Hm ...

https://github.com/google/lut3d_utils

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Tone Map Metadata (3D Look-Up-Table) Injector

A tool for manipulating production metadata, specifically tone map metadata (3D LUT), in MP4 and MOV files. It can be used to inject 3D LUT metadata into a file or validate metadata in an existing file.

Usage

Python 3.11 must be used to run the tool. >From within the directory above lut3d_utils:

Help

python lut3d_utils -h

Prints help and usage information.

Inject

python lut3d_utils -inject_lut3d -i ${input_file} -o ${output_file} -l ${lut3d_file} -p COLOUR_PRIMARIES_BT709 -t COLOUR_TRANSFER_CHARACTERISTICS_GAMMA22

Loads a tone mapping (3D LUT) metadata from lut3d_file and inject it to input_file(.mov or .mp4). The specified output_colour_primaries and output_colour_transfer_characteristics are injected too. It saves the result to output_file.
input_file and output_file must not be the same file.

Examine

python lut3d_utils -retrieve_lut3d -i ${input} -l ${lut3d_file}

Checks if input_file contains 3D LUT metadata. If so, parses the metadata and prints it out. In addition, it saves the 3D LUT entries to lut3d_file as a ".cube" file.

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soooooo .... in theory you can use those for injecting and exporting those 3d luts in mp4/mov ..

I wonder if ffmpeg/libavformat can be teached to do this, too?