8 :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3 5678 :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3 567  :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3 5 7  :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3 5 78 :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3 5  8 :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 3 5    :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1 345    :                                 1 1 1 1         1 1 1   1 1 1 1
S 1 345  8 :                                 1 1 1 1         1 1 1   1 1 1 1
S 1 345 78 :                                 1 1 1 1         1 1 1 1 1 1 1 1
S 1 345 7  :                                 1 1 1 1         1 1 1 1 1 1 1 1
S 1 34567  :
S 1 345678 :
S 1 3456 8 :                                                 1 1         1 1
S 1 3456   :                                                 1 1
S 1 34 6   :         1 1     1 1 1 1 1 1         1 1         1 1 1 1 1 1 1 1
S 1 34 6 8 :         1 1     1 1 1 1 1 1         1 1         1 1 1 1 1 1 1 1
S 1 34 678 :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1         1 1 1 1 1 1 1 1
S 1 34 67  :         1 1 1 1 1 1 1 1 1 1 1 1   . 1 1         1 1 1 1 1 1 1 1
S 1 34  7  :                     1 1         1 1 1 1         1 1 1 1 1 1 1 1
S 1 34  78 :                     1 1         1 1 1 1         1 1 1 1 1 1 1 1
S 1 34   8 :                     1 1         1 1 1 1         1 1 1 1 1 1 1 1
S 1 34     :                     1 1         1 1 1 1         1 1 1 1 1 1 1 1
S 1  4     :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1  4   8 :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1  4  78 :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1  4  7  :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1  4 67  :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1  4 678 :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1  4 6 8 :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1  4 6   :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1  456   :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1  456 8 :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1  45678 :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1  4567  :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1  45 7  :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1  45 78 :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1  45  8 :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1  45    :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1   5    :                                 1 1 1 1 1 1 1 1
S 1   5  8 :                                 1 1 1 1 1 1 1 1
S 1   5 78 :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1   5 7  :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1   567  :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1   5678 :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S 1   56 8 :                                 1 1 1 1 1 1 1 1
S 1   56   :                                 1 1 1 1 1 1 1 1
S 1    6   :
S 1    6 8 :
S 1    678 :
S 1    67  :
S 1     7  :
S 1     78 :
S 1      8 :
S 1        :
S01        :
S01      8 :
S01     78 :
S01     7  :
S01    67  :
S01    678 :
S01    6 8 :
S01    6   :
S01   56   :                                 1 1 1 1   1 1 1
S01   56 8 :                                 1 1 1 1   1 1 1
S01   5678 :
S01   567  :
S01   5 7  :                 1 1     1 1     1 1 1 1 1 1 1 1
S01   5 78 :                 1 1     1 1     1 1 1 1 1 1 1 1
S01   5  8 :                                 1 1 1 1 1 1 1 1
S01   5    :                                 1 1 1 1 1 1 1 1
S01  45    :                 1 1     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01  45  8 :                 1 1     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01  45 78 :                 1 1     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01  45 7  :                 1 1     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01  4567  :                                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01  45678 :                                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01  456 8 :                 1 1             1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01  456   :                 1 1             1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01  4 6   :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01  4 6 8 :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01  4 678 :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01  4 67  :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01  4  7  :                 1 1     . .     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01  4  78 :                 1 1     . .     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01  4   8 :                 1 1     . .     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01  4     :                 1 1     . .     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S01 34     :                                                 . 1 1 . 1 1
S01 34   8 :                                                 . 1 1 . 1 1
S01 34  78 :                                                 . 1 1 . 1 1
S01 34  7  :                                                 . 1 1 . 1 1
S01 34 67  :                                                 1 1 1 1 1 1 .
S01 34 678 :                                                 1 1 1 1 1 1 1
S01 34 6 8 :                                                 1 1 1 1 1 1 .
S01 34 6   :                                                 1 1 1 1 1 1 .
S01 3456   :
S01 3456 8 :
S01 345678 :
S01 34567  :
S01 345 7  :
S01 345 78 :
S01 345  8 :
S01 345    :
S01 3 5    :                 1 1 1 1 1 1 1 1                 1 1 1 1 1 1 1 1
S01 3 5  8 :                 1 1 1 1 1 1 1 1                 1 1 1 1 1 1 1 1
S01 3 5 78 :                 1 1 1 1 1 1 1 1                 1 1 1 1 1 1 1 1
S01 3 5 7  :                 1 1 1 1 1 1 1 1                 1 1 1 1 1 1 1 1
S01 3 567  :                 1 1 1 1 1 1 1 1                 1 1 1 1 1 1 1 1
S01 3 5678 :                 1 1 1 1 1 1 1 1                 1 1 1 1 1 1 1 1
S01 3 56 8 :                 1 1 1 1 1 1 1 1                 1 1 1 1 1 1 1 1
S01 3 56   :                 1 1 1 1 1 1 1 1                 1 1 1 1 1 1 1 1
S01 3  6   :                 1 1 1 1                         1 1 1 1 . . . .
S01 3  6 8 :                 1 1 1 1                         1 1 1 1 . . . .
S01 3  678 :                 1 1 1 1                         1 1 1 1 . 1 . .
S01 3  67  :                 1 1 1 1                         1 1 1 1 . . . .
S01 3   7  :                                                 . . 1 1 . . . .
S01 3   78 :                                                 . . 1 1 . . . .
S01 3    8 :                                                 . . 1 1 . . . .
S01 3      :                                                 . . 1 1 . . . .
S0123      :
S0123    8 :
S0123   78 :
S0123   7  :
S0123  67  :
S0123  678 :
S0123  6 8 :
S0123  6   :
S0123 56   :
S0123 56 8 :
S0123 5678 :
S0123 567  :
S0123 5 7  :
S0123 5 78 :
S0123 5  8 :
S0123 5    :
S012345    :
S012345  8 :
S012345 78 :
S012345 7  :
S01234567  :
S012345678 :
S0123456 8 :
S0123456   :
S01234 6   :
S01234 6 8 :
S01234 678 :
S01234 67  :
S01234  7  :
S01234  78 :
S01234   8 :
S01234     :
S012 4     :
S012 4   8 :
S012 4  78 :
S012 4  7  :
S012 4 67  :
S012 4 678 :
S012 4 6 8 :
S012 4 6   :
S012 456   :
S012 456 8 :
S012 45678 :
S012 4567  :
S012 45 7  :
S012 45 78 :
S012 45  8 :
S012 45    :
S012  5    :
S012  5  8 :
S012  5 78 :
S012  5 7  :
S012  567  :
S012  5678 :
S012  56 8 :
S012  56   :
S012   6   :
S012   6 8 :
S012   678 :
S012   67  :
S012    7  :
S012    78 :
S012     8 :
S012       :
S0 2       :                                 1 1 1 1 1 1 1 1
S0 2     8 :                                 1 1 1 1 1 1 1 1
S0 2    78 :                                 1 1 1 1 1 1 1 1
S0 2    7  :                                 1 1 1 1 1 1 1 1
S0 2   67  :                                 1 1 1 1 1 1 1 1
S0 2   678 :                                 1 1 1 1 1 1 1 1
S0 2   6 8 :                                 1 1 1 1 1 1 1 1
S0 2   6   :                                 1 1 1 1 1 1 1 1
S0 2  56   :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2  56 8 :         . . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2  5678 :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2  567  :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2  5 7  :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . .
S0 2  5 78 :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . .
S0 2  5  8 :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . . . .
S0 2  5    :                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . . . .
S0 2 45    :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2 45  8 :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2 45 78 :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2 45 7  :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2 4567  :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2 45678 :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2 456 8 :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2 456   :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2 4 6   :         1 1     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2 4 6 8 :         1 1     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2 4 678 :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2 4 67  :         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2 4  7  :                 1 1 1 1 . . . . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2 4  78 :                 1 1 1 1 . . . . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2 4   8 :                 1 1 1 1 . . . . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 2 4     :                 1 1 1 1 . . . . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0 234     :
S0 234   8 :
S0 234  78 :
S0 234  7  :
S0 234 67  :
S0 234 678 :
S0 234 6 8 :
S0 234 6   :
S0 23456   :
S0 23456 8 :
S0 2345678 :
S0 234567  :
S0 2345 7  :
S0 2345 78 :
S0 2345  8 :
S0 2345    :
S0 23 5    :                   . .   . .       1 1 1 1 1 1   . . 1 1 1 1 1 1
S0 23 5  8 :                   . .   . .       1 1 1 1 1 1   . . 1 1 1 1 1 1
S0 23 5 78 :                 1 1 1 1 1 1 1     1 1 1 1 1 1   1 1 1 1 1 1 1 1
S0 23 5 7  :                 1 1 1 1 1 1 1     1 1 1 1 1 1   1 1 1 1 1 1 1 1
S0 23 567  :                     . . 1 1 1 1   1 1 1 1 1 1   1 1 1 1 1 1 1 1
S0 23 5678 :                     1 1 1 1 1 1   1 1 1 1 1 1   1 1 1 1 1 1 1 1
S0 23 56 8 :                   1 1 1 1 1       1 1 1 1 1 1 . 1 1 1 1 1 1 1 1
S0 23 56   :                   1 1 1 1 1       1 1 1 1 1 1 . 1 1 1 1 1 1 1 1
S0 23  6   :                                         1 1 1 1         1 1 1 1
S0 23  6 8 :                                         1 1 1 1         1 1 1 1
S0 23  678 :                                         1 1 1 1 1 1 1 1 1 1 1 1
S0 23  67  :                                         1 1 1 1 1 1 1 1 1 1 1 1
S0 23   7  :                                                         1 1 1 1
S0 23   78 :                                                         1 1 1 1
S0 23    8 :                                                         1 1 1 1
S0 23      :                                                         1 1 1 1
S0  3      : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3    8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3   78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3   7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3  67  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3  678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3  6 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3  6   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3 56   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3 56 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3 5678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3 567  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3 5 7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3 5 78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3 5  8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3 5    : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  345    : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  345  8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  345 78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  345 7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  34567  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  345678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3456 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  3456   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  34 6   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  34 6 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  34 678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  34 67  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  34  7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  34  78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  34   8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0  34     : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   4     : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   4   8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   4  78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   4  7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   4 67  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   4 678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   4 6 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   4 6   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   456   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   456 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   45678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   4567  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   45 7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   45 78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   45  8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0   45    : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0    5    : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0    5  8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0    5 78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0    5 7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0    567  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0    5678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0    56 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0    56   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0     6   : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0     6 8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0     678 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0     67  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0      7  : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0      78 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0       8 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
S0         : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

I was thinking a bit more about downward-self-forcing blocks and automatically detecting them when I realized there is a much more powerful (more general) technique very close to what the code already does.

This sounds interesting. I wonder if it can be applied to B248/S0258. This rule seems to have limited f2b partial results, but I'm not sure if it does so in a way that can be picked up by a proj001/proj003 search.

[amling]

I've just pushed 8b3e8eb9c2f2 which reworks somewhat how proj002 works. Mainly:

(*) Switch to left side. I know this is a jarring change but there are algorithm issues that make the left side more efficient and thus allow the later changes.

(*) Allow u_size to be completely independent of AF2 (larger, smaller, whatever) and require it as an extra argument. This means even with AF2=3 you can run much bigger blocks.

(*) Operate via list of JSON blocks and magic "@proj002:..." grid, similar to proj003.

(*) Explicitly detect a zero bottom edge and refuse (panic). Arguably the data could still be correct (the left edge blocks in nonzero stripes), but I can't (yet) imagine what you'd use it for.

After this you can run stuff like...

Code: Select all

rlife llsss-recentering-wao c1-f2b --rule 'B267/S02568' '@zero' --wao-left-pad 00 --wao-right-pad 00 --wao-idx ALL --ends proj002:01:02:10:A01.blocks XX
rlife llsss-recentering c1-f2b --rule 'B267/S02568' '@proj002:02:A01.blocks' --ends proj002:01:02:10:A02.blocks XX
...

...to run the proj002 workflow for 2x10 blocks. I am almost positive it would not work out in that particular case, but it hopefully makes clear how the commands/arguments have changed.

[LaundryPizza03]

Which branch was proj002 folded into after the previous post?

I also seek to set a similar project for still lifes, using the list I compiled at viewtopic.php?f=11&t=5474&p=209864#p209864.

[amling]

Which branch was proj002 folded into after the previous post?

I also seek to set a similar project for still lifes, using the list I compiled at viewtopic.php?f=11&t=5474&p=209864#p209864.

Generally if I have not named a branch when talking about pushing it's going to have been included in the codeberg "master" branch. Sometimes you could figure out whether or not a feature is included by trying it and seeing if it works, e.g. those commands as written I believe will work on the current master branch (and would not without the changes I had made). Sometimes you could figure out by querying source control, e.g. "git merge-base --is-ancestor 8b3e8eb9c2f2 HEAD" can answer (by exit code) if that named commit is included in whatever you've got checked out.

All the above search/proof techniques should be equally applicable to ruling out existence for still lifes (or "p1" objects as LLSSS sees them). I think there are maybe even more tricks available in that block sets (or forbidden blocks) could be rotated 90 degrees, but perhaps we can worry about such trickery once already-implemented techniques are exhausted. I guess let me know how it goes and especially if you get stuck on any juicy rules.

[LaundryPizza03]

I ran the proj002 workflow on p1 in B245678/S125678 using 3*4 blocks, and got the following eight blocks after four iterations:

Code: Select all

[1,0,0,0]
[1,0,0,1]
[1,0,0,2]
[1,0,0,4]
[1,0,5,4]
[1,3,0,1]
[2,6,0,2]
[4,5,0,4]

I'm pretty sure this means I've ruled out rules with at least B245678 and at most S125678. Is that correct?

[amling]

I ran the proj002 workflow on p1 in B245678/S125678 using 3*4 blocks, and got the following eight blocks after four iterations:

Code: Select all

[1,0,0,0]
[1,0,0,1]
[1,0,0,2]
[1,0,0,4]
[1,0,5,4]
[1,3,0,1]
[2,6,0,2]
[4,5,0,4]

I'm pretty sure this means I've ruled out rules with at least B245678 and at most S125678. Is that correct?

What depth (w_pos) did it take for that set to reproduce itself? When I ran this, my set of blocks after two steps matches those 8 but the next step has an extra 9th block ("[2,6,0,4]") as far as I have run it so far (w_pos 15).

EDIT: Having pushed on I believe there is an 11 block set that reproduces itself, but more important is to debug your understanding here. What exactly did you do and why do you think you did it? "Four iterations"? Why four? How long did you let each run? How big were the block sets after each? Can you explain back to me in complete sentences that require no context for an outsider to understand how you think proj002 is used to produce proofs of nonexistence? Especially what exactly must be true of the sequence of searches/block sets for it to constitute a proof?

[LaundryPizza03]

I ran the proj002 workflow on p1 in B245678/S125678 using 3*4 blocks, and got the following eight blocks after four iterations:

Code: Select all

[1,0,0,0]
[1,0,0,1]
[1,0,0,2]
[1,0,0,4]
[1,0,5,4]
[1,3,0,1]
[2,6,0,2]
[4,5,0,4]

I'm pretty sure this means I've ruled out rules with at least B245678 and at most S125678. Is that correct?

What depth (w_pos) did it take for that set to reproduce itself? When I ran this, my set of blocks after two steps matches those 8 but the next step has an extra 9th block ("[2,6,0,4]") as far as I have run it so far (w_pos 15).

EDIT: Having pushed on I believe there is an 11 block set that reproduces itself, but more important is to debug your understanding here. What exactly did you do and why do you think you did it? "Four iterations"? Why four? How long did you let each run? How big were the block sets after each? Can you explain back to me in complete sentences that require no context for an outsider to understand how you think proj002 is used to produce proofs of nonexistence? Especially what exactly must be true of the sequence of searches/block sets for it to constitute a proof?

First, I did this and got intitial four blocks:

Code: Select all

./rlife llsss-recentering-wao p1 --rule 'B245678/S125678' '@zero' --wao-left-pad 00 --wao-right-pad 00 --wao-idx ALL --ends proj002:01:03:04:A01.blocks XX

I was told only to run this until this repeats; it encodes blocks on the left-hand side of the pattern, such that each one must run until it repeats:

Code: Select all

./rlife llsss-recentering p1 --rule 'B245678/S125678' '@proj002:03:A01.blocks' --ends proj002:01:03:04:A02.blocks XX

I'm not sure how to tell where to stop each run.

[amling]

EDIT: No, no, no, I did this all wrong. Confused and wrecked by my own messy tools. I was running with starts like "proj002:02:A01.blocks" which is the wrong magic grid and it should be "proj002:03:A01.blocks" as these blocks are 3 (W) rows tall. With this fixed it does stabilize on the fourth round at your set of 8 blocks. GDI. I have edited the below to contain the correct commands, numbers, etc.

First, I did this and got intitial four blocks:

Code: Select all

./rlife llsss-recentering-wao p1 --rule 'B245678/S125678' '@zero' --wao-left-pad 00 --wao-right-pad 00 --wao-idx ALL --ends proj002:01:03:04:A01.blocks XX

I was told only to run this until this repeats; it encodes blocks on the left-hand side of the pattern, such that each one must run until it repeats:

Code: Select all

./rlife llsss-recentering p1 --rule 'B245678/S125678' '@proj002:03:A01.blocks' --ends proj002:01:03:04:A02.blocks XX

I'm not sure how to tell where to stop each run.

I'm not quite sure I understand, and I'm quite sure I don't understand what you do or don't understand. I guess I will just try to put a fresh and complete explanation of proj002 from the top here, but I'm not sure how much more helpful it's going to be as compared to the one I wrote when I first wrote the code.

So step one, from zeros search for still lifes, dumping out the possible left-most 3x4 blocks starting at depth 1 into "A01.blocks":

Code: Select all

rlife llsss-recentering-wao p1 --rule 'B245678/S125678' '@zero' --ends proj002:01:03:04:A01.blocks

This includes among its output:

Code: Select all

...
20250413 18:02:46 [INFO] Proj002Step depth 1 updating to 8 blocks...
20250413 18:02:46 [DEBUG] Completed w_pos 3: 576 B [+100.00%], 12.750103ms [+54.20%]
...
20250413 18:02:46 [INFO] Proj002Step depth 1 updating to 4 blocks...
20250413 18:02:46 [DEBUG] Completed w_pos 4: 1.00 KB [+56.00%], 30.233321ms [+81.35%]
...

Meaning the first set of blocks it had was 8, but as the search continued eventually it was reduced to 4. It's possible if left run for long enough it could reduce further. What is right to do here? Hard to say. There is a mathematical final answer but I do not know how to know when it is reached. Any set of blocks output is "legal" to proceed to later steps with but larger sets are less likely to complete successfully. The important point here is these are an upper bound on the possible blocks at depth 1 of any pattern. We'll continue with these 4 (saved in "A01.blocks").

Step two: search starting with any slice beginning with one of those 4 blocks and dumping out the leftmost blocks at depth 1:

Code: Select all

rlife llsss-recentering p1 --rule 'B245678/S125678' '@proj002:03:A01.blocks' --ends proj002:01:03:04:A02.blocks XX

Outputs:

Code: Select all

...
20250413 18:21:17 [INFO] Proj002Step depth 1 updating to 10 blocks...
20250413 18:21:17 [DEBUG] Completed w_pos 3: 6.83 KB, 40.050986ms
...
20250413 18:21:17 [INFO] Proj002Step depth 1 updating to 5 blocks...
20250413 18:21:17 [DEBUG] Completed w_pos 4: 16.43 KB [+82.57%], 42.641695ms [+6.27%]
...

Similar issues apply, namely that there is an absolute limit, I have no idea how to know when you're there, any set legal, smaller sets better. What's important is these are an upper bound of blocks at depth 2 (of original pattern). We'll continue with 5 (saved in "A02.blocks").

Step three: search starting with any slice beginning with one of those 5 blocks:

Code: Select all

rlife llsss-recentering p1 --rule 'B245678/S125678' '@proj002:03:A02.blocks' --ends proj002:01:03:04:A03.blocks XX

Code: Select all

...
20250413 18:22:04 [INFO] Proj002Step depth 1 updating to 13 blocks...
20250413 18:22:04 [DEBUG] Completed w_pos 3: 7.35 KB, 27.495267ms
...
20250413 18:22:05 [INFO] Proj002Step depth 1 updating to 8 blocks...
20250413 18:22:05 [DEBUG] Completed w_pos 4: 18.34 KB [+85.52%], 34.927242ms [+23.81%]
...

An upper bound of blocks at depth 3 (of original pattern).

Step four:

Code: Select all

rlife llsss-recentering p1 --rule 'B245678/S125678' '@proj002:03:A03.blocks' --ends proj002:01:03:04:A04.blocks XX

Code: Select all

...
20250413 18:22:37 [INFO] Proj002Step depth 1 updating to 16 blocks...
20250413 18:22:37 [DEBUG] Completed w_pos 3: 9.08 KB, 36.490125ms
...
20250413 18:22:37 [INFO] Proj002Step depth 1 updating to 8 blocks...
20250413 18:22:37 [DEBUG] Completed w_pos 4: 20.24 KB [+76.15%], 18.184968ms [-66.96%]
...

At this point A03.blocks and A04.blocks are the same set:

Code: Select all

$ diff A03.blocks A04.blocks
$

So now this upper bound of possible blocks on left side of pattern is stable forever and the proof is complete.

If it were possible for there to be a finite pattern somewhere in there the search would find an all-zeros row and the Proj002Step would (intentionally) crash out.