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I recently fixed a broken link to a PlanetMath page, by changing http://planetmath.org/encyclopedia/RotationalInvarianceOfCrossProduct.html to http://planetmath.org/RotationalInvarianceOfCrossProduct.

Some links also have .html at the end, without /encyclopedia/ see e.g. http://planetmath.org/FullyIndecomposableMatrix.html from this Answer.

I also found some other links that I cannot understand, but now link to the homepage. These links start with planetmath.org/?op and now redirect to the homepage. I'm not sure what they were supposed to link to, however. I found this by performing a search for PlanetMath on MO. An example post there is this one.

There are also posts starting with planetmath.org/sites (as pointed out by Martin/hardmath). Some of these even link to PDF files that are no longer there.

As mentioned by Glorfindel, some posts are not fixed by the above procedure. I would guess that some pages have been renamed or deleted. It might be worth pointing out that PlanetMath has an index page which we can use to check before making the change.

Here are the posts that we can be sure have broken links:

  1. (From Martin's comment) Searching$^{1}$ with url:"*planetmath.org/encyclopedia*" gives 178 hits.

  2. Searching$^2$ with url:"*planetmath.org/?op*" gives a further 17 hits.

  3. Trying to find posts with .html at the end: url:"*planetmath.org/*html" gives 248 results. If the wildcard * works in the middle of the search input, this should strictly contain the results of point 1.

  • Are there other possible formats of PlanetMath links that are now broken?

  • How shall we go about fixing the links?


1. Note: searching for "PlanetMath" only gives 146 hits, but "url:"*planetmath.org/*"" gives 953 hits. So searching just for the website name does not search in the embedded links. Also note that wildcards * are supported in SE's built-in search.

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Because the ideal tool for a job like this, the mass-replacement tool, which can repair posts without bumping them, doesn't work in this case, I have fired up a script (a derivation of the Broken Image Repairer) to repair these links on half a dozen websites across the network, including Mathematics Stack Exchange. The script runs once every three days, bumping three questions at a time, in order not to flood the homepage with trivial edits.

I just did a dry run of the script and here is a list of URLs it won't be able to replace; these will need manual action. Here is another list with replacements it will make (scroll to the right to see the actual replacement links). You'll notice that it will update other links, e.g. HTTP to HTTPS. (I see some replacements are not necessary, e.g. for books.google.com. It's good to see the results upfront...)

I'm open for objections or suggestions. Following Martin Sleziak's comment, I can have the script try to repair planetmath.org/sites links as well, e.g. https://planetmath.org/sites/default/files/texpdf/40203.pdf in this question has a Wayback Machine copy.

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  • $\begingroup$ Excellent, thank you! Do you expect to be able to fix every such broken link, and if not can you put out a list of exceptional cases? I'd agree with fixing the /sites links too. $\endgroup$ Jan 14 at 9:08
  • $\begingroup$ You're welcome! I expect the /encyclopedia fix to be highly effective, since that is just reindexed content; for /sites I'm not sure, but I can do a dry run first and check which URLs can only be fixed manually (and post them here of course). $\endgroup$
    – Glorfindel
    Jan 14 at 9:16
  • $\begingroup$ Sorry, I meant to ask about cases like in your comment here where converting http://planetmath.org/encyclopedia/Rotate.html to https://planetmath.org/encyclopedia/Rotate doesn't work and the correct answer is instead https://planetmath.org/euclideantransformation. It should be easy to check for false-positives by matching with the entries as listed out in PlanetMath's index page, but I expect the fix requires a human..? $\endgroup$ Jan 14 at 11:39
  • $\begingroup$ Thanks. Three a day is quite conservative for a large volume site like Math.SE, but if it works across a spectrum of StackExchange sites, I'm happy with that. $\endgroup$
    – hardmath
    Jan 15 at 16:43
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    $\begingroup$ @CalvinKhor it's not that many broken links, and since Stack Exchange posts should never rely on links for crucial information, I prefer a slow pace. I'll update my answer with links (oh, the irony) to the results of a dry run. $\endgroup$
    – Glorfindel
    Jan 16 at 14:26
  • $\begingroup$ bug? :) I am slowly going through the failures, and I found that there were 3 hits for http://planetmath.org/encyclopedia/ProofThatAllNormsOnFiniteVectorSpaceAreEquivalent.html but the failures list says 2 hits. Perhaps this one was the culprit link since it just includes the url directly in the post instead of formatting it properly $\endgroup$ Jan 22 at 14:48
  • $\begingroup$ @CalvinKhor my script should detect those 'bare' links as well, I have no idea what happened :) $\endgroup$
    – Glorfindel
    Jan 22 at 16:01
  • $\begingroup$ Similarly had two hits instead of one for http://planetmath.org/encyclopedia/CompactMetricSpacesAreSecondCountable.html, hit1 and hit2; hit2 had a bare link. If its not too much trouble to check the script... :) Otherwise I'll stop updating you / other people until they're all done $\endgroup$ 2 days ago
  • $\begingroup$ Thanks @CalvinKhor - I'll have a look tonight, I found another example: https://math.stackexchange.com/search?q=url%3A%22planetmath.org%2Fencyclopedia%2FCondensationPoints.html%22 gives two hits while my results only show one failure. $\endgroup$
    – Glorfindel
    2 days ago
  • $\begingroup$ Hmm ... that last search now gives only one hit. I don't I can figure out what's wrong with the script. We'll see how many replacements it can make. $\endgroup$
    – Glorfindel
    22 hours ago
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I researched the twenty-four posts that Martin's planetmath.org/sites query finds. One post has three such links (the rest have one apiece), and one linked URL is shared by two posts, but two dozen is a pretty accurate estimate of the broken links.

Fourteen of the links can be retrieved from the Wayback archive. I'm reluctant to automatically use them as replacements. A few cases also give "parallel" links to "topic" pages at PlanetMath, which I think should be preferred as these are more apt to be maintained.

I'm seeing two main purposes of the broken links. Some are referencing otherwise well-known definitions, formulas, or propositions. For those I'd be happy to find authoritative substitutes. I'll call these Plan A (for authority!).

In most other cases a Question is motivated by a proof step cited in one of those notes, usually to the effect that the step is not obvious. For those the Wayback archive copies may be the best alternative to give Readers the original context of the problem. I'll call these Plan Q (for qontext!).

Naturally I'd love to have the Math.SE post authors agree to any fixes, which dovetails with the slow pace at which we're attempting them. I'll be leaving Comments for such folks (as this does not bump the posts) with suggestions.

UPDATE: Three of the two dozen posts are fixed, and I have left comments for the original posters on ten others. It seems most of the PDF files were converted to HTML topic pages, so even where there is no Wayback archive result, the majority will be on PlanetMath in somewhat faithful form. The conversions are imperfect but at least tolerable in appearance.

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