This particular page I submitted is just a page where you can enter a URL and see all threads, and there is a bookmarklet to open it quicker. It does send the URL to Ampie's server to search for the URL. The extension that you can also install uses a local cache of links (around 100Mb for just HN links, but it doesn't show HN comments) to show the counts of how many times the link has appeared on HN / twitter, and sends the request only when you click on it to load the particular HN posts or tweets that it appeared in.
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[ 2.7 ms ] story [ 14.7 ms ] threadI use it mainly to decide if I should read an article. When it was shared many times on twitter or HR I'll prioritise it in my reading backlog.