I think this is the official J implementation as it stood in 1990 when this paper was originally published, it kept being developed but not this document which describes it. Perhaps someone else knows these details?
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The current version is at https://github.com/jsoftware/jsource
There is a relatively recent episode of the ArrayCast array language podcast with Henry Rich who is the primary maintainer and developer of J, talking about new features: https://www.arraycast.com/episodes/episode104-j96
Click on the show notes and there are links to previous episodes with him, talking about the J engine implementation, updates in J 9.03, threading and faster bignum calculations in J 9.04, updates in J 9.5, his views on tacit programming, etc.