How can an audio segment report an integrated loudness (LUFS) greater than 0 According to my very rudimentary understanding of the ITU-R BS.1770 standard, I thought that the LUFS (LKFS) value for any audio signals should not ever go positive.
However, there is a 5-second segment from an audio file I have whose integrated loudness level is +1.28 when measured using ffmpeg, and +1.44 when measured using pyloudnorm:
(stereo, source audio resampled at 48000 Hz, 16-bit signed little-endian integer waveform PCM)
[Parsed_loudnorm_0 @ 0x7fc245008680]
{
    &quot;input_i&quot; : &quot;1.28&quot;,
    &quot;input_tp&quot; : &quot;0.86&quot;,
    &quot;input_lra&quot; : &quot;2.90&quot;,
    &quot;input_thresh&quot; : &quot;-10.16&quot;,
    ...

How is this possible? Could this be an issue related to the implementations (i.e. ffmpeg and pyloudnorm) and not the algorithm itself?
I concede that I don't fully understand the math in the algorithm, and so if the algorithm does allow a positive value in certain situations, please explain.
I did download this annoying video and analyzed the part with a vuvuzela. You should take a note that:

This part is clipped
The audio is stereo

And that pretty much solves the mystery.

If you calculate the loudness for each of the channels separately you will get approximately -1.4 LUFS. Since this is a stereo track you add those levels together. For incoherent sources, you would roughly expect a 3dB of boost. Lo and behold, the total loudness calculated from the stereo track is approximately 1.6 LUFS (+3.2).
If you think about it, this makes perfect sense. What happens if you take one of those clipped channels and play it back through a speaker? You gonna get some SPL. Now, add a second speaker and play the other channel, you would expect to be even louder (3dB louder to be precise). Therefore LUFS accounts for that.