Level wave speed limit?

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amling
Posts: 704
Joined: April 2nd, 2020, 9:47 pm

Level wave speed limit?

Post by amling » January 26th, 2023, 9:16 pm

Are there any known bounds on what level wave speed limits are possible? By "level" I mean something like:

Code: Select all

x = 63, y = 4, rule = B3/S23
3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o$3obo3bob3obo3bob3ob
o3bob3obo3bob3obo3bob3obo3bob3o$obo7bobo7bobo7bobo7bobo7bobo7bobo$4b2o
b2o5b2ob2o5b2ob2o5b2ob2o5b2ob2o5b2ob2o!
Contrast with something like:

Code: Select all

x = 54, y = 30, rule = B3/S23
bo$b2o$2b4o$2o2bo2bo$3bo3b2o$4bo3b4o$6b2o2bo2bo$9bo3b2o$10bo3b4o$12b2o
2bo2bo$15bo3b2o$16bo3b4o$18b2o2bo2bo$21bo3b2o$22bo3b4o$24b2o2bo2bo$27b
o3b2o$28bo3b4o$30b2o2bo2bo$33bo3b2o$34bo3b4o$36b2o2bo2bo$39bo3b2o$40bo
3b4o$42b2o2bo2bo$45bo3b2o$46bo3b4o$48b2o2bo$51bo$52bo!
which I would not describe as level.

In terms of speed orthogonal to the level I find it suspicious that nothing between c/2 and c is known. By reading slanted waves the "wrong" way I am pretty sure it's going to be possible to get speeds between c/2 and c (or even over c!) which is why I limit my question to level waves. Also c itself (reduced) is definitely achievable even in level waves, e.g. 2c/2:

Code: Select all

x = 62, y = 2, rule = B3/S23
62o$2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o!
I hacked up a copy of LLSSS to do some weird wrapping searches and barring a bug I believe it has shown there are no level waves of unreduced speeds 2c/3, 3c/4, 3c/5, 4c/5, 4c/6, 5c/6, 4c/7, 5c/7, 6c/7, 5c/8, 6c/8, 7c/8, 6c/9, 7c/9, 8c/9, 7c/10, 8c/10, or 9c/10 (all periods up to 10 except for 5c/9 and 6c/10). It tended to run slower and take more memory closer to c/2 (which is why I did not complete 5c/9 or 6c/10).

I would conjecture there are no level waves between c/2 and c and in fact more strongly that there are no "level back half planes" there either, by which I mean any full plane pattern traveling at a speed between c/2 and c which has a level front half plane of all zero must be all zero everywhere.

Relatedly it is known that there are no back half planes of a specific spatial slope which travel faster than c/2, but the argument fundamentally relies on the spatial slope of the half plane division and any sort of argument like this would some how have to "allow c through".

Also relatedly it is known that for any traveling plane at a speed < c with a level front half of parallel zebra stripes must be all zebra stripes. This is tantalizingly close to what we want to show and how the "< c" part shakes out is maybe interesting, but I see no way to repurpose the argument here.

EDIT: As a perhaps related question is it possible for a slanted wave to have its two orthogonal speeds both be > c/2? I would think not but am not immediately sure how to prove any such thing. The usual argument about c/2 upper bound for finite patterns seems very tied to its specific spatial slope.

EDIT2: I had forgotten about this horrible thing I had found earlier when digging in 2c/3. I would describe it as a "slanted back half plane" for speeds 2c/3 and 4c/7 (both faster than c/2):

Code: Select all

x = 60, y = 78, rule = B3/S23
o$bo$b2o$bo$2ob2o$3b2o$2o3bo$4ob2o$5bobo$7b2o$4bo2bo$5ob2ob2o$9b2o$5ob
2o3bo$10ob2o$11bobo$13b2o$10bo2bo$11ob2ob2o$15b2o$11ob2o3bo$16ob2o$17b
obo$19b2o$16bo2bo$17ob2ob2o$21b2o$17ob2o3bo$22ob2o$23bobo$25b2o$22bo2b
o$23ob2ob2o$27b2o$23ob2o3bo$28ob2o$29bobo$31b2o$28bo2bo$29ob2ob2o$33b
2o$29ob2o3bo$34ob2o$35bobo$37b2o$34bo2bo$35ob2ob2o$39b2o$35ob2o3bo$40o
b2o$41bobo$43b2o$40bo2bo$41ob2ob2o$45b2o$41ob2o3bo$46ob2o$47bobo$49b2o
$46bo2bo$47ob2ob2o$51b2o$47ob2o3bo$52ob2o$53bobo$55b2o$52bo2bo$53ob2ob
2o$57b2o$53ob2o3bo$58obo$59bo2$58bo$59o2$59o$60o!
It means if my implied conjecture about slanted waves having to have at least one side <= c/2 is true it's true in a very weird way (that depends on the front-to-back finite depth).

amling
Posts: 704
Joined: April 2nd, 2020, 9:47 pm

Re: Level wave speed limit?

Post by amling » January 30th, 2023, 2:52 am

amling wrote:
January 26th, 2023, 9:16 pm
It means if my implied conjecture about slanted waves having to have at least one side <= c/2 is true it's true in a very weird way (that depends on the front-to-back finite depth).
It is just plain false:

Code: Select all

x = 304, y = 751, rule = B3/S23:T304,751+351
o$2o$2bo$3o$3bo$5o$5bo$6o$6bo$8o$8bo$9o$9bo$11o$11bo$12o$12bo$14o$14bo
$15o$15bo$17o$17bo$18o$18bo$20o$20bo$11o4b6o$13bo7bo$10o4bo2b6o$10bo
12bo$12o7b5o$12bo6b2o3bo$13o6bo3b3o$13bo5bo2bo2b2o$15o4b2obobo2bo$15bo
6b2obobo$16o4bobo5bo$16bo5bobob4o$18o2bobo7bo$18bo2b2o3b5o$17o3b8o3bo$
20bo7bo2b2o$16o5bo4bobo2b3o$16bobo6b2obo5bo$16o2b3o7b2ob4o$15bo2bobo4b
3o2bo4bo$14o3b2o5bo5b7o$18bo3b2o2bo2b2o6bo$13o3bo3b2o11b5o$13b2o6bo3bo
6bo5bo$14obobobo3bo8b8o$15b2ob2o3b2o6bo8bo$14ob2obobo9b11o$16bobobo3bo
4bo11bo$13o4b2obo2bo5b14o$13bob2obo2b2obo3bo14bo$10o4b2o6bo4b17o$17b6o
3bo17bo$9o4bo2bo9b20o$9bo7bo2b2o2bo4b2o15bo$11o11bob3o6b14o$11bo15bo4b
o14bo$12o10bo10b16o$12bo18bo17bo$14o17b19o$14bo15bo19bo$15o14b23o$15bo
12bo23bo$17o11b25o$17bo9bo25bo$18o8b29o$18bo6bo29bo$20o5b31o$20bo3bo
31bo$14o4bobo2b35o$58bo$13o6bob28o4b6o$13bo6bo30bo7bo$15o9b24o4bo2b6o$
15bo32bo12bo$16o9b25o7b5o$16bo7bo25bo6b2o3bo$18o5b28o6bo3b3o$18bo3bo
28bo5bo2bo2b2o$19o3b31o4b2obobo2bo$19bobo31bo6b2obobo$13o2b2o2bobo2b2o
2b26o4bobo5bo$17bobobobo30bo5bobob4o$11o4bo2b2ob2o2bo4b26o2bobo7bo$11b
o4b2obobob2o4bo26bo2b2o3b5o$12o7bobo7b26o3b8o3bo$12bo6bobo6bo29bo7bo2b
2o$14o5bobo5b27o5bo4bobo2b3o$14bo3b2ob2o3bo27bobo6b2obo5bo$15o11b28o2b
3o7b2ob4o$15bo9bo27bo2bobo4b3o2bo4bo$17obo3bob28o3b2o5bo5b7o$17bo5bo
32bo3b2o2bo2b2o6bo$18o5b28o3bo3b2o11b5o$19b3o29b2o6bo3bo6bo5bo$19obob
30obobobo3bo8b8o$53b2ob2o3b2o6bo8bo$19obob30ob2obobo9b11o$15b2o3bo3b2o
28bobobo3bo4bo11bo$13o6b3o6b23o4b2obo2bo5b14o$13bo3bobobobo3bo23bob2ob
o2b2obo3bo14bo$13o5bo3bo5b20o4b2o6bo4b17o$13bo2bo2bobo2bo2bo27b6o3bo
17bo$15obo7bob21o4bo2bo9b20o$15bo2bo3bo2bo21bo7bo2b2o2bo4b2o15bo$18o5b
26o11bob3o6b14o$18bo3bo26bo15bo4bo14bo$19o3b28o10bo10b16o$20bo29bo18bo
17bo$52o17b19o$52bo15bo19bo$53o14b23o$53bo12bo23bo$55o11b25o$55bo9bo
25bo$56o8b29o$56bo6bo29bo$58o5b31o$58bo3bo31bo$52o4bobo2b35o$96bo$51o
6bob28o4b6o$51bo6bo30bo7bo$53o9b24o4bo2b6o$53bo32bo12bo$54o9b25o7b5o$
54bo7bo25bo6b2o3bo$56o5b28o6bo3b3o$56bo3bo28bo5bo2bo2b2o$57o3b31o4b2ob
obo2bo$57bobo31bo6b2obobo$51o2b2o2bobo2b2o2b26o4bobo5bo$55bobobobo30bo
5bobob4o$49o4bo2b2ob2o2bo4b26o2bobo7bo$49bo4b2obobob2o4bo26bo2b2o3b5o$
50o7bobo7b26o3b8o3bo$50bo6bobo6bo29bo7bo2b2o$52o5bobo5b27o5bo4bobo2b3o
$52bo3b2ob2o3bo27bobo6b2obo5bo$53o11b28o2b3o7b2ob4o$53bo9bo27bo2bobo4b
3o2bo4bo$55obo3bob28o3b2o5bo5b7o$55bo5bo32bo3b2o2bo2b2o6bo$56o5b28o3bo
3b2o11b5o$57b3o29b2o6bo3bo6bo5bo$57obob30obobobo3bo8b8o$91b2ob2o3b2o6b
o8bo$57obob30ob2obobo9b11o$53b2o3bo3b2o28bobobo3bo4bo11bo$51o6b3o6b23o
4b2obo2bo5b14o$51bo3bobobobo3bo23bob2obo2b2obo3bo14bo$51o5bo3bo5b20o4b
2o6bo4b17o$51bo2bo2bobo2bo2bo27b6o3bo17bo$53obo7bob21o4bo2bo9b20o$53bo
2bo3bo2bo21bo7bo2b2o2bo4b2o15bo$56o5b26o11bob3o6b14o$56bo3bo26bo15bo4b
o14bo$57o3b28o10bo10b16o$58bo29bo18bo17bo$90o17b19o$90bo15bo19bo$91o
14b23o$91bo12bo23bo$93o11b25o$93bo9bo25bo$94o8b29o$94bo6bo29bo$96o5b
31o$96bo3bo31bo$90o4bobo2b35o$134bo$89o6bob28o4b6o$89bo6bo30bo7bo$91o
9b24o4bo2b6o$91bo32bo12bo$92o9b25o7b5o$92bo7bo25bo6b2o3bo$94o5b28o6bo
3b3o$94bo3bo28bo5bo2bo2b2o$95o3b31o4b2obobo2bo$95bobo31bo6b2obobo$89o
2b2o2bobo2b2o2b26o4bobo5bo$93bobobobo30bo5bobob4o$87o4bo2b2ob2o2bo4b
26o2bobo7bo$87bo4b2obobob2o4bo26bo2b2o3b5o$88o7bobo7b26o3b8o3bo$88bo6b
obo6bo29bo7bo2b2o$90o5bobo5b27o5bo4bobo2b3o$90bo3b2ob2o3bo27bobo6b2obo
5bo$91o11b28o2b3o7b2ob4o$91bo9bo27bo2bobo4b3o2bo4bo$93obo3bob28o3b2o5b
o5b7o$93bo5bo32bo3b2o2bo2b2o6bo$94o5b28o3bo3b2o11b5o$95b3o29b2o6bo3bo
6bo5bo$95obob30obobobo3bo8b8o$129b2ob2o3b2o6bo8bo$95obob30ob2obobo9b
11o$91b2o3bo3b2o28bobobo3bo4bo11bo$89o6b3o6b23o4b2obo2bo5b14o$89bo3bob
obobo3bo23bob2obo2b2obo3bo14bo$89o5bo3bo5b20o4b2o6bo4b17o$89bo2bo2bobo
2bo2bo27b6o3bo17bo$91obo7bob21o4bo2bo9b20o$91bo2bo3bo2bo21bo7bo2b2o2bo
4b2o15bo$94o5b26o11bob3o6b14o$94bo3bo26bo15bo4bo14bo$95o3b28o10bo10b
16o$96bo29bo18bo17bo$128o17b19o$128bo15bo19bo$129o14b23o$129bo12bo23bo
$131o11b25o$131bo9bo25bo$132o8b29o$132bo6bo29bo$134o5b31o$134bo3bo31bo
$128o4bobo2b35o$172bo$127o6bob28o4b6o$127bo6bo30bo7bo$129o9b24o4bo2b6o
$129bo32bo12bo$130o9b25o7b5o$130bo7bo25bo6b2o3bo$132o5b28o6bo3b3o$132b
o3bo28bo5bo2bo2b2o$133o3b31o4b2obobo2bo$133bobo31bo6b2obobo$127o2b2o2b
obo2b2o2b26o4bobo5bo$131bobobobo30bo5bobob4o$125o4bo2b2ob2o2bo4b26o2bo
bo7bo$125bo4b2obobob2o4bo26bo2b2o3b5o$126o7bobo7b26o3b8o3bo$126bo6bobo
6bo29bo7bo2b2o$128o5bobo5b27o5bo4bobo2b3o$128bo3b2ob2o3bo27bobo6b2obo
5bo$129o11b28o2b3o7b2ob4o$129bo9bo27bo2bobo4b3o2bo4bo$131obo3bob28o3b
2o5bo5b7o$131bo5bo32bo3b2o2bo2b2o6bo$132o5b28o3bo3b2o11b5o$133b3o29b2o
6bo3bo6bo5bo$133obob30obobobo3bo8b8o$167b2ob2o3b2o6bo8bo$133obob30ob2o
bobo9b11o$129b2o3bo3b2o28bobobo3bo4bo11bo$127o6b3o6b23o4b2obo2bo5b14o$
127bo3bobobobo3bo23bob2obo2b2obo3bo14bo$127o5bo3bo5b20o4b2o6bo4b17o$
127bo2bo2bobo2bo2bo27b6o3bo17bo$129obo7bob21o4bo2bo9b20o$129bo2bo3bo2b
o21bo7bo2b2o2bo4b2o15bo$132o5b26o11bob3o6b14o$132bo3bo26bo15bo4bo14bo$
133o3b28o10bo10b16o$134bo29bo18bo17bo$166o17b19o$166bo15bo19bo$167o14b
23o$167bo12bo23bo$169o11b25o$169bo9bo25bo$170o8b29o$170bo6bo29bo$172o
5b31o$172bo3bo31bo$166o4bobo2b35o$210bo$165o6bob28o4b6o$165bo6bo30bo7b
o$167o9b24o4bo2b6o$167bo32bo12bo$168o9b25o7b5o$168bo7bo25bo6b2o3bo$
170o5b28o6bo3b3o$170bo3bo28bo5bo2bo2b2o$171o3b31o4b2obobo2bo$171bobo
31bo6b2obobo$165o2b2o2bobo2b2o2b26o4bobo5bo$169bobobobo30bo5bobob4o$
163o4bo2b2ob2o2bo4b26o2bobo7bo$163bo4b2obobob2o4bo26bo2b2o3b5o$164o7bo
bo7b26o3b8o3bo$164bo6bobo6bo29bo7bo2b2o$166o5bobo5b27o5bo4bobo2b3o$
166bo3b2ob2o3bo27bobo6b2obo5bo$167o11b28o2b3o7b2ob4o$167bo9bo27bo2bobo
4b3o2bo4bo$169obo3bob28o3b2o5bo5b7o$169bo5bo32bo3b2o2bo2b2o6bo$170o5b
28o3bo3b2o11b5o$171b3o29b2o6bo3bo6bo5bo$171obob30obobobo3bo8b8o$205b2o
b2o3b2o6bo8bo$171obob30ob2obobo9b11o$167b2o3bo3b2o28bobobo3bo4bo11bo$
165o6b3o6b23o4b2obo2bo5b14o$165bo3bobobobo3bo23bob2obo2b2obo3bo14bo$
165o5bo3bo5b20o4b2o6bo4b17o$165bo2bo2bobo2bo2bo27b6o3bo17bo$167obo7bob
21o4bo2bo9b20o$167bo2bo3bo2bo21bo7bo2b2o2bo4b2o15bo$170o5b26o11bob3o6b
14o$170bo3bo26bo15bo4bo14bo$171o3b28o10bo10b16o$172bo29bo18bo17bo$204o
17b19o$204bo15bo19bo$205o14b23o$205bo12bo23bo$207o11b25o$207bo9bo25bo$
208o8b29o$208bo6bo29bo$210o5b31o$210bo3bo31bo$204o4bobo2b35o$248bo$
203o6bob28o4b6o$203bo6bo30bo7bo$205o9b24o4bo2b6o$205bo32bo12bo$206o9b
25o7b5o$206bo7bo25bo6b2o3bo$208o5b28o6bo3b3o$208bo3bo28bo5bo2bo2b2o$
209o3b31o4b2obobo2bo$209bobo31bo6b2obobo$203o2b2o2bobo2b2o2b26o4bobo5b
o$207bobobobo30bo5bobob4o$201o4bo2b2ob2o2bo4b26o2bobo7bo$201bo4b2obobo
b2o4bo26bo2b2o3b5o$202o7bobo7b26o3b8o3bo$202bo6bobo6bo29bo7bo2b2o$204o
5bobo5b27o5bo4bobo2b3o$204bo3b2ob2o3bo27bobo6b2obo5bo$205o11b28o2b3o7b
2ob4o$205bo9bo27bo2bobo4b3o2bo4bo$207obo3bob28o3b2o5bo5b7o$2o3b2o200bo
5bo32bo3b2o2bo2b2o6bo$3bo5b199o5b28o3bo3b2o11b5o$3bo4bo200b3o29b2o6bo
3bo6bo5bo$9b200obob30obobobo3bo8b8o$7bo235b2ob2o3b2o6bo8bo$7b202obob
30ob2obobo9b11o$6bo198b2o3bo3b2o28bobobo3bo4bo11bo$5b2o2b194o6b3o6b23o
4b2obo2bo5b14o$4b3o196bo3bobobobo3bo23bob2obo2b2obo3bo14bo$5bo4b193o5b
o3bo5b20o4b2o6bo4b17o$5b2ob2o193bo2bo2bobo2bo2bo27b6o3bo17bo$8b197obo
7bob21o4bo2bo9b20o$13b2o190bo2bo3bo2bo21bo7bo2b2o2bo4b2o15bo$10bo6b
191o5b26o11bob3o6b14o$10bo5bo191bo3bo26bo15bo4bo14bo$17b192o3b28o10bo
10b16o$15bo194bo29bo18bo17bo$15b227o17b19o$14bo227bo15bo19bo$13b2o2b
226o14b23o$12b3o228bo12bo23bo$13bo4b227o11b25o$13b2ob2o227bo9bo25bo$
16b230o8b29o$21b2o223bo6bo29bo$18bo6b223o5b31o$18bo5bo223bo3bo31bo$25b
217o4bobo2b35o$23bo262bo$23b218o6bob28o4b6o$22bo218bo6bo30bo7bo$21b2o
2b218o9b24o4bo2b6o$20b3o220bo32bo12bo$21bo4b218o9b25o7b5o$21b2ob2o218b
o7bo25bo6b2o3bo$24b222o5b28o6bo3b3o$29b2o215bo3bo28bo5bo2bo2b2o$26bo6b
214o3b31o4b2obobo2bo$26bo5bo214bobo31bo6b2obobo$33b208o2b2o2bobo2b2o2b
26o4bobo5bo$31bo213bobobobo30bo5bobob4o$31b208o4bo2b2ob2o2bo4b26o2bobo
7bo$30bo208bo4b2obobob2o4bo26bo2b2o3b5o$29b2o2b207o7bobo7b26o3b8o3bo$
28b3o209bo6bobo6bo29bo7bo2b2o$29bo4b208o5bobo5b27o5bo4bobo2b3o$29b2ob
2o208bo3b2ob2o3bo27bobo6b2obo5bo$32b211o11b28o2b3o7b2ob4o$37b2o204bo9b
o27bo2bobo4b3o2bo4bo$34bo6b204obo3bob28o3b2o5bo5b7o$34bo5bo204bo5bo32b
o3b2o2bo2b2o6bo$41b205o5b28o3bo3b2o11b5o$39bo207b3o29b2o6bo3bo6bo$39b
208obob30obobobo3bo8b6o$38bo242b2ob2o3b2o6bo$37b2o2b206obob30ob2obobo
9b8o$36b3o204b2o3bo3b2o28bobobo3bo4bo$37bo4b199o6b3o6b23o4b2obo2bo5b9o
$37b2ob2o199bo3bobobobo3bo23bob2obo2b2obo3bo$40b201o5bo3bo5b20o4b2o6bo
4b11o$45b2o194bo2bo2bobo2bo2bo27b6o3bo$42bo6b194obo7bob21o4bo2bo9b12o$
42bo5bo194bo2bo3bo2bo21bo7bo2b2o2bo4b2o$49b197o5b26o11bob3o6b5o$47bo
198bo3bo26bo15bo4bo$47b200o3b28o10bo10b5o$46bo201bo29bo18bo$45b2o2b
231o17b7o$44b3o233bo15bo$45bo4b231o14b9o$45b2ob2o231bo12bo$48b235o11b
10o$53b2o228bo9bo$50bo6b227o8b12o$50bo5bo227bo6bo$57b229o5b13o$55bo
230bo3bo$55b225o4bobo2b15o$54bo$53b2o2b222o6bob17o$52b3o224bo6bo$53bo
4b223o9b14o$53b2ob2o223bo$56b226o9b13o$61b2o219bo7bo$58bo6b219o5b15o$
58bo5bo219bo3bo$65b220o3b16o$63bo221bobo$63b216o2b2o2bobo2b2o2b10o$62b
o220bobobobo$61b216o4bo2b2ob2o2bo4b8o$60bo216bo4b2obobob2o4bo$60b218o
7bobo7b9o$59bo218bo6bobo6bo$58b2o2b218o5bobo5b11o$57b3o220bo3b2ob2o3bo
$58bo4b218o11b12o$58b2ob2o218bo9bo$61b222obo3bob14o$66b2o3b2o3b2o3b2o
200bo5bo$63bo5bo4bo4bo5b199o5b15o$63bo5bo4bo4bo4bo200b3o$85b200obob16o
$83bo$83b202obob16o$82bo198b2o3bo3b2o$81b2o2b194o6b3o6b10o$80b3o196bo
3bobobobo3bo$81bo4b193o5bo3bo5b10o$81b2ob2o193bo2bo2bobo2bo2bo$84b197o
bo7bob12o$89b2o190bo2bo3bo2bo$86bo6b191o5b15o$86bo5bo191bo3bo$93b192o
3b16o$91bo194bo$91b213o$90bo$89b2o2b211o$88b3o$89bo4b210o$89b2ob2o$92b
212o$97b2o$94bo6b203o$94bo5bo$101b203o$99bo$99b205o$98bo$97b2o2b203o$
96b3o$97bo4b202o$97b2ob2o$100b204o$105b2o$102bo6b195o$102bo5bo$109b
195o$107bo$107b197o$106bo$105b2o2b195o$104b3o$105bo4b194o$105b2ob2o$
108b196o$113b2o$110bo6b187o$110bo5bo$117b187o$115bo$115b189o$114bo$
113b2o2b187o$112b3o$113bo4b186o$113b2ob2o$116b188o$121b2o$118bo6b179o$
118bo5bo$125b179o$123bo$123b181o$122bo$121b2o2b179o$120b3o$121bo4b178o
$121b2ob2o$124b180o$129b2o$126bo6b171o$126bo5bo$133b171o$131bo$131b
173o$130bo$129b2o2b171o$128b3o$129bo4b170o$129b2ob2o$132b172o$137b2o$
134bo6b163o$134bo5bo$141b163o$139bo$139b165o$138bo$137b167o$136bo$136b
168o$135bo$134b2o2b166o$133b3o$134bo4b165o$134b2ob2o$137b167o$142b2o3b
2o3b2o3b2o$139bo5bo4bo4bo5b143o$139bo5bo4bo4bo4bo$161b143o$159bo$159b
145o$158bo$157b2o2b143o$156b3o$157bo4b142o$157b2ob2o$160b144o$165b2o$
162bo6b135o$162bo5bo$169b135o$167bo$167b137o$166bo$165b2o2b135o$164b3o
$165bo4b134o$165b2ob2o$168b136o$173b2o$170bo6b127o$170bo5bo$177b127o$
175bo$175b129o$174bo$173b2o2b127o$172b3o$173bo4b126o$173b2ob2o$176b
128o$181b2o$178bo6b119o$178bo5bo$185b119o$183bo$183b121o$182bo$181b2o
2b119o$180b3o$181bo4b118o$181b2ob2o$184b120o$189b2o$186bo6b111o$186bo
5bo$193b111o$191bo$191b113o$190bo$189b2o2b111o$188b3o$189bo4b110o$189b
2ob2o$192b112o$197b2o$194bo6b103o$194bo5bo$201b103o$199bo$199b105o$
198bo$197b2o2b103o$196b3o$197bo4b102o$197b2ob2o$200b104o$205b2o$202bo
6b95o$202bo5bo$209b95o$207bo$207b97o$206bo$205b2o2b95o$204b3o$205bo4b
94o$205b2ob2o$208b96o$213b2o$210bo6b87o$210bo5bo$217b87o$215bo$215b89o
$214bo$213b91o$212bo$212b92o$211bo$210b2o2b90o$209b3o$210bo4b89o$210b
2ob2o$213b91o$218b2o3b2o3b2o3b2o$215bo5bo4bo4bo5b67o$215bo5bo4bo4bo4bo
$237b67o$235bo$235b69o$234bo$233b2o2b67o$232b3o$233bo4b66o$233b2ob2o$
236b68o$241b2o$238bo6b59o$238bo5bo$245b59o$243bo$243b61o$242bo$241b2o
2b59o$240b3o$241bo4b58o$241b2ob2o$244b60o$249b2o$246bo6b51o$246bo5bo$
253b51o$251bo$251b53o$250bo$249b2o2b51o$248b3o$249bo4b50o$249b2ob2o$
252b52o$257b2o$254bo6b43o$254bo5bo$261b43o$259bo$259b45o$258bo$257b2o
2b43o$256b3o$257bo4b42o$257b2ob2o$260b44o$265b2o$262bo6b35o$262bo5bo$
269b35o$267bo$267b37o$266bo$265b2o2b35o$264b3o$265bo4b34o$265b2ob2o$
268b36o$273b2o$270bo6b27o$270bo5bo$277b27o$275bo$275b29o$274bo$273b2o
2b27o$272b3o$273bo4b26o$273b2ob2o$276b28o$281b2o$278bo6b19o$278bo5bo$
285b19o$283bo$283b21o$282bo$281b2o2b19o$280b3o$281bo4b18o$281b2ob2o$
284b20o$289b2o$286bo6b11o$286bo5bo$293b11o$291bo$291b13o$290bo$289b15o
$288bo$288b16o$287bo$286b2o2b14o$285b3o$286bo4b13o$286b2ob2o$289b15o$
294b2o3b2o$291bo5bo4bo$291bo5bo4bo!
This 2c/3 up wave has a spatial period of (76 right, 100 down), and although we would not choose to view it that way normally, can be read as 76c/150 sideways. Both 2c/3 and 76c/150 are faster than c/2.

HartmutHolzwart
Posts: 840
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Location: Germany

Re: Level wave speed limit?

Post by HartmutHolzwart » January 30th, 2023, 5:44 am

A good conjecture which turned out to be false! These hyper speed waves are super-interesting. Could you find more examples?

The general hypothesis with CGol: If there is no small local argument that something is impossible, then it's possible, if you just enlarge the search space enough.

Great work!

amling
Posts: 704
Joined: April 2nd, 2020, 9:47 pm

Re: Level wave speed limit?

Post by amling » January 30th, 2023, 4:02 pm

HartmutHolzwart wrote:
January 30th, 2023, 5:44 am
Could you find more examples?
My techniques can probably be guessed from the shape of the result, but for completeness what I have done...

I had originally looked at specifying both speeds explicitly and doing a wrapped LGOL search. I had done 2c/3 and speeds between c/2 and c, e.g. 2c/3 x 2c/3, 2c/3 x 3c/4, 2c/3 x 3c/5, 2c/3 x 4c/5, etc... These were mostly finishing quickly and negatively but 2c/3 x 4c/7 (and multiples) find that cycle of stripes and speeds near c/2, like 2c/3 x 9c/17 were taking long and producing huge partials with suggestive shapes (mostly that same 2c/3 x c/2 front but with a little "jumps" in the middle). I killed 10c/19 rather than wait it out and went to try to solve just a single jump in 2c/3.

This is non-wrapped so it can use LLSSS which can search very large 2c/3 boards quickly. I set up two almost-aligned 2c/3 x c/2 edges with the "bottom" side one gen forward from where it would have been to match the "top" side. Any solution connecting them, no matter how wide, would make it faster than c/2 when read sideways. Somewhere in some output I spotted a front that had led to known 2c/3 bits I could patch up by hand to complete the front "spreading" side. Making the back "clearing" side was always going to be easy and was just a matter of getting everything aligned (e.g. I chose to double the front).

This sort of dirty trick is going to be limited to 2c/3 x some speed just a hair over c/2, of which I am sure I could produce endless examples. I may eventually go back and run more of the LGOL two-specified-speed searches with various speeds strictly between c/2 and c (stuff like 3c/5 x 4c/7).

I am still quite shocked by these existing. They defy my intuition that c/2 is the fastest speed anything can travel without something pulling it. Whenever I looked at a wave that could be read as greater than c/2 one way it was always clear to me it was being pulled from that side, but now this wave is pulling itself from both sides?
Last edited by amling on January 31st, 2023, 3:39 am, edited 1 time in total.

amling
Posts: 704
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Re: Level wave speed limit?

Post by amling » January 31st, 2023, 3:39 am

amling wrote:
January 30th, 2023, 4:02 pm
I may eventually go back and run more of the LGOL two-specified-speed searches with various speeds strictly between c/2 and c (stuff like 3c/5 x 4c/7).
I had forgotten, but I had run some already and I ran some more. In the end I did this vaguely haphazard assortment of pairs (mostly lowish numerators and/or whatever finished under a short timeout). Within a pair the earlier (numerator, denominator) is listed first (e.g. 2c/3 < 4c/5 due to 2 < 4 and 2c/3 < 2c/4 due to 2 == 2 and 3 < 4). Pairs are then sorted by (first numerator, first denominator, second numerator, second denominator):

Code: Select all

c x 2c/3
c x 3c/4
c x 3c/5
c x 4c/5
c x 4c/6
c x 4c/7
c x 5c/6
c x 5c/7
c x 5c/8
c x 5c/9
c x 6c/7
c x 6c/8
c x 6c/9
c x 6c/10
c x 6c/11
c x 7c/8
c x 7c/9
c x 7c/10
c x 7c/11
c x 7c/12
c x 7c/13
2c/2 x 2c/3
2c/2 x 3c/4
2c/2 x 3c/5
2c/2 x 4c/5
2c/2 x 4c/6
2c/2 x 4c/7
2c/2 x 5c/6
2c/2 x 5c/7
2c/2 x 5c/8
2c/2 x 5c/9
2c/2 x 6c/7
2c/2 x 6c/8
2c/2 x 6c/9
2c/2 x 6c/10
2c/2 x 6c/11
2c/2 x 7c/8
2c/2 x 7c/9
2c/2 x 7c/10
2c/2 x 7c/11
2c/2 x 7c/12
2c/2 x 7c/13
2c/3 x 2c/3
2c/3 x 3c/3
2c/3 x 3c/4
2c/3 x 3c/5
2c/3 x 4c/4
2c/3 x 4c/5
2c/3 x 4c/6
2c/3 x 4c/7
2c/3 x 5c/5
2c/3 x 5c/6
2c/3 x 5c/7
2c/3 x 5c/8
2c/3 x 5c/9
2c/3 x 6c/6
2c/3 x 6c/7
2c/3 x 6c/8
2c/3 x 6c/9
2c/3 x 6c/10
2c/3 x 6c/11
2c/3 x 7c/7
2c/3 x 7c/8
2c/3 x 7c/9
2c/3 x 7c/10
2c/3 x 7c/11
2c/3 x 7c/12
2c/3 x 7c/13
2c/3 x 8c/9
2c/3 x 8c/10
2c/3 x 8c/11
2c/3 x 8c/12
2c/3 x 8c/13
2c/3 x 8c/14
2c/3 x 8c/15
2c/3 x 9c/10
2c/3 x 9c/11
2c/3 x 9c/12
2c/3 x 9c/13
2c/3 x 9c/14
2c/3 x 9c/15
2c/3 x 9c/16
2c/3 x 9c/17
2c/3 x 10c/11
2c/3 x 10c/12
2c/3 x 10c/13
2c/3 x 10c/14
2c/3 x 10c/15
2c/3 x 10c/16
2c/3 x 10c/17
2c/3 x 10c/18
2c/3 x 11c/12
2c/3 x 11c/13
2c/3 x 11c/14
2c/3 x 11c/15
2c/3 x 11c/16
2c/3 x 11c/17
2c/3 x 12c/13
2c/3 x 12c/14
2c/3 x 12c/15
2c/3 x 12c/16
2c/3 x 12c/17
2c/3 x 13c/14
2c/3 x 13c/15
2c/3 x 13c/16
2c/3 x 13c/17
2c/3 x 14c/15
2c/3 x 14c/16
2c/3 x 14c/17
2c/3 x 15c/16
2c/3 x 15c/17
2c/3 x 16c/17
3c/3 x 3c/4
3c/3 x 3c/5
3c/3 x 4c/5
3c/3 x 4c/6
3c/3 x 4c/7
3c/3 x 5c/6
3c/3 x 5c/7
3c/3 x 5c/8
3c/3 x 5c/9
3c/3 x 6c/7
3c/3 x 6c/8
3c/3 x 6c/9
3c/3 x 6c/10
3c/3 x 6c/11
3c/3 x 7c/8
3c/3 x 7c/9
3c/3 x 7c/10
3c/3 x 7c/11
3c/3 x 7c/12
3c/3 x 7c/13
3c/4 x 3c/4
3c/4 x 3c/5
3c/4 x 4c/4
3c/4 x 4c/5
3c/4 x 4c/6
3c/4 x 4c/7
3c/4 x 5c/5
3c/4 x 5c/6
3c/4 x 5c/7
3c/4 x 5c/8
3c/4 x 5c/9
3c/4 x 6c/6
3c/4 x 6c/7
3c/4 x 6c/8
3c/4 x 6c/9
3c/4 x 6c/10
3c/4 x 6c/11
3c/4 x 7c/7
3c/4 x 7c/8
3c/4 x 7c/9
3c/4 x 7c/10
3c/4 x 7c/11
3c/4 x 7c/12
3c/5 x 3c/5
3c/5 x 4c/4
3c/5 x 4c/5
3c/5 x 4c/6
3c/5 x 4c/7
3c/5 x 5c/5
3c/5 x 5c/6
3c/5 x 5c/7
3c/5 x 5c/8
3c/5 x 5c/9
3c/5 x 6c/6
3c/5 x 6c/7
3c/5 x 6c/8
3c/5 x 6c/9
3c/5 x 6c/10
3c/5 x 7c/7
3c/5 x 7c/8
3c/5 x 7c/9
3c/5 x 7c/10
3c/5 x 7c/11
4c/4 x 4c/5
4c/4 x 4c/6
4c/4 x 4c/7
4c/4 x 5c/6
4c/4 x 5c/7
4c/4 x 5c/8
4c/4 x 5c/9
4c/4 x 6c/7
4c/4 x 6c/8
4c/4 x 6c/9
4c/4 x 6c/10
4c/4 x 7c/8
4c/4 x 7c/9
4c/4 x 7c/10
4c/4 x 7c/11
4c/5 x 4c/5
4c/5 x 4c/6
4c/5 x 4c/7
4c/5 x 5c/5
4c/5 x 5c/6
4c/5 x 5c/7
4c/5 x 5c/8
4c/5 x 5c/9
4c/5 x 6c/6
4c/5 x 6c/7
4c/5 x 6c/8
4c/5 x 6c/9
4c/5 x 6c/10
4c/5 x 7c/7
4c/5 x 7c/8
4c/5 x 7c/9
4c/5 x 7c/10
4c/5 x 7c/11
4c/6 x 4c/6
4c/6 x 4c/7
4c/6 x 5c/5
4c/6 x 5c/6
4c/6 x 5c/7
4c/6 x 5c/8
4c/6 x 5c/9
4c/6 x 6c/6
4c/6 x 6c/7
4c/6 x 6c/8
4c/6 x 6c/9
4c/6 x 7c/7
4c/6 x 7c/8
4c/6 x 7c/9
4c/7 x 4c/7
4c/7 x 5c/5
4c/7 x 5c/6
4c/7 x 5c/7
4c/7 x 5c/8
4c/7 x 5c/9
4c/7 x 6c/6
4c/7 x 6c/7
4c/7 x 7c/7
5c/5 x 5c/6
5c/5 x 5c/7
5c/5 x 5c/8
5c/5 x 5c/9
5c/5 x 6c/7
5c/5 x 6c/8
5c/5 x 6c/9
5c/5 x 6c/10
5c/5 x 7c/8
5c/5 x 7c/9
5c/5 x 7c/10
5c/5 x 7c/11
5c/6 x 5c/6
5c/6 x 5c/7
5c/6 x 5c/8
5c/6 x 5c/9
5c/6 x 6c/6
5c/6 x 6c/7
5c/6 x 6c/8
5c/6 x 6c/9
5c/6 x 7c/7
5c/6 x 7c/8
5c/6 x 7c/9
5c/6 x 7c/10
5c/7 x 5c/7
5c/7 x 5c/8
5c/7 x 5c/9
5c/7 x 6c/6
5c/7 x 6c/7
5c/7 x 6c/8
5c/7 x 7c/7
5c/7 x 7c/8
5c/7 x 7c/9
5c/8 x 5c/8
5c/8 x 5c/9
5c/8 x 6c/6
5c/8 x 6c/7
5c/8 x 7c/7
6c/6 x 6c/7
6c/6 x 6c/8
6c/6 x 6c/9
6c/6 x 7c/8
6c/6 x 7c/9
6c/6 x 7c/10
6c/7 x 6c/7
6c/7 x 6c/8
6c/7 x 7c/7
6c/7 x 7c/8
6c/7 x 7c/9
6c/8 x 6c/8
6c/8 x 7c/7
6c/8 x 7c/8
6c/9 x 7c/7
7c/7 x 7c/8
7c/7 x 7c/9
7c/7 x 7c/10
7c/8 x 7c/8
7c/8 x 7c/9
No results except for those same stripe cycles at 2c/3 x 4c/7 and multiples.

Some of these can be statically proven to not even have a front. In particular I think any pair of a speed with itself should be impossible via an envelope argument (diagonal envelope can only advance one every other generation due to 4 missing from the S part of S23/B3). Interestingly then 4c/7 x 4c/7 (even multiples) cannot have a front but 2c/3 x 4c/7 does even though 2c/3 > 4c/7 is faster!

amling
Posts: 704
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Re: Level wave speed limit?

Post by amling » February 4th, 2023, 4:22 pm

amling wrote:
January 26th, 2023, 9:16 pm
I hacked up a copy of LLSSS to do some weird wrapping searches and barring a bug I believe it has shown there are no level waves of unreduced speeds 2c/3, 3c/4, 3c/5, 4c/5, 4c/6, 5c/6, 4c/7, 5c/7, 6c/7, 5c/8, 6c/8, 7c/8, 6c/9, 7c/9, 8c/9, 7c/10, 8c/10, or 9c/10 (all periods up to 10 except for 5c/9 and 6c/10). It tended to run slower and take more memory closer to c/2 (which is why I did not complete 5c/9 or 6c/10).
5c/9 completed. 6c/10 did not complete given 60G of memory.

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pzq_alex
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Re: Level wave speed limit?

Post by pzq_alex » February 5th, 2023, 12:14 am

HartmutHolzwart wrote:
January 30th, 2023, 5:44 am
The general hypothesis with CGol: If there is no small local argument that something is impossible, then it's possible, if you just enlarge the search space enough.
This topic was also brought up on Discord a while ago. It was proved that

Theorem. For a range-1 rule and a speed (x, y)c/p, we have the following dichotomy:
  • Either there is a (x, y)c/p object in the rule;
  • or there exists u, v with u>2x, v>2y such that no nonempty u by v pattern satisfies that it truncated to (u-2x) by (v-2y), translated by (x, y) matches its generation p.
Basically, a rule has no (x, y)c/p iff one can rule such patterns out by an argument in a fix-sized box. The argument translates over to two speeds with no problem. However, one catch is that the objects can be infinite! I don't know of a version of this theorem that asserts the existence of finite objects.

By the way, the same argument also shows that a pattern has no predecessor (aka is a GoE) iff there exists a finite set of cells such that setting the rest to "don't care" cells has no predecessor (aka contains an orphan).
\sum_{n=1}^\infty H_n/n^2 = \zeta(3)

How much of current CA technology can I redevelop "on a desert island"?

HartmutHolzwart
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Location: Germany

Re: Level wave speed limit?

Post by HartmutHolzwart » February 6th, 2023, 7:15 am

I think that your example is optimal for the slope, i.e. given a pattern that is completely contained in one half plane of that slope, then it cannot move with speed higher than the ones you reached with the pattern. At least for slope near 1 it should be provable by looking at how the boundary can move in 4 generations.

I have to think about that in more detail!

amling
Posts: 704
Joined: April 2nd, 2020, 9:47 pm

Re: Level wave speed limit?

Post by amling » February 7th, 2023, 3:48 pm

HartmutHolzwart wrote:
February 6th, 2023, 7:15 am
I think that your example is optimal for the slope, i.e. given a pattern that is completely contained in one half plane of that slope, then it cannot move with speed higher than the ones you reached with the pattern. At least for slope near 1 it should be provable by looking at how the boundary can move in 4 generations.

I have to think about that in more detail!
A 7/6 slope envelope looks like this:

Code: Select all

??.................
??.................
???................
????...............
?????..............
??????.............
???????............
????????...........
????????...........
?????????..........
??????????.........
???????????........
????????????.......
?????????????......
??????????????.....
??????????????.....
???????????????....
????????????????...
?????????????????..
??????????????????.
???????????????????
Mostly diagonal but with vertical "jogs" every 6 columns. I believe the usual diagonal envelope argument (the one that relies on the missing S4) will rule out a bunch of cells two generations later, giving us this envelope:

Code: Select all

???................
????...............
????...............
?????..............
??????.............
???????............
????????...........
?????????..........
??????????.........
??????????.........
???????????........
????????????.......
?????????????......
??????????????.....
???????????????....
????????????????...
????????????????...
?????????????????..
??????????????????.
???????????????????
???????????????????
Everything has moved up 1 and the jogs have moved two columns right. Repeating this twice more, 6 generations later the jogs will have returned to their original positions and we will have moved 3 steps up from the normal pace plus 1 from having hiked up one jog. This gives a 4c/6 north bound (2c/3 reduced) on speed and the ratio with the slope gives us a 4c/7 (reduced) east.

More generally for (N+K)/N slope where K is small enough to separate the jogs this argument is going to give us (1/2 + K/N)c north and (N/2 + K)/(N + K)c east. Above N = 6, K = 1 and we recover 2c/3 and 4c/7.

EDIT: N=8, K=1 is 5c/8 x 5c/9 which had produced a modest partial:

Code: Select all

.                                       
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..                                      
...                                     
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*.....                                  
**.....                                 
*.......                                
*.**.....                               
*.*.*....                               
*...*.....                              
..**.*.....                             
*.**.**.....                            
..**.*.*.....                           
*.**...**.....                          
*...**..**.....                         
.*.**...*.......                        
*...*...*.**.....                       
 ...*...***.*....                       
  *.....*...*.....                      
   ***.*..**.*.....                     
   ?*.....**.**.....                    
    ?..*.*.*.*.*.....                   
     ..*.****..**.....                  
      ......*...**.....                 
       **.***...*.......                
        .*.*....*.**.....               
         ..*....*.*.*....               
          ...****...*.....              
           *.......*.*.....             
           .***.**...**.....            
            ....*....*.*.....           
             ?*..*.....**.....          
              ?*...***..**.....         
               *.*..*...*.......        
                ..**..*.*.**.....       
                 .*...*****.*....       
                  *...***...*.....      
                   *......**.*.....     
                   ?.*.*..**.**.....    
                    .*...*.*.*.*.....   
                     ***....*..**.....  
                      *.....*...**..... 
                       ?....*...*.......
                        .*......*.**....
                         *.*.*..*.*.*...
                          ....**.*..*...
                           .*.**..**.*..
                           .*.**..**.**.
                            ..*...**.*.*
                             ?..*.*..*.*
                              .**..*.*..
                               *.**.....
                                .*.*....
                                 ..*.*..
                                  **....
                                   .*.*.
                                   .*..*
                                    ..*.
                                     *..
                                      ?*
                                       ?
N=10, K=1 is 6c/10 x 6c/11 which is out of reach for my current wrapped search tools.

amling
Posts: 704
Joined: April 2nd, 2020, 9:47 pm

Re: Level wave speed limit?

Post by amling » February 13th, 2023, 4:42 pm

amling wrote:
January 26th, 2023, 9:16 pm
Are there any known bounds on what level wave speed limits are possible?

I hacked up a copy of LLSSS to do some weird wrapping searches and barring a bug I believe it has shown there are no level waves of unreduced speeds 2c/3, 3c/4, 3c/5, 4c/5, 4c/6, 5c/6, 4c/7, 5c/7, 6c/7, 5c/8, 6c/8, 7c/8, 6c/9, 7c/9, 8c/9, 7c/10, 8c/10, or 9c/10 (all periods up to 10 except for 5c/9 and 6c/10). It tended to run slower and take more memory closer to c/2 (which is why I did not complete 5c/9 or 6c/10).
With all the wild changes in LLSSS those hacks had been tossed in order to let me simplify things. Rewritten against the current code base they can do a lot, lot better. 5c/9 completes 4.59G and 6c/10 completes in 8.01G. I've sketched some additional hacks to dream up what a partial result might look like by picking a vertical slice at random and extending it both left and right however many columns, again choosing these extensions randomly. The width is sort of meaningless since the the hacks don't search with a fixed wrap, it's just a matter of how much crap you want to see.

When I ran 5c/9 the partials all looked similar and the last one was this:

Code: Select all

|                                            |                                            |                                            |                                            |                                            |                                            |                                            |                                            | .......................................... |
|                                            |                                            |                                            |                                            |                                            |                                            | .......................................... | .......................................... | .......................................... |
|                                            |                                            |                                            |                                            | .......................................... | .......................................... | .......................................... | .......................................... | .......................................... |
|                                            |                                            | .......................................... | .......................................... | .......................................... | .......................................... | .......................................... | ..........................*............... | .........................**............... |
| .......................................... | .......................................... | .......................................... | .......................................... | .......................................... | ..........................*............... | ..........*..............***.............. | ..........**.............**............... | ...........*.......***.................... |
| .......................................... | .......................................... | .......................................... | .......................................... | .........................***.............. | .........***.............***.............. | ........****............*................. | ........*...*.....*****.*.***.......**.... | .......***.*********..***..******..*...... |
| .......................................... | .......................................... | .......................................... | ........................*****............. | ........*****...........*...*............. | ........**..*....**.....***.*............. | ........*..**....********...**.....****... | **.....**....*****..***..*...*****.*****.. | **.****.**..**...**....*.*...*.........*.. |
| .......................................... | .......................................... | ...............*.......*******............ | .......*******.**..*...*.***..*........... | .......*..***...****...*....*............. | ........*....*..*..*****....**....******.. | ***.....*..*.****.**...**.....******..**.. | .******.*..*..***....*.....*..******..**.. | *...**..*....*......*...*.**.............. |
| ....................*..................... | ..............***..**.*********........... | ......***********.***..**...***........... | .......***.......**.*.*...*....*.......... | ...........**...***.***...**..**.********. | ****..**..*.**.**...***...***.****..**..*. | *..*****....**.........*...**...........*. | ..**..**..........*...***..**.......*...** | ......****.***...*******..*..*.********.** |
| ........*.**.*****.*************.......... | .....*********...*.*.....***...*.......... | ....*.....****.*.*.**..*.....***.......... | .....*.**...........*..**......*********** | *****.**......*...*........*...*..**..**.. | .**.**.........**.*...........****......*. | ....**..****..****...*......***..**.***.** | *..*.....***.**...**.*.....**........*..*. |                                            |
| ....****.*.*..***....****...****.......... | *...******...*...*..............*......... | **..*........*..***........*....********** | *****....*...***...*********....**..**..** | *..**....*.....*...****....**............. | ......**.**..............*.*.......*..***. |                                            |                                            |                                            |
| **.*..*...**...*......*..*...*.*.......... | **.*..**.*..*...*.....*..**......********* | .*.*.....**.*...**...**.***.***...**..**.. | .**..**.*..****...*......***.*..*......... |                                            |                                            |                                            |                                            |                                            |
| .*.*......**..*.....*...*.***.*.********** | .*.*.....*...****...*.***.********..**..** |                                            |                                            |                                            |                                            |                                            |                                            |                                            |
| ..*....*..*.**.*.*.*.**..*........**..**.. |                                            |                                            |                                            |                                            |                                            |                                            |                                            |                                            |
Subjectively it does not give me anxiety about the original conjecture about the nonexistence of level waves between c/2 and c. However for 6c/10 the last partial was this:

Code: Select all

|                                            |                                            |                                            |                                            |                                            |                                            |                                            |                                            |                                            | .......................................... |
|                                            |                                            |                                            |                                            |                                            |                                            |                                            | .......................................... | .......................................... | .......................................... |
|                                            |                                            |                                            |                                            |                                            | .......................................... | .......................................... | .......................................... | .......................................... | ...........***...........***...........*** |
|                                            |                                            |                                            |                                            | .......................................... | .......................................... | .......................................... | .......................................... | *.........*****.........*****.........**** | .*..***..*.....*..***..*.....*..***..*.... |
|                                            |                                            | .......................................... | .......................................... | .......................................... | .....*.............*.............*........ | .......................................... | **.......*******.......*******.......***** | **.*****.*******.*****.*******.*****.***** | .**.***.**.....**.***.**.....**.***.**.... |
| .......................................... | .......................................... | .......................................... | .......................................... | ....***...........***...........***....... | .....*......*......*......*......*......*. | ***..*..*********..*..*********..*..****** | .*********.....*********.....*********.... | .*.......*.***.*.......*.***.*.......*.*** | ....***...........***...........***....... |
| .......................................... | .......................................... | .......................................... | ...*****.........*****.........*****...... | ..*.....*..***..*.....*..***..*.....*..*** | ****.*.*****.*****.*.*****.*****.*.*****.* | *..**.**..*****..**.**..*****..**.**..**** | ...*****.........*****.........*****...... | **.......**...**.......**...**.......**... | .**.....**...****.....**.....**.....**...* |
| ............*.............*.............*. | .......................................... | ..*******.......*******.......*******..... | *.*******.*****.*******.*****.*******.**** | .**.....**.***.**.....**.***.**.....**.*** | .**.....**.....**.....**.....**.....**.... | ...*...*...*.*...*...*...*.*...*...*...*.* | *..*...*..**.**..*.***..**.**..*...*..**.* | ...*...*..**....*....*...***...*...*..**.. | *****.......**..**..*.*.*********.......** |
| .....*......*......*......*......*......*. | .*********..*..*********..*..*********..*. | ***.....*********.....*********.....****** | ..*.***.*.......*.***.*.......*.***.*..... | ...........***...........***...........*** | ...........*.*...........*.*...........*.* | .....**...........*..............**....... | ....*.*...*.....*.*.......*.....*.*...*... | ..*.**....**.**.*.**.*....*...*.**....**.* | ..*..**...***.*.*.**.*........*..**...***. |
| *****.*****.*.*****.*****.*.*****.*****.*. | *..*****..**.**..*****..**.**..*****..**.* | *.........*****.........*****.........**** | ..**...**.......**...**.......**...**..... | .**.....**.....****...**.....**.....**.... | ....******.*.*.*****............******.*.* | ...*.....*.*.*..***.......*....*.....*.*.* | ..***.........*.*....*....*...***......... | ..*.**.........*..*..**..**...*.**........ | ....***.***.*...*.**.....**.....***.***.*. |
| .**.....**.....**.....**.....**.....**.... | *...*.*...*...*...*.*...*...*...*.*...*... | *..**.**..***.*..**.**..*...*..**.**..***. | *...***...*....*....**..*...*...***...*... | ********.*.*..**..**.......*********.*.*.. | ...*****.*.***.......**....*...*****.*.*** | *.**.....*.*.*.*.**.***...***.**.....*.*.* | ..**....*....*....*****...**..**....*....* | .......***...**.*....**............***...* | .**.*..*...****.**..*....**..**.*..*...*.* |
| ....*.*...........*.*...........*.*....... | .............*...........**..............* | .....*.......*.*.....*...*.*.....*.......* | .*...*....*.**.*.**.**....**.*...*....*.** | .*........*.**.*.*****.....*.*........*.** | .*.*...**....*.*.....*....**.*.*...**....* | ...*.*.*.....*.......*.*.......*.*.*.....* | ...*..*.**.*..*.****.....***...*..*.**.*.. | *.**....*****.*.*....*...*..*.**....****** | .***...*..**........***......***...*..**.. |
| ............*****.*.*.******............** | *...*........***..*.*.*.....*...*........* | **...*....*....*.*.........***...*....*... | .*...*...**..*.*.*...........*...*...**..* | .....**..***.*...****....*.......**..***.* | ..*......***.*...*....*.****..*......***.* | ...*..*..***.....*..******.....*..*..***.. | .......*..*.*.*.*.*........*.......*..*.*. | ..*..*......***....*.....*..*..***......*. |                                            |
| *...**...**.......***.*.*****...**...**... | **...**..***.**.*.*.*.*.....**...**..***.* | *..**.**.*****..*.*...*....**..**.**.***** | ......*..*...*......*.*.*.**......*..*...* | ***..........*.*.....*.**.*.***........... | ***..**.*..*...*.***.*.*....***..**.*...** | *.*****......*.*.*.*.*.******....**......* | .**..***.*.*...***...*....*.*.*.**.**.***. |                                            |                                            |
| *.*...**..*.....*....*..*...*.*...**..*... | *.*.*.**..*....*.*.***.**...*.*.*.**..*... | ..***......*.*.***********....***......*.* | .**.....**.*.*.**...*...**...**.....**.... | .*...*..**.*...**....*.*****..*..*..***.*. | .*..**.***.**.**..**.*........**..****.*.. |                                            |                                            |                                            |                                            |
| .**.*...**....*.*........**..**.*...**.... | *.*..**.**....*.........*.***.*..**.**.... | *...*....*....*...*...*...***...***.*..*.* | *...**....*.***.*...........***..***...*.* | ...*.***.**.*...******..*..**..*..**....*. |                                            |                                            |                                            |                                            |                                            |
| .*..*..*.....*.****.*....**..*..*..*.....* | ....*..**....*.....***..**...***.....**.** | ....*...*..*..*...********.**..*...*..**.. |                                            |                                            |                                            |                                            |                                            |                                            |                                            |
| **..*.*......*..*...**.*...**........*.*.* |                                            |                                            |                                            |                                            |                                            |                                            |                                            |                                            |                                            |
This makes me quite suspicious the conjecture could be false. At a minimum if it's true it will have to be true in a way other than what I would have expected. Namely I had assumed the way it would be true is that no wave front would exist to "pull the rest" (something something lightspeed exceptions somehow able to support themselves). The partials I saw for 5c/9 (and a few other speeds I reran) seem plausible for this sort of belief, but this 6c/10 partial shakes it to the core. That 6c/10 front seems like it's keeping itself up the same way the 2c/2 level wave does.

Unfortunately I'm sort of at a loss for what to do next. Doubling to 12c/20 to try for a completion of this is hopeless. I can get the code to run but it's clearly gonna fill memory and die before it gets anywhere. I may give up on this 6c/10 partial and instead push the original searches to 6c/11, 6c/12, etc. TBD.

HartmutHolzwart
Posts: 840
Joined: June 27th, 2009, 10:58 am
Location: Germany

Re: Level wave speed limit?

Post by HartmutHolzwart » February 13th, 2023, 7:04 pm

could you post that in rle format? Or something Golly compatible?

Thanks in advance!

hotdogPi
Posts: 1589
Joined: August 12th, 2020, 8:22 pm

Re: Level wave speed limit?

Post by hotdogPi » February 13th, 2023, 7:22 pm

HartmutHolzwart wrote:
February 13th, 2023, 7:04 pm
could you post that in rle format? Or something Golly compatible?

Thanks in advance!
You can paste it into Golly as is, although you'll have to remove the dividers.
User:HotdogPi/My discoveries

Periods discovered: 5-16,⑱,⑳G,㉑G,㉒㉔㉕,㉗-㉛,㉜SG,㉞㉟㊱㊳㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,62-66,68,70,73,74S,75,76S,80,84,88,90,96
100,02S,06,08,10,12,14G,16,17G,20,26G,28,38,47,48,54,56,72,74,80,92,96S
217,486,576

S: SKOP
G: gun

amling
Posts: 704
Joined: April 2nd, 2020, 9:47 pm

Re: Level wave speed limit?

Post by amling » February 13th, 2023, 7:24 pm

hotdogPi wrote:
February 13th, 2023, 7:22 pm
HartmutHolzwart wrote:
February 13th, 2023, 7:04 pm
could you post that in rle format? Or something Golly compatible?

Thanks in advance!
You can paste it into Golly as is, although you'll have to remove the dividers.
Normally I provide the first generation separately in partials I post, but for these it's so short that one generation really doesn't make much sense on its own. The raw format also makes clear the difference between "this cell is off" (period) and "this cell is not part of the display (space).

Here is the RLE of the 5c/9 all mashed together:

Code: Select all

x = 439, y = 82, rule = B3/S23
16$12bo44bo44bo44bo44bo44bo44bo44bo44bo44bo$12bo44bo44bo44bo44bo44bo
44bo44bo44bo44bo$12bo44bo44bo44bo44bo44bo44bo44bo44bo44bo$12bo44bo44bo
44bo44bo44bo44bo44bo27bo16bo26b2o16bo$12bo44bo44bo44bo44bo44bo27bo16bo
11bo14b3o15bo11b2o13b2o16bo12bo7b3o21bo$12bo44bo44bo44bo44bo26b3o15bo
10b3o13b3o15bo9b4o12bo18bo9bo3bo5b5obob3o7b2o5bo8b3ob9o2b3o2b6o2bo7bo$
12bo44bo44bo44bo25b5o14bo9b5o11bo3bo14bo9b2o2bo4b2o5b3obo14bo9bo2b2o4b
8o3b2o5b4o4bob2o5b2o4b5o2b3o2bo3b5ob5o3bob2ob4ob2o2b2o3b2o4bobo3bo9bo
3bo$12bo44bo44bo16bo7b7o13bo8b7ob2o2bo3bob3o2bo12bo8bo2b3o3b4o3bo4bo
14bo9bo4bo2bo2b5o4b2o4b6o3bob3o5bo2bob4ob2o3b2o5b6o2b2o3bo2b6obo2bo2b
3o4bo5bo2b6o2b2o3bobo3b2o2bo4bo6bo3bob2o15bo$12bo21bo22bo15b3o2b2ob9o
12bo7b11ob3o2b2o3b3o12bo8b3o7b2obobo3bo4bo11bo12b2o3b3ob3o3b2o2b2ob8o
2bob4o2b2o2bob2ob2o3b3o3b3ob4o2b2o2bo2bobo2b5o4b2o9bo3b2o11bo2bo3b2o2b
2o10bo3b3o2b2o7bo3b2obo7b4ob3o3b7o2bo2bob8ob2obo$12bo9bob2ob5ob13o11bo
6b9o3bobo5b3o3bo11bo5bo5b4obobob2o2bo5b3o11bo6bob2o11bo2b2o6b11obob5ob
2o6bo3bo8bo3bo2b2o2b2o3bo2b2ob2o9b2obo11b4o6bo2bo5b2o2b4o2b4o3bo6b3o2b
2ob3ob2obobo2bo5b3ob2o3b2obo5b2o8bo2bo2bo44bo$12bo5b4obobo2b3o4b4o3b4o
11bobo3b6o3bo3bo14bo10bob2o2bo8bo2b3o8bo4b10obob5o4bo3b3o3b9o4b2o2b2o
2b2obobo2b2o4bo5bo3b4o4b2o14bo7b2ob2o14bobo7bo2b3o2bo44bo44bo44bo$12bo
b2obo2bo3b2o3bo6bo2bo3bobo11bob2obo2b2obo2bo3bo5bo2b2o6b9obo2bobo5b2ob
o3b2o3b2ob3ob3o3b2o2b2o3bo2b2o2b2obo2b4o3bo6b3obo2bo10bo44bo44bo44bo
44bo44bo$12bo2bobo6b2o2bo5bo3bob3obob10obo2bobo5bo3b4o3bob3ob8o2b2o2b
2obo44bo44bo44bo44bo44bo44bo44bo$12bo3bo4bo2bob2obobobob2o2bo8b2o2b2o
3bo44bo44bo44bo44bo44bo44bo44bo44bo!
And the 6c/10:

Code: Select all

x = 501, y = 65, rule = B3/S23
14$11bo44bo44bo44bo44bo44bo44bo44bo44bo44bo44bo$11bo44bo44bo44bo44bo
44bo44bo44bo44bo44bo44bo$11bo44bo44bo44bo44bo44bo44bo44bo44bo44bo12b3o
11b3o11b3obo$11bo44bo44bo44bo44bo44bo44bo44bo44bobo9b5o9b5o9b4obo2bo2b
3o2bo5bo2b3o2bo5bo2b3o2bo5bo$11bo44bo44bo44bo44bo44bo6bo13bo13bo9bo44b
ob2o7b7o7b7o7b5obob2ob5ob7ob5ob7ob5ob5obo2b2ob3ob2o5b2ob3ob2o5b2ob3ob
2o5bo$11bo44bo44bo44bo44bo5b3o11b3o11b3o8bo6bo6bo6bo6bo6bo6bo2bob3o2bo
2b9o2bo2b9o2bo2b6obo2b9o5b9o5b9o5bo2bo7bob3obo7bob3obo7bob3obo5b3o11b
3o11b3o8bo$11bo44bo44bo44bo4b5o9b5o9b5o7bo3bo5bo2b3o2bo5bo2b3o2bo5bo2b
3obob4obob5ob5obob5ob5obob5obobobo2b2ob2o2b5o2b2ob2o2b5o2b2ob2o2b4obo
4b5o9b5o9b5o7bob2o7b2o3b2o7b2o3b2o7b2o4bo2b2o5b2o3b4o5b2o5b2o5b2o3bobo
$11bo13bo13bo13bo2bo44bo3b7o7b7o7b7o6bobob7ob5ob7ob5ob7ob4obo2b2o5b2ob
3ob2o5b2ob3ob2o5b2ob3obo2b2o5b2o5b2o5b2o5b2o5b2o5bo4bo3bo3bobo3bo3bo3b
obo3bo3bo3bobobobo2bo3bo2b2ob2o2bob3o2b2ob2o2bo3bo2b2obobo4bo3bo2b2o4b
o4bo3b3o3bo3bo2b2o3bob5o7b2o2b2o2bobob9o7b2obo$11bo6bo6bo6bo6bo6bo6bo
2bo2b9o2bo2b9o2bo2b9o2bo2bob3o5b9o5b9o5b6obo3bob3obo7bob3obo7bob3obo6b
o12b3o11b3o11b3obo12bobo11bobo11bobobo6b2o11bo14b2o8bo5bobo3bo5bobo7bo
5bobo3bo4bo3bob2o4b2ob2obob2obo4bo3bob2o4b2obobo3bo2b2o3b3obobob2obo8b
o2b2o3b3o2bo$11bob5ob5obob5ob5obob5ob5obo2bobo2b5o2b2ob2o2b5o2b2ob2o2b
5o2b2obobobo9b5o9b5o9b4obo3b2o3b2o7b2o3b2o7b2o3b2o6bo2b2o5b2o5b4o3b2o
5b2o5b2o5bo5b6obobob5o12b6obobobo4bo5bobobo2b3o7bo4bo5bobobobo3b3o9bob
o4bo4bo3b3o10bo3bob2o9bo2bo2b2o2b2o3bob2o9bo5b3ob3obo3bob2o5b2o5b3ob3o
bo2bo$11bo2b2o5b2o5b2o5b2o5b2o5b2o5bobo3bobo3bo3bo3bobo3bo3bo3bobo3bo
4bobo2b2ob2o2b3obo2b2ob2o2bo3bo2b2ob2o2b3o2bobo3b3o3bo4bo4b2o2bo3bo3b
3o3bo4bob8obobo2b2o2b2o7b9obobo3bo4b5obob3o7b2o4bo3b5obob3obobob2o5bob
obobob2ob3o3b3ob2o5bobobobo3b2o4bo4bo4b5o3b2o2b2o4bo4bobo8b3o3b2obo4b
2o12b3o3bobo2b2obo2bo3b4ob2o2bo4b2o2b2obo2bo3bobobo$11bo5bobo11bobo11b
obo8bo14bo11b2o14bobo6bo7bobo5bo3bobo5bo7bobo2bo3bo4bob2obob2ob2o4b2ob
o3bo4bob2obo2bo8bob2obob5o5bobo8bob2obo2bobo3b2o4bobo5bo4b2obobo3b2o4b
obo4bobobo5bo7bobo7bobobo5bobo4bo2bob2obo2bob4o5b3o3bo2bob2obo3bobob2o
4b5obobo4bo3bo2bob2o4b6obo2b3o3bo2b2o8b3o6b3o3bo2b2o3bo$11bo13b5obobob
6o12b2obobo3bo8b3o2bobobo5bo3bo8bobob2o3bo4bo4bobo9b3o3bo4bo4bo2bo3bo
3b2o2bobobo11bo3bo3b2o2bobo6b2o2b3obo3b4o4bo7b2o2b3obobo3bo6b3obo3bo4b
ob4o2bo6b3obobo4bo2bo2b3o5bo2b6o5bo2bo2b3o3bo8bo2bobobobobo8bo7bo2bobo
2bo3bo2bo6b3o4bo5bo2bo2b3o6bo2bo44bo$11bobo3b2o3b2o7b3obob5o3b2o3b2o4b
ob2o3b2o2b3ob2obobobobo5b2o3b2o2b3obobobo2b2ob2ob5o2bobo3bo4b2o2b2ob2o
b5obo7bo2bo3bo6bobobob2o6bo2bo3bobob3o10bobo5bob2obob3o12bob3o2b2obo2b
o3bob3obobo4b3o2b2obo3b2obobob5o6bobobobobob6o4b2o6bobo2b2o2b3obobo3b
3o3bo4bobobob2ob2ob3o2bo44bo44bo$11bobobo3b2o2bo5bo4bo2bo3bobo3b2o2bo
4bobobobob2o2bo4bobob3ob2o3bobobob2o2bo4bo3b3o6bobob11o4b3o6bobobo2b2o
5b2obobob2o3bo3b2o3b2o5b2o5bo2bo3bo2b2obo3b2o4bob5o2bo2bo2b3obo2bo2bo
2b2ob3ob2ob2o2b2obo8b2o2b4obo3bo44bo44bo44bo44bo$11bo2b2obo3b2o4bobo8b
2o2b2obo3b2o5bobobo2b2ob2o4bo9bob3obo2b2ob2o5bobo3bo4bo4bo3bo3bo3b3o3b
3obo2bobobobo3b2o4bob3obo11b3o2b3o3bobobo4bob3ob2obo3b6o2bo2b2o2bo2b2o
4bo2bo44bo44bo44bo44bo44bo$11bo2bo2bo2bo5bob4obo4b2o2bo2bo2bo5bobo5bo
2b2o4bo5b3o2b2o3b3o5b2ob2obo5bo3bo2bo2bo3b8ob2o2bo3bo2b2o3bo44bo44bo
44bo44bo44bo44bo44bo$11bob2o2bobo6bo2bo3b2obo3b2o8bobobobo44bo44bo44bo
44bo44bo44bo44bo44bo44bo!

amling
Posts: 704
Joined: April 2nd, 2020, 9:47 pm

Re: Level wave speed limit?

Post by amling » April 12th, 2023, 2:42 pm

Here is a 2c/3 x 30c/57 wave:

Code: Select all

x = 60, y = 167, rule = B3/S23:T60,200-76
o$o$bo$3o$3bo$b3o$o3bo$2o2b2o$bo2b3o$bo5bo$3ob4o$4bo3bo$o5b4o$bo2bo4b
2o$4bobobo2bo$4bob2obobo$6bo5bo$6bo2bob3o$5b2o2b2o3bo$5b3o4bo2bo$2o9bo
3bo$b2ob2o5bobo2bo$b2ob5ob2o2b4o$5bobobo8bo$3b2ob2ob3o3b4o$19bo$2o3bo
2bobo3b3o2b2o$4bo3bobo3bobo2b3o$3b2o3bo7bo5bo$3b3o10bobob3o$o3b3obo6b
2obo4bo$o3bo2b2o7bo4b4o$o4bo4bo13b2o$3b9o6bo2bobo2bo$o3bo2bo3bob4o4b2o
bobo$5bob3o7bobo3bo3bo$o3bobo2b5o3b12o$ob2o5b5obo7b2o4bo$2b2o3bo5b2o4b
2o4bobo2bo$o2bo2bobo5bo3b3o5bo3bo$o3b3o6bo9b2obobo2bo$4o4b2o4bo3bo7bob
ob3o$4b4obo4b2o10bobo4bo$4o4bobo5b3o7b2obob3o$4b4o2bo4b2o2bo8b3o3bo$2b
2o4bob2o5b4o4bobo2b2o2b2o$bo2bo5b5o6b2obo6bo2b3o$2b2o3bo4b3o3b2o4bo2bo
3bo5bo$2o2b3o6bo2b2obob2o4b6ob4o$3b5ob4o4b2o3bo11bo3bo$4o3bo2bobo4bobo
4b4ob2o5b4o$7bob2obo11b5o2bo2bo4b2o$obo3bo3bo3b2obo2bo13bobobo2bo$b2o
2bo5b3o2bo6b3ob2o5bob2obobo$4b2o3bo4b3ob2o9bo6bo5bo$o9b4o6bo5b2o8bo2bo
b3o$6bo7b4o2bo5bobo6b2o2b2o3bo$4b3o5b2o4bob2o2bo2b3o5b3o4bo2bo$3bo3bo
3bo2b2o2bo4bo6b2o9bo3bo$3b6o3b2o6bo2bo3b3ob2ob2o5bobo2bo$2bo6b3o2b4o5b
o7b2ob5ob2o2b4o$b4o2b3o2b2o6bo3b2obobo5bobobo8bo$o9b3o5bob2ob5o5b2ob2o
b3o3b4o$3o6bo6b2o2bobobo3b2o19bo$3bo4b3ob3o9bo2b5o3bo2bobo3b3o2b2o$bob
2o2bo5b3o4b4o2bo7bo3bobo3bobo2b3o$bo5b4o13b3ob2o3b2o3bo7bo5bo$b3o2bo9b
o2b5o4b2o3b3o10bobob3o$6bobo2bo12b4o2bo3b3obo6b2obo4bo$5obo7b3o4b3o4bo
bo3bo2b2o7bo4b4o$4bobob2o4bo2bo6b5obo4bo4bo13b2o$5obo7b4o4b2o2b2o5b9o
6bo2bobo2bo$12bo6bobo2bo4b2o3bo2bo3bob4o4b2obobo$3ob2obo4b8o2b2o2bo8bo
b3o7bobo3bo3bo$3bo7bo3b2o3b2o6bobo3bobo2b5o3b12o$o3b2o4b3o6bo7b4ob2o5b
5obo7b2o4bo$o4bo3bo3bo5bob3obobo4b2o3bo5b2o4b2o4bobo$9bob3o4bo4bo2b5o
2bo2bobo5bo3b3o5bo$2o3b3o3bo2bo2b4obo3bo2b2o3b3o6bo9b2obobo$2o3b2ob2o
2bo3bo4b6o3b4o4b2o4bo3bo7bobo$3bo3bobobo2bobob4o2b2o8b4obo4b2o10bobo$b
8ob4o2bob2o5bo4b4o4bobo5b3o7b2obo$bo12bobo2bo6bo7b4o2bo4b2o2bo8b2o$b
14obo7b4o4b2o4bob2o5b4o4bobo$ob2o12bobo4bo4bo2bo2bo5b5o6b2obo$6b8ob3o
4b8o2b2o3bo4b3o3b2o4bo2bo$5bo9bo5bo8b2o2b3o6bo2b2obob2o4b3o$5bo4b2o2b
2o5b3o4bo4b5ob4o4b2o3bo$4bo4bo10bo9b4o3bo2bobo4bobo4b4obo$4bobo9bo2b4o
5bo8bob2obo11b5o$4b2o4bo5bo2bo3b2o3b3obo3bo3bo3b2obo2bo$10b2o3bo2b2o3b
2o2bo3b2o2bo5b3o2bo6b3ob2o$4bo4bo5bo3bobo2bob4o4b2o3bo4b3ob2o9bo$9bob
6obo2b2o3bo3bo9b4o6bo5b2o$4b2o2b2obo5bo6bobo9bo7b4o2bo5bobo$5bob3o2b
13obob2o4b3o5b2o4bob2o2bo2b3o$4bob2o2bo15bo6bo3bo3bo2b2o2bo4bo$6b2o2b
15o2bo5b6o3b2o6bo2bo3b3o$26bo5bo6b3o2b4o5bo$7b3ob6o2b6o6b4o2b3o2b2o6bo
3b2obobo$5bo3bob3o8b2o2bo3bo9b3o5bob2ob5o$5bobobo6bo2bo4b2o4b3o6bo6b2o
2bobobo3b2o$6b2obo14b2o3bo3bo4b3ob3o9bo2b3o$7bobobo2b2o4b2o3bo2bo2bob
2o2bo5b3o4b4o2bo$9b2o3bobo2bobo3bobobobo5b4o13b3ob2o$6b2obobob2obo2bob
2ob2o3bob3o2bo9bo2b5o4b2o$9bo3bo3b2o4bo12bobo2bo12b4o$6b2obob2o2b2o2b
2ob13obo7b3o4b3o4bo$5b2ob2o4bo2b2o2bo12bobob2o4bo2bo6b5o$4bo2bobo5bo3b
o5b10obo7b4o4b2o2b2o$4bo2bobo3bo28bo6bobo2bo4bo$7bobob5o2bo7b7ob2obo4b
8o2b2o2bo$5bo20b3o4bo7bo3b2o3b2o6bo$5bobobo3b4o8b2o3bo3b2o4b3o6bo7b3o$
11bo5bo12bo4bo3bo3bo5bob3obobo$14b4o21bob3o4bo4bo2b4o$13bo4bo11b2o3b3o
3bo2bo2b4obo3bo2bo$12b8o9b3o3b2ob2o2bo3bo4b6o$11bo8bo8bo3bo3bobobo2bob
ob4o2b2o$11b10o8bob8ob4o2bob2o5bo$10bo10bo6b2obo12bobo2bo6bo$9b4o2b8o
8b14obo7b4o$8bo13b2o4bobob2o12bobo4bo4bo$8bobo6bobobobo3bo8b8ob3o4b8o$
7b2obo5bo4bo2bobo2bo5bo9bo5bo$11bo4bo2b5o2b2obo5bo4b2o2b2o5b3o4bo$7b4o
6b2o5b2o8bo4bo10bo$7bo4b4o4bo2bob4o5bobo9bo2b4o5bo$13b2o5bo4b2o7b2o4bo
5bo2bo3b2o3b2o$40b2o3bo2b2o3b2o2bo$34bo4bo5bo3bobo2bob4o$39bob6obo2b2o
3bo$34b2o2b2obo5bo6bobo$35bob3o2b13obob2o$34bob2o2bo15bo$36b2o2b15o2bo
$56bo$37b3ob6o2b6o$35bo3bob3o8b2o2bo$35bobobo6bo2bo4b2o$36b2obo14b2o3b
o$37bobobo2b2o4b2o3bo2bo$39b2o3bobo2bobo3bobobo$36b2obobob2obo2bob2ob
2o3bo$39bo3bo3b2o4bo$36b2obob2o2b2o2b2ob8o$35b2ob2o4bo2b2o2bo$34bo2bob
o5bo3bo5b5o$34bo2bobo3bo$37bobob5o2bo7b4o$35bo20b3o$35bobobo3b4o8b2o$
41bo5bo$44b4o$43bo4bo$42b8o9bo$41bo8bo8bo$41b10o8bo$40bo10bo6b2o$39b4o
2b8o$38bo13b2o4bo$38bobo6bobobobo3bo$37b2obo5bo4bo2bobo2bo$41bo4bo2b5o
2b2obo$37b4o6b2o5b2o$37bo4b4o4bo2bob4o$43b2o5bo4b2o!
This was found by starting with LGOL double-wrapped search for 2c/3x10c/19, spotting an especially juicy partial (it's still running), and completing a 3x multiple of it in LLSSS 2c/3 f2b.

EDIT: Before 10c/19 I had run 2c/3, 3c/5, 4c/7, 5c/9, 6c/11, 7c/13, 8c/15, and 9c/17 all with no results (for 2c/3 x Nc/(2N - 1)). They might still have a result with a multiple (like 27c/51 or something) like I had to resort to here.

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