XRAY
LITHE
MOLE
HOXI

I removed the list in my previous post as the koans AK and E disproved at least some of my rules there.

I doubt that symmetry is really the key to this rule, since GRAY has buddha-nature but GRUY does not.

My thoughts actually went more in the direction of rules like "AKHTBN if if contains two vertically symmetric letters that have distance at least 10 in the alphabet."

Some new koans:
AA
AAA
AAAA
AAAAA
AAAAAA
GRAYL
ABL
TRYL
REDL

@Proxima: I noticed two typos in your list: ABNZ should be ABNS and NEGOTIONABLE should be NEGOTIATIONABLE.

No new koans right now, but a discussion about properties of the Buddha-nature. Given the tested koans so far, the following three rules seem to hold:
R1: The Buddha-nature does not depend on the order of the letters in the koan.
R2: The Buddha-nature only depends on whether a letter occurs in the koan, but not how often it occurs.
R3: Letters that have neither vertical nor horizontal mirror symmetry (i.e. FGJLNPQRSZ) have no impact at all on the Buddha-nature.
I am fairly sure of R1 and R3, but I wouldn't bet on R2 as we have only few test strings for this one.

Here a list of all koans testet so far, after ordering the letters alphabetically and removing all non-symmetric ones.

EDIT: List removed because of disproved rules.

Three more koans:
QJRGLPFAB
ABZ
ABNS

GRBY
GRAAY
GRAYGRAY
GRAYGREY
GREYGREY

YGRA
AYGR
GARY
NEGOTIABLEQ

Taxing 2: Finally solved it without glitching. A brilliant level, though I would rate it at least end of Taxing.
Mayhem 24: After reading namida's comment, I realized what I did wrong and the new solution is much better (and even saves 97%). But I am still no fan of this level.
Mayhem 28: No miner turnaround trick needed here, cf. my solution to V1 (together with using the two skills I had left over to make the fall on the right survivable).

Here my impressions of the new/revised levels:

Tricky 10: Two solutions.
Tricky 27: It can be beaten with only one builder as well http://www.lemmingsforums.com/Smileys/lemmings/tongue.gif" alt=":P" title="Tongue" class="smiley" />. But I agree on the "good level" part of namida's remark.
Tricky 28: Solvable and not as hard as namida's remark would suggest. Tricky 29 is far harder...
Taxing 1: Likely the same backroute as namida's.
Taxing 2: Huh... even the solution I thought was intended doesn't work any more, because I can't turn around the lemmings which are going to the gap on the left. But with a little glitching the level becomes quite simple.
Taxing 4: The now deadly fall makes the level much more interesting, but the variety of skills still creates many solutions. Attached only one no-builder solution, but if you want, I can record several more.
Taxing 6: I agree with namida's remark.
Taxing 18: My solution still works.
Taxing 22: This one turned now into an excellent level!
Taxing 25: Not sure whether this is intended?
Taxing 26: Much more interesting than in V1.
Taxing 27: Good chance that this is a backroute as well.
Taxing 28: Not much difference to before.
Mayhem 4: The level got somewhat harder, though I am still not sure about having found the intended solution.
Mayhem 7: Solution with only 7 builders (because when planning my solution, I was somehow under the impression that I had only so many builders http://www.lemmingsforums.com/Smileys/lemmings/XD.gif" alt=":XD:" title="XD" class="smiley" />)
Mayhem 8: My solution is exactly the same as before. I don't even know what has changed?
Mayhem 10: Good level.
Mayhem 11: Absolutely excellent level http://www.lemmingsforums.com/Smileys/lemmings/thumbsup.gif" alt=":thumbsup:" title="Thumbs Up" class="smiley" />!
Mayhem 12: 99% saved.
Mayhem 13: Good level, though I already knew this trick from the Lix community level pack.
Mayhem 14: I too can save 96% without much trouble.
Mayhem 15: The time limit is very tight and the level is solvable with 5 skills of each (though my solution uses 6 builders for convenience).
Mayhem 16: My backroute still works. And you forgot this level when setting your one-way arrows to "only on terrain".
Mayhem 17: 100% possible.
Mayhem 18: Another absolutely excellent level http://www.lemmingsforums.com/Smileys/lemmings/thumbsup.gif" alt=":thumbsup:" title="Thumbs Up" class="smiley" />!
Mayhem 19: I still have one basher left over. But it already was and still remains a very good level!
Mayhem 24: This is the least endearing change you made from V1 to V2. The method is the same as in the first appearence of this level, but only much much more fiddly.
Mayhem 26: The third absolutely excellent level you added http://www.lemmingsforums.com/Smileys/lemmings/thumbsup.gif" alt=":thumbsup:" title="Thumbs Up" class="smiley" />!
Mayhem 27: My solution is not much different from my previous one...
Mayhem 29: Pretty sure, this is not quite intended.
Mayhem 30: Far better than V1, though I still have a few spare skills.

A new solution for Lixes in Arms, which is more or less a simplified version of my previous one...

Fierce 8: I disagree with Fierce 8 not being "too hard". Up to now I checked quite a few approaches, but all of them broke down at some point and none of them would have saved the required 92% anyway... As I will never ever read hints to levels I haven't solved yet, you may have to wait some more before you get a solution for this level (at least from me).

Fierce 11: It's a pity that you decided not to fix this level. Although it's of course your decision whether to stay with the current version or not: Have you considered going back to the level in V1? In my opinion, the current version features some solutions that are relatively standard and uninteresting, like my sol. 4.

Fierce 13: Finally solved this one - great level http://www.lemmingsforums.com/Smileys/lemmings/thumbsup.gif" alt=":thumbsup:" title="Thumbs Up" class="smiley" />. The solution's elegance was a pleasant surprise as I expected that I had to use

some trick using the new basher-mechanics.

Fierce 14: I can save 90%, so it's likely another backroute...

Bad news first: The fouth builder in Fierce 11 created some new backroutes, e.g. my solution to the very first version during the test period reappeared (sorry for not seeing that earlier).

Nevertheless the following three changes should remove all solutions known to me (reasons given below)
- 3) Shorten (but NOT remove) the pipe
- 4) Move the upper right platform at the newly added gap down and to the right a few pixels (assuming this doesn't conflict with the intended solution)
- 2) Make the bomber a pickup skill (or alternatively choose 1) if you want to be completely sure to remove the backroutes, though I think this would make the level quite a bit easier)

Reason for 3) This seems to be the only way to get rid of solution 2 (apart from going back to a version requiring only 3 builders). And as you already noted it removes the solution in my previous post. Nevertheless completely removing this pipe seems not to be a good idea, as one could then build three stairs from the one-way wall to the left, fiddle a little bit around at the pipes in the top left corner and then take the ceiling route with all lemmings (though I am not sure if this actually would work).

Reason for 4) This would take care of solution 1 and 3. Moreover it would make solutions like 5 or 6 at least harder. Hopefully being able to close the gap using a builder starting from the lower platform does not create new backroutes.

Reason for 2) Seems necessary to remove solution 4. Perhaps one doesn't even need this to remove approaches like 5 or 6 (note that solution 6 only fails because I couldn't make basher-miner cancelling work in NeoLemmix). But making the bomber a pick-up skill definitely removes solution 6 and would at least require the basher-miner cancelling in solution 5. Together with the change 4) I feel reasonable certain that this takes care of solution 5. Moreover depending on the new location of the pickup bomber, this would give another reason why solution 3 no longer works.

Fierce 11 still causes problems... On the positive side, contrary to Fierce 15, I see hardly any way to modify my solution. So there is a good chance, that your next fix will actually remove my way to solve the level.

Fierce 11, 12 and 15 have previously been beaten via backroutes, but the new update has fixed those backroutes and no new solutions (backroute or otherwise) have been found.

This has changed now, though I fear you won't be happy with the results.

Rough 8: Definitely much harder than its place as my solution requires several tricks and

at least my solution wouldn't work under traditional Lemmix mechanics, making it even harder for those who are used to them.

Fierce 7: Sorry, but I hate that level. Counting pixels on absolutely uniformily coloured pipes is pure hell!
Fierce 10: My main problem with this level was, that I had problems recognizing most of the steel. I always thought you had to mine down in the middle to let the lemmings from downstairs come up into the pit directly on the left of the exit. Once one realizes that this won't work because of a steel wall in between, there isn't much left one can try and the solution is relatively easy to find. Good level though.
And now I wonder, why all the non-rectangular steel is there? As far as I can tell, no backroutes would appear if one replaces them with usual terrain.
Fierce 11: Giving back the fourth builder was likely a mistake...
Fierce 12: I am getting closer to the desired 89%.
Fierce 15: I am deeply sorry, but this level still needs major changes. This time I essentially ran the "skills you can't live without" challenge (as I found this an efficient way to find alternative solutions): I got down to 1 climber, 3 bomber, 3 builder, 1 basher and 1 miner. One can still save 90% or solve the level in 1:30. Nevertheless many of these solutions turned out to be quite interesting and fun. Good luck removing all these solutions http://www.lemmingsforums.com/Smileys/lemmings/devil.gif" alt=":evil:" title="Evil" class="smiley" />.

Thanks for creating these excellent levels http://www.lemmingsforums.com/Smileys/lemmings/thumbsup.gif" alt=":thumbsup:" title="Thumbs Up" class="smiley" /> http://www.lemmingsforums.com/Smileys/lemmings/thumbsup.gif" alt=":thumbsup:" title="Thumbs Up" class="smiley" /> http://www.lemmingsforums.com/Smileys/lemmings/thumbsup.gif" alt=":thumbsup:" title="Thumbs Up" class="smiley" />!

Fun 30: A great level for finishing Fun.
Tricky 4: Another great level, but too hard for its position.
Tricky 6: A level that feels like it could become a great puzzle. Unfortunately it has an easy solution saving 100%.
Tricky 12: I agree with namida about the bomber placement.
Tricky 19: Nice little level - assuming you reduce the skill set... At the moment it feels very much like a Fun level.
Tricky 21: An excellent level. Far too hard for Tricky though, because one has so many possible approaches to this level. See my comment to Taxing 20 as well.
Tricky 26: I don't need the pixel-precision of namida, but my solution is nevertheless nothing you should have in Tricky. And please make it clear to the player that the direct drom from the middle platform is survivable (it's only 61 pixels). When I first reached this level, I spent quite some time planning how to get the lemmings down, when this is trivial and automatic.
Tricky 27: This is another trick that is very well-known. Contrary to namida and geoo, this is not one my favourite Tricky levels (though it's definitely not bad).
Tricky 30: A very long level and I need every of the 20 builders (and during my first attempt I was even 1 builder short and had to do almost everything again). Together with Mayhem 28 my least favourite.
Taxing 2: A very good level. But you should raise the save requirements to remove the backroute I attached (assuming it is indeed a backroute).
Taxing 7: very generous on the save requirements.
Taxing 9: A good level - for early Tricky. It is easily solvable with only 2 climbers, 2 floaters, 1 blocker and 1 miner.
Taxing 12: One of the very few builder-heavy levels I ever encountered that I really liked.
Taxing 13: Good level, even if it's not really hard to save 90%.
Taxing 14: I can't agree with namida's remark - I had over 1 minute left.
Taxing 15: Way too easy with a great deal more skills than needed.
Taxing 17: I guess I found the same backroute as namida.
Taxing 19: Another very good level that is easier than placed. I used only 4 skills.
Taxing 20: This level is easier than Tricky 21 and I don't think the beginning is that great...
Taxing 22: Though not completely original, it's always nice to see such a level again.
Taxing 23: Absolutely unique and excellent level!
Taxing 24: Contrary to namida, timing is an issue with my solution. Nevertheless my basher usage is a strong indicator that I found a backroute.
Taxing 25: A very very good level.
Taxing 26: Sorry, but this level is straight-forward and not interesting at all.
Taxing 27: Feels like a slight variation of the intended solution.
Taxing 29: A very good idea and my solution doesn't rely on the glitchy behaviour namida mentiones.
Mayhem 1: Again a direct drop works, though it is not necessary. Whenever I want to remove this possibility of a direct drop, I try to place a small terrain piece behind the exit directly over its trigger area. Then the falling lemmings usually splat (as they should) instead of jumping into the exit.
Mayhem 2: One of the three best levels in your pack! Even if it didn't take me long to work out the solution.
Mayhem 4: Fortunately one can save 90% and thus reduce the amount of bomber timing.
Mayhem 5: So much unused terrain about... I really wonder whether my solution is intended?
Mayhem 8: Way too easy for Mayhem and more or less staight-forward.
Mayhem 9: Even if your level isn't the first that features this strategy, it was very enjoyable.
Mayhem 10: Not a fan of this one.
Mayhem 14: An absolutely excellent level http://www.lemmingsforums.com/Smileys/lemmings/thumbsup.gif" alt=":thumbsup:" title="Thumbs Up" class="smiley" />! But please remove the backroute I attached as a second solution.
Mayhem 15: And again a very good idea, even though the first half was pretty uninteresting.
Mayhem 17: I already solved the first version of this level in this way.
Mayhem 19: Digger placement was slightly annoying, but otherwise a good level.
Mayhem 20: I likely backrouted this one.
Mayhem 21: ...and another likely backroute.
Mayhem 22: Together with Mayhem 2 and 14 the best level! I never needed pixel-precise skill assignment anywhere.
Mayhem 23: Another backroute.
Mayhem 25: Apart from a very precise bomber placement, this level was much fun, though easier than its placement.
Mayhem 26: A few good ideas, but too heavy on builders.
Mayhem 27: An excellent mulit-tasking level! As with Tricky 26, please make sure that the player doesn't mistake the drop on the very right for a splatting fall.
Mayhem 30: I guess this is more or less the same relatively easy solution namida already found.

Dodgy 15: Actually I already got this solution when DynaLem asked whether 100% is possible during the pre-testing period, but I forgot to send it to you until now.
Fierce 11: This fix won't work. In fact, it would make the solution even easier:

Stop the basher with the additional bomber and then you can send another climber late enough such that it turns in the miner tunnel instead of the blocker.