The notes here https://web.eecs.umich.edu/~cpeikert/lic13/lec04.pdf have the note 'Small decryption exponent $d$: so far the best known attack recovers $d$ if it is less than $N^{.292}$. This uses a bivariate version of Coppersmith that lacks a rigorous proof of correctness, but seems to work well in practice'. It looks like the paper in question of Coppersmith is https://www.di.ens.fr/~fouque/ens-rennes/coppersmith.pdf and in particular Theorem 2, Corollary 2 and Theorem 3.

A corrected version of Corollary 2 following Theorem 2 was posted in 'A Note on the Bivariate Coppersmith Theorem' by Jean-Sébastien Coron et al and so I assume Theorem 2 is OK. However it does not state anything about Theorem 3. Relevant link is https://link.springer.com/content/pdf/10.1007%2Fs00145-012-9121-x.pdf. Do we know if theorem 3 in 'Small Solutions to Polynomial Equations, and Low Exponent RSA Vulnerabilities' by Don Coppersmith is also valid?

In the conference version https://nymity.ch/anomalous-tor-keys/pdf/Coppersmith1996a.pdf in theorem $3$ he has a result where root bounds depend on individual degree ($\delta$ is $x$-degree and $\tau$ is $y$-degree) rather than total degree. It does not look like this version appears in journal version in introduction in this post. Is this version of the theorem correct? Is there references appearing beyond this conference publication?