user18196: 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.)

user18196: 
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.


18196: <p>Typical path notation for a BIP44 child private key would be something like:</p>

<pre><code>m/44'/0'/0'
</code></pre>

<p>The public key is</p>

<pre><code>point(m/44'/0'/0')
</code></pre>

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

<p>Is there any standard notation for the <code>xpub</code> calculated from a hardened child private key?</p>

<p>(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.)</p>
 18196: <blockquote>
  <p>Is there any standard notation for the xpub calculated from a hardened child private key?</p>
</blockquote>

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

<pre><code>[m/44'/0'/0']
</code></pre>

<p>Is the public key derived from the hardened child private key. </p>

<pre><code>[m/44'/0'/0']/0/0
</code></pre>

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

<p>This notation has some useful characteristics:</p>

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