@StupidQuestionsInc Hi, thank you for your encouragement. There have been a few people asked me about means of donations. Given that I am struggle to find free time to move a0 forward, as corona virus indeed distract me in someway -- I have been blocked from entering US for further developing my research work based on approach0, and I have to live with a temporary full-time job in China now.

I think it can be a good idea to try accepting donations, therefore I did take a few minutes to setup a Github sponsor account, I will let you once it is ready to receive donation. Anyway, I thank you in advance.

@StupidQuestionsInc As for your observed problem, could you be more specific? Which query you find works better before than currently? I have not changed much algorithmic aspects of search engine, only Webpage interface changes recently, so it may be just the index is getting out of date.

@StupidQuestionsInc Your second question is similar to what I answered about a few days before: chat.stackexchange.com/transcript/message/54486288#54486288, however, I do observe the uparrow query finds a few exact matches but they are not being prioritized to the top search results. This is unexpected, I will look into this issue now, it can be a bug.

@WeiZhong I hope your situation improves soon, and yes corona has impacted pretty much everyone now in a bad way

@WeiZhong i will try to find some example and i will send it to you. I'm glad to hear that the algorithms didn't change much so it's probably just me ... lol

@StupidQuestionsInc Thank you. Yes, please send me if you find any case not working as expected.

BTW. I've just looked your "uparrow query", it turns out every search result, no matter it is uparrow or rightarrow, has a ranking score of 62.479 (you can check these scores from browser inspect tool, it is in a hidden span HTML tag around each result snippet).

I can confirm approach0 treats uparrow and rightarrow symbol differently, however, to explain why they produce the same score in this query case, I have to put some technical details here (it involves technical details that even I fail to spot at first), approach0 tries to improve efficiency by grouping the leaf-root paths of math expression trees if some paths are of the same tokens (in this way it can speed up the matching by just calculating the min value of a pair of number),

in this case, the leaf to root paths from leaf token c and x out of $\lim_{x\uparrow c}$ are the same length and same tokens, so they are grouped together, and their path symbol difference is sort of getting ignored.

One example would be $a+b+c$ will be grouped into (add, 3) where 3 means there are 3 leafs in this expression tree. In this way it is fast to tell $a+b+c$ and $x+y$ match 2 tokens, by taking the minimal of 3 and 2. However, due to this trick, we have lost the ability to differentiate some symbol differences, for example, if you have $a+b \oplus c$ and $x+y$, the operator difference in the first one gets ignored because it has to choose only one operator to represent the grouped expression.

@WeiZhong thanks for the technical explanation, i understood the root of the problem

@StupidQuestionsInc You are welcome, thank you for reporting this issue. I think I have come up an idea to fix this. Next version of approach0 will have this issue fixed.