As of February 2019:

Code Ocean DOIs take the following form:

10.24433/CO.<slug>.v<version> , such as 10.24433/CO.8419810.v1. 

You can access this particular DOI via https://doi.org/10.24433/CO.8419810.v1

The 'slug' is the the seven number string in a capsule's URL after the word capsule. (If the URL is https://codeocean.com/capsule/9859661/tree, the slug is 9859661.)
The version is whichever version you are currently publishing, v1 by default.

(Note that any published capsule will have a different slug from the capsule it was generated from.)

Prior to February 2019, capsule DOIs looked different, e.g. https://doi.org/10.24433/CO.0a812d9b-0ff3-4eb7-825f-76d3cd049a43. We shortened these for simplicity.

Where can I find my capsule's DOI?

A published capsule's DOI is available in its metadata page, under the 'Basic Info' section. This field will be auto-populated upon capsule publication. 

When are DOIs minted?

After publication. See Code Ocean's verification process for computational reproducibility for more on the publication process.

How are DOIs minted?

DOIs are generated here: https://datacite.org/dois.html

Can I identify the capsule's DOI before publication?

Yes; your capsule's URL has the slug and version, and the prefix is always 10.24433/CO. .  

Are DOIs assigned at the capsule level or the level of individual files?

DOIs are assigned at the capsule level, encompassing code, data, metadata and environment.

If I update my capsule, will it get a new DOI?

Yes. Updating your compute capsule will yield a new DOI; v1  will become .v2 , .v3 , etc.

My DOI is very long, how can I shorten it?

http://shortdoi.org/ may be useful.

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