jpeg2000 lossless encoding followup questions

Question

In a prior discussion Re: Does Media Encoder support lossless JPEG 2000 MXF, or only lossy? the winning post was that it's lossless. But subsequently I've learned that there are two kinds of lossless files: mathematically lossless and visually lossless. For example this link discusses visually lossless compression https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3649057/

So my questions are:

1. Is the jpeg2000 output mathematically lossless or visually lossless?

2. If it's not proprietary information, what compression method is used in jpeg2000 encoded files?

3. Why does the lossless metadata flag not appear in MediaIinfo, for example. This caused me to wonder if the prior answer that it is lossless was accurate. MediaInfo of another jpeg2000 file shows this but the AME created file does not:

Compression mode

: Lossless

Jerry Carlin · Answer

At this point I assume that the jpeg2000 encoding is not mathematically lossless and will act accordingly.

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