Smallest Spaceships Supporting Specific Speeds (5s) Project

[Aleph]

Double post, but (8,1)c/9:

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(...)

This and the (7,1)c/8 look so...different from other relativistic oblique spaceships. What was the search methodology used to find it?

[LaundryPizza03]

Double post, but (8,1)c/9:

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(...)

This and the (7,1)c/8 look so...different from other relativistic oblique spaceships. What was the search methodology used to find it?

They used LLS to find promising frontends and backends. Then they searched those rules with LLSSS using a custom search orientation.

[NimbleRogue]

Double post, but (8,1)c/9:

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(...)

This and the (7,1)c/8 look so...different from other relativistic oblique spaceships. What was the search methodology used to find it?

I found some p1 orthogonal backends and then thought about extending the concept to obliques. May13's OT (2,1)c/3s were the inspiration for these specific backend. Me and Ampere have been working on finding completions for a bit now.
Here are some preliminary results
https://conwaylife.com/forums/viewtopic ... 98#p235398

There were a bunch of things that were tried but what ended up planning out was doing LLS searches for frontends while forcing the trailing edge to be completely filled while also requiring a partial backend to work. I have attached the LLS search where the precurser rule to the (7,1)c/8 was found. After finding a frontend the key was running LLSSS on a bunch of related rules to see if any ships pop out

[NimbleRogue]

Me and Ampere are working on finding (9,1)c/10 there are some worries about finding period 1 backends and signals that will work, but I expect something will turn up soon

If this rule had B8 this would be an incredibly small (8,1)c/9

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x = 22, y = 23, rule = B2-ik3-aiky4cqtw5-ijy67/S012i3cjky4acejkry5-ac6-i78
4b3ob3ob3obo$2b2o4b6obob3o$2bob5ob5obobo$b4ob10ob4o$bo4b14o$19o$2b16o$
2b15o$2b14o$2b13o$2b12o$2b11o$2b10o$2b9o$2b8o$2b7o$2b6o$2b5o$2b4o$2b3o
$2b2o$3o$bo!

Edit 1:

1 cell off

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x = 21, y = 24, rule = B2ace3-aiky4cqtw5-ijy67/S012in3cjky4-inqwz5-ac6-i78
8bobo$3b3o2bobo2b3obo$b2obob2ob2ob3o3bo$2b2o2bob2ob2obobob2o$2o2b12obo
$b19o$2b17o$3b16o$4b15o$5b14o$6b13o$7b12o$8b11o$9b10o$10b9o$11b8o$12b
7o$13b6o$14b5o$15b4o$16b3o$17b2o$18b3o$19bo!

New smallest (8,1)c/9 minpop 427

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x = 36, y = 39, rule = B2-ik3-aiky4ejtwyz5-ciry67e8/S012i3cjky4-intwz5-ace678
8b3o$2bob2o4b4ob3o$bo4bobobo4bo2bo$2b4o2b3obo3b2o$11obob4o$b15obo2bo$
2b6ob10obo$3b18o$4b15obo$5b14o2b4o$6b17o$7b19o$8b18o$9b16o$10b17o$11b
15o$12b14o$13b13o$14b12o$15b13o$16b11obo$17b13o$18b11obo$19b12o$20b10o
$21b11o$22b9obo$23b7o4bo$24b12o$25b10o$26b6ob2o$27b8o$28b7o$29b7o$30b
4o$31b3o$32b2o$33b3o$34bo!

Edit 2:

Smallest known (7,1)c/8 (minpop 354) from a relative of the minpop 427 (8,1)c/9

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x = 30, y = 32, rule = B2ace3cejny4qtyz5-k6ace78/S01c2ikn3-einr4ajkr5ijknq678
6bobobobob3o$4b2obo4bob2ob2o$bobob3obob4o2b2o$2ob12obobo$b10ob3ob4o$2b
10ob3ob3obo$3b9o2b5o2bo$4b12o2b3o$5b12o4bo$6b15obo$7b15o$8b13o$9b13o$
10b18o$11b16o$12b14o$13b14o$14b14o$15b13o$16b13o$17b12o$18b11o$19b10o$
20b9o$21b8o$22b7o$23b7o$24b4o$25b3o$26b2o$27b3o$28bo!

[yyh_baboon]

With recent progress I’m somewhat positive about the existence of lightspeed spaceships with a clean backend and signal emitters in the front that sends signals which either extends or collapses the side.
Maybe you can find it

[AforAmpere]

(9,1)c/10:

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x = 125, y = 128, rule = B2aci3ceqry4-cejrz5-eikq6aek78/S01e2-ai3cnq4-nw5-ajy6-e78
110bo3bo$103bob3o2b5o2b2o$100b2o2b2o2b5o2b2o$99b4o2b8o2b2o4b2o$100b4o
2b19o$99bob3o2b5o3b2ob7o$98bob6ob16o$96b10o2b14o$94b2o2b8ob14o$92b28o$
93b26o$90b28o$89bob26o$90b26o$89b26o$88b26o$84b3ob25o$86bob24o$84b3ob
23o$82bobo2b23o$83b4ob21o$82bobobob20o$81b3ob22o$79bo2b2ob21o$80b2o2b
21o$79b25o$78b25o$77b2ob22o$77bob22o$78bob20o$74b3obob19o$75b23o$75b
22o$72b3ob20o$74b21o$72b3ob18o$70bobobobob15o$69b2o3b18o$70b21o$69bob
19o$68b2ob18o$63b3o3bob17o$62bo2bo2bob17o$62bobobob18o$65b20o$62b2ob
19o$62bob19o$58b2ob2ob18o$57bo4b19o$57bob21o$57b22o$58bob18o$57b20o$
52b2ob21o$51bob2ob6ob12o$51b7ob15o$51bob5ob14o$53b5ob13o$50b21o$50b20o
$42bobo4bob18o$42bo6b19o$42b2ob22o$42b2o2bo2b17o$37b2o2b4o3b17o$36b28o
$34b3ob25o$33b2obob24o$33b3o2b23o$34b3ob22o$33b4ob21o$36b22o$32bob23o$
32b24o$29bobob22o$28bob24o$28b25o$27b25o$27bob22o$27b2ob20o$27bo3b18o$
27b2ob18o$25b22o$22bob22o$20b25o$20b24o$20b2o2b19o$23b19o$19b22o$19b
12ob8o$21b9ob8o$18b20o$16bob19o$18b18o$15b2ob17o$14b3o2b15o$14b19o$13b
19o$12bob17o$14b16o$14b15o$12b16o$13b14o$10b16o$10b15o$8b16o$8b15o$5b
2o2b13o$6bob13o$5b2ob12o$4b15o$b6ob10o$2b6ob8o$bob13o$2b2ob10o$4b10o$
3b10o$b11o$2b9o$ob8o$2b7o$3b5o$bob4o$3b3o$2b3o$3bo$bo$2bo!

With that, all possible (n,1)c/(n+1) ships have been found, as very's proof extended to obliques eliminates the possibility of any others.

[WhiteHawk]

(9,1)c/10:

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With that, all possible (n,1)c/(n+1) ships have been found, as very's proof extended to obliques eliminates the possibility of any others.

What happens in an (10,1)c/11 ship search?

[AforAmpere]

What happens in an (10,1)c/11 ship search?

You end up getting nothing out. Frontends at that speed can't exist, so LLS searches for them UNSAT (very quickly, too).

Also, smaller (9,1)c/10:

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x = 71, y = 71, rule = B2aci3eqr4ainqtwy5ajnry6aei78/S01e2-ai3nq4-cnw5-ajy6-ei78
67bo$66b2o$65b4o$64b5o$63b5o$62b5o$61b6ob3o$60b11o$59b10o$58b13o$57b
12o$56b10ob4o$55b11ob3o$54b12o3b2o$53b14o2bo$52b16ob2o$51b19o$50b19obo
$49b21o$48b16o2b3obo$47b21o2bo$46b18o2b3o$45b23o$44b23ob2o$43b24ob2o$
42b19o2b2obobo$41b20o2bo$40b18o4b3o$39b19o2b4o$38b23o2bo$37b19o2b5o$
36b20o3b2o$35b25ob2o$34b19ob2o2bob3o$33b20ob3o3bo$32b19o2bo5bo$31b17ob
o$30b23o$29b19o2bobo$28b20ob2obo$27b22o2bo$26b22o$25b22o$24b21o2bo$23b
25o$22b19obob3o$21b18ob6o$20b21ob3o$19b24obo$18b18ob4ob2o$17b18o3b2o$
16b19ob2ob2o$15b20o4bo$14b20obobobo$13b22o$12b17o2b3obo$11b17o2b5o$10b
17o2bobo2bo$9b18o3b4o$8b22obo$7b19ob4ob2o$6b18ob2ob2ob3o$5b22o4bo$4b
23o3bo$3b19ob4obo$2b21ob2ob2o$o2bo3b16o3bo$bo3bo4bo3bo3b5o$8bo3bo3bo3b
2o2$20bo!

[NimbleRogue]

Even smaller (7,1)c/8 minpop 223

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x = 21, y = 24, rule = B2-ik3cejny4ktyz5-jry67e8/S01c2ik3-einr4-wy5cinqr678
3bo2b3obo$2bo2b2ob5ob3o$2b4o3bo3bo2bo$2b4o4b3obobo$9obo4bobo$b8o3bo6bo
$2b10ob6o$3b18o$4b16o$5b15o$6b14o$7b13o$8b12o$9b11o$10b10o$11b9o$12b8o
$13b7o$14b7o$15b4o$16b3o$17b2o$18b3o$19bo!