Below are the results of the observations made on May 19th 2021 by Dave Gault and Peter Nosworthy. These were the first known detections of the suspected satellite of (4337) Arecibo.
Peter Nosworthy's light curve (click image to enlarge)
Dave Gault's's light curve (click image to enlarge)
Both Curves on The Same Time Scale (click image to enlarge)
The chords from the initial observations on May 19 indicate a main body diameter of 24.5km (assuming a circular fit). The diameter of the moon is not clear because both chords appear to be very close to the edge of the object.
If the observations were the result of one body occulting two components of a double star, it would require that one component of the double be brighter than G-band mag. 14.4. This possibility can be excluded by confirming that the target star dropped below mag. 14.4 during both occultation events.
We used dim comparison stars in the field of view to measure the limiting magnitudes of the recordings.
The limiting magnitudes were 15.4 (Gault) and 15.5 (Nosworthy). This confirms that the target star dropped below G-band mag. 14.7 during all four recorded events.
The asteroid was mag. 17.0, well below the limiting magnitude of both recordings.
From this we conclude that a single body occulting a double star could not account for the observations. This makes the case for a 'moon' much more likely.
On June 9, 2021 two observers in California, Kirk Bender and Richard Nolthenius, observed this event in which (4337) Arecibo occulted a mag. 12 star in Ophiuchus.
Both observers detected double occultation events consistent with a satellite of Arecibo.
See also Richard's page describing the event.
Kirk Bender's light curve (click image to enlarge)
Richard Nolthenius's light curve (click image to enlarge)
The chords from the June 9 observations were plotted with assumed circular fits for both objects. This indicates diameters of 24.4km and 13.5km for the two objects.