I read the pre-publishing version of this paper, and there was then and still is a serious problem with their logic, consistent with if not bad faith, something akin to it:

Assume for a moment their core hypothesis is correct, there were transient objects captured on film pre-Sputnik in LEO objects.

What might we say about their nature?

The authors' undisguised implication is "it's aliens" to be blunt; that's their motivation for this work.

Consequently they put effort (which may not be noted in the final published papers...) into the question of whether they could make any meaningful inference about the geometry and spectral properties of their "transients," their interest (of course) was that if they could make a meaningful argument for regular geometry, they had the story of the century in effect.

These efforts failed totally.

A natural inference might be, among the reasons this might be, is that the objects (remember we are assuming they exist) do not have such characteristics. The primary reason that would be true is if they were naturally occurring objects.

I looked this up and was surprised to learn that there are currently estimated to be on the order of a million small objects in the inner solar system.

So: the entire hypothesis hinges on "significant correlation with nuclear testing." Because otherwise, once can reasonably assume that transient traces of objects—when they are actually traces of objects—would in a quotidian way presumably be caused by some of these million objects.

Or so say I.

There is no end of peculiar and provacative history and data in UFOlogy, and even more murk; one needs to tread very carefully to not go down (or, be led down) to false conclusions, disinformation, and the like.

The authors of this paper seem singularly disinterested in that caution.

Assuming what you say is true then couldn't that be validated by making additional observations in the present day? Since we'd assume some sort of statistical distribution for such objects. Is there any reason that would be unrealistic?

That was the era of above ground testing. Is it possible that some of these tests kicked pieces of metal into LEO? Though I suppose that those orbits would see streaks, not point sources, in the photographs when you have an hour exposure.

If you want to downvote, I invite an alternate explanation for their behavior and the contextualizing media posture,

which regularly situates what they are willing to say in print, within unsupported and click-bait-worthy speculation.

Another example of bad faith: curve-fitting around what constitutes "nuclear testing."