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I have got into contact with a fellow researcher at a conference, discussing a preprint of his. It turns out that his research complements mine, and I would like to see his research published so that I can (officially) use it.

However, the draft needs some reworking before published. He offered me to make this a joint authorship if I would finish this work. Having taken a look, the topic intrigues me - I could probably rewrite it considerably and contribute some additional results.

Is this acceptable by academic standards? -or- How can I ensure that my contributions are strong enough so that joint authorship is rock solid justified? Is it recommendable to note the original preprint explicitly in the final draft or to the journal editor? The field is pure mathematics.

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    Yes, it is acceptable by academic standards. If the original preprint is publicly available, then, you should cite it and you should explain how the extended version improves upon it, otherwise, there's nothing to cite and no explanation to give.
    – user2768
    Aug 24, 2016 at 12:01

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This is an absolutely normal and exemplary case of collaboration.

Work together on the final article and, if you meet the normal criteria for authorship in your field, then you should be an author. If not, you can be in the acknowledgements.

As for the preprint: if it is a separate standalone document like a tech report, then cite and state that this is an extended version. If it in a service that supports updating like arXIv, then you should end up with an updated preprint with your name on it in any case!

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