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From this article on page 673:

The "von Kármán line" appears to be what mathematicians refer to as a "folk theorem", arising out of a conference discussion but never formally published by him. It was fleshed out in later publications, especially in the influential work of Haley (1963) and there is some justification for calling it the "von Kármán-Haley line".

Question: What was that conference and when and where was it held ?

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It appears this was suggested in 1959 at the First Colloquium on the Law of Outer Space:

Jastrow, Robert. "Definition of Air Space." Proceedings of the First Colloquium on the Law of Outer Space,. Wien: Springer-Verlag. Vol. 82. 1959.

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    $\begingroup$ Welcome to Space Exploration SE ! Do you have a link to this book or can you show an image of the page where the "von Kármán line" was mentioned.? Also was Theodore von Kármán himself at that Colloquium ? $\endgroup$
    – Cornelis
    Commented Oct 26, 2018 at 16:26
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    $\begingroup$ Thanks! I don't have a link I'm afraid, this is the earliest mention I can find in the literature: sciencedirect.com/science/article/pii/S0094576518308221. The proceedings are in a foreign language and I can't find the part the author is referring to: cambridge.org/core/journals/… $\endgroup$
    – Diamond
    Commented Oct 26, 2018 at 16:34

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