Path notation for extended public key of hardened child? Typical path notation for a BIP44 child private key would be something like:

m/44'/0'/0'


The public key is

point(m/44'/0'/0')


Where point is the ECC multiply function. Is there any better notation than this? It would not be right to use M/44'/0'/0' as this path is not derivable. 

Is there any standard notation for the xpub calculated from a hardened child private key?

(Note: I'm looking for notation that would be useful to parse and then re-derive this key, not necessarily the type of notation that would be intuitive in an academic paper.)
Is there any standard notation for the xpub calculated from a hardened child private key?


I have chosen to use the below notation. Others may use it if they find it useful.

[m/44'/0'/0']


Is the public key derived from the hardened child private key. 

[m/44'/0'/0']/0/0


Is a child public key derived from the master private key m. However, [m/44'/0'/0'] may be stored as a separate public key, essentially as a checkpoint in the HD tree.

This notation has some useful characteristics:


Easy to parse. 
Shows exactly where the private->public derivation was done. So, while [m/44'/0'/0']/0/0 and [m/44'/0'/0'/0]/0 my produce the same xpub, the calculations done to derive that xpub were quite different.
Inside of brackets, hardened notation may be used, but outside of brackets only non-hardened notation is permitted.