It's perfectly reasonable for reviewers to assume that a common expression can be explained by consulting ordinary reference works. They shouldn't have to do that search. If it can't be, it's up to the asker to demonstrate that it can't be. Something like "I researched but maybe I missed it" isn't particularly helpful in this case: if you researched and didn't find anything, at least show where you looked.
Doing the research may find something relevant, but it might be unintelligible or not completely helpful. In that case, show what you found. This means that others don't repeat the search you've done, and they can focus any answer on expanding on those findings. Don't just link to it: if it doesn't explain what you want to know, quote the relevant bits and explain why they don't. Doing this also helps the asker to sort out in his own mind what the problem actually is in order to express it clearly.
In common with other Stack Exchange sites, ELU should not simply be asked gimme the codez — we expect an amount of independent research, and understanding of what the problem is, to be evident in the question.
The answer to "how much research is needed?" is "Enough to show:— that you have done some; that you understand what you are asking about; and you can explain all of that to people who have no prior knowledge of the problem at all." Every question needs at least one of those criteria to be satisfied; most need more than one and many need all three.
By way of example, I'll make a start on reworking this question:
This quote was revealed to exemplify Definition 1, but working backwards, how would you determine the meaning of contingent? Even after seeing the context, I'm still vacillating between definitions 1 (not 1.1, the one above 1.1) and 3. Don't they both look right?
But, while personal biographies and group histories are mutually immanent, they are relationally irreducible. The same context may produce several different collective 'histories', differentiating as well as linking biographies through contingent specificities. In turn, articulating cultural practices of the subjects so constituted mark contingent collective 'histories' with variable new meanings.
Source: PP 177, Cartographies of Diaspora: Contesting Identities, by Avtar Brah
Rule 1. State what you're asking about first
Here, the quotation is relegated to a very much lower status than it actually needs. The question is built upon the quotation: mention it early.
Rule 2. Never just link. Always quote with attribution.
"Definition 1" is from ODO. The question mentions 1.0 (I'll call it 1.0 for ease of reference) and 3. Don't expect readers to click through and swap back and forward to compare your question with your dictionary link. Quote the dictionary definition you're referring to. Using the citation, people can click through to check or see if something else is relevant, but you are basing your question on your prior research: including that research in the question itself is crucial.
Always, always, refer to more than one dictionary.
Rule 3. Use simple language. Assume all your readers are from Missouri
You need to demonstrate what you don't understand. Don't dress it up in fancy language; just say what you don't understand.
This quotation uses the word contingent:
But, while personal biographies and group histories are mutually immanent, they are relationally irreducible. The same context may produce several different collective 'histories', differentiating as well as linking biographies through contingent specificities. In turn, articulating cultural practices of the subjects so constituted mark contingent collective 'histories' with variable new meanings.
Source: Cartographies of Diaspora: Contesting Identities, by Avtar Brah, page 177
Looking up the word contingent in ODO, I think these definitions may be valid
1. Subject to chance:
the contingent nature of the job
3. Philosophy True by virtue of the way things in fact are and not by logical necessity:
that men are living creatures is a contingent fact
Merriam-Webster has a number of uses all related to the main definition
depending on something else that might or might not happen
...but if I attempt to replace the word contingent with something derived from the definitions, it just doesn't make sense. Is the author using contingent in one of these ways here?
By doing this, you are showing that the use of contingent isn't easily answered by referring to standard works. You have already done that search and you have shown what you found. You state how you have attempted to deal with what you found, and you explain what the problem is: you can't actually find a definition which appears to fit contingent as it's used here.
[As an aside, I would say that in this particular quotation, contingent is the least of the problems! Mutually immanent, relationally irreducible, and specificities provide for a particularly impenetrable passage. Its opacity may well be why it doesn't make sense when you try to expand the dense text with simpler words.]
What is very, very important is not to treat ELU as a personal comprehension-exercise service; nor to be seen to be doing that. Putting a lot of effort into questions (and almost certainly more than I have here) is absolutely vital. This suggested question is an improvement, but it's by no means finished.
Asking good questions takes time. Questions should not simply be thrown together, and it's very unlikely that they can be templated and simply adapted from one to the next. All the research is unique to each question. Even writing this answer, which is heavily based on something already written, has taken a surprising amount of time. Invest in asking to realise a useful return in a comprehensive answer. I would certainly expect someone producing questions for ELU not to manage more than two per day before becoming worn out with the effort.