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If non-nil, Gnus will attempt to build old threads by fetching more old headers—headers to articles marked as read. If you would like to display as few summary lines as possible, but still connect as many loose threads as possible, you should set this variable to some or a number. If you set it to a number, no more than that number of extra old headers will be fetched. In either case, fetching old headers only works if the back end you are using carries overview files—this would normally be nntp, nnspool, nnml, and nnmaildir. Also remember that if the root of the thread has been expired by the server, there's not much Gnus can do about that.

This variable can also be set to invisible. This won't have any visible effects, but is useful if you use the A T command a lot (see Finding the Parent).

The server has to support NOV for any of this to work.

This feature can seriously impact performance it ignores all locally cached header entries. Setting it to t for groups for a server that doesn't expire articles (such as, leads to very slow summary generation.

Same as gnus-fetch-old-headers, but only used for ephemeral newsgroups.
Fetching old headers can be slow. A low-rent similar effect can be gotten by setting this variable to some. Gnus will then look at the complete References headers of all articles and try to string together articles that belong in the same thread. This will leave gaps in the threading display where Gnus guesses that an article is missing from the thread. (These gaps appear like normal summary lines. If you select a gap, Gnus will try to fetch the article in question.) If this variable is t, Gnus will display all these “gaps” without regard for whether they are useful for completing the thread or not. Finally, if this variable is more, Gnus won't cut off sparse leaf nodes that don't lead anywhere. This variable is nil by default.
This is a rather obscure variable that few will find useful. It's intended for those non-news newsgroups where the back end has to fetch quite a lot to present the summary buffer, and where it's impossible to go back to parents of articles. This is mostly the case in the web-based groups.

If you don't use those, then it's safe to leave this as the default nil. If you want to use this variable, it should be a regexp that matches the group name, or t for all groups.