If you ever find an example where you think they don't work, please ping me. I've looked into many of these cases, and the material does appear on the page as we've seen it.
If I take the quote: "At the beginning of this section, we posed the question: can we show that our two definitions of the nearby-relation are equivalent?"
Searching on google lead to 2 dead link, and another website republishing the book as pdf.
Others search engines give me the link of the page I got the quote from, as the first result.
That's not a sign that quote search doesn't work. In fact, the opposite. The pages you get all appear to have that really long quoted phrase. Instead, it's a sign we don't have one particular page with that quote indexed. Certainly better if we did have that page included in our index, of course. I'll pass it on.
But a false negative (not getting a page that has the phrase) isn't the same as a false positive (getting a page that doesn't have the phrase), which is what the GP is talking about.
Sad that the only way to get Google to “listen” is to back channel requests via some obscure web forum and not through any official google-provided channel.
Here's a separate issue I ran into the other day that almost made it impossible to find something Google had indexed. Type in "mumbai comes to norway," and you get a page and a half of results, with the date on almost all of them being 2011. Now give it a time range between 1900 and today (IE, all results with a time stamp should be included). All of the results disappear except for one.
For whatever reason any effort to use the time range can remove _many_ search results that Google knows are from that time range and that should be included. That can make it almost impossible to find old articles, particularly since Google pushes new less relevant hits if you don't restrict the time range.
The only way I was able to find this article the first time was by searching through social media, which sometimes has less crazy search algorithms.
See this Twitter thread I shared (I work for Google Search) on our before/after commands we added to make it easier to do this type of searching. It also explains why it is sometimes difficult for us to determine the date of a document: https://twitter.com/searchliaison/status/1115706765088182272
I don't think this has to do with the issue I mentioned. Google has gives a date for these articles when you do a regular search. As I mentioned, these are mostly around 2011. Again, these dates are coming from Google, not the site. If I do a time range that includes 2011 in it, even a time range that includes the entire existence of the internet (1900 to 2022), all of the sites except one disappear. It's not a matter of Google getting a date wrong, it's a matter of Google not displaying hits that it should be displaying per the data in its own system.
I've also seen cases where the quote seems to be ignored. I don't have a full theory yet but I think it might be when the contained string is too long? Next time I see it I'll send it to you.