Google Checkout - XML API associate callback serial number with original order

Via the XML API, how do you associate an Google Checkout callback serial number with the original order?

On the same line - What does the serial number in the "Option B - Submit a Server-to-Server Checkout API Request" section of the XML API doc correspond to (format: serial-number="981283ea-c324-44bb-a10c-fc3b2eba5707")? Does it relate to the serial sent by the callback URL (numeric-only)?

The way I've done this in the past is using the <merchanrt-private-data> tag in the original cart, so something like:

<checkout-shopping-cart xmlns='http://checkout.google.com/schema/2'>
 <shopping-cart>
  <merchant-private-data>
   <merchant-note>[some secret about the cart on my system]</merchant-note>
  </merchant-private-data>
  <items>
   ...
  </items>
 </shopping-cart>
</checkout-shopping-cart>

Then, after Google has called back with a serial number, I use the Notification History API to retrieve the order details, which then includes my private data, something like:

<new-order-notification xmlns="http://checkout.google.com/schema/2" serial-number="[serial number from google]">
 <buyer-billing-address>
  ...
 </buyer-billing-address>
 <timestamp>...</timestamp>
 <google-order-number>...</google-order-number>
 <order-summary>
  <total-chargeback-amount currency="GBP">...</total-chargeback-amount>
  <google-order-number>...</google-order-number>
  <total-charge-amount currency="GBP">...</total-charge-amount>
  <total-refund-amount currency="GBP">...</total-refund-amount>
  <purchase-date>...</purchase-date>
  <archived>false</archived>
  <shopping-cart>
   <merchant-private-data>
    <merchant-note>[the secret about the cart from my system]</merchant-note>
   </merchant-private-data>
   <items>
   </items>
  </shopping-cart>
  <order-adjustment>
   ...
  </order-adjustment>
  <promotions />
  <buyer-id>...</buyer-id>
  <buyer-marketing-preferences>
   <email-allowed>false</email-allowed>
  </buyer-marketing-preferences>
  <buyer-shipping-address>
   ...
  </buyer-shipping-address>
  <order-total currency="GBP">...</order-total>
  <fulfillment-order-state>NEW</fulfillment-order-state>
  <financial-order-state>REVIEWING</financial-order-state>
 </order-summary>
 <shopping-cart>
  <merchant-private-data>
    <merchant-note>[the secret about the cart from my system]</merchant-note>
  </merchant-private-data>
  <items>
  </items>
 </shopping-cart>
 <order-adjustment>
  ...
 </order-adjustment>
 <promotions />
 <buyer-id>...</buyer-id>
 <buyer-marketing-preferences>
  <email-allowed>false</email-allowed>
 </buyer-marketing-preferences>
 <buyer-shipping-address>
  ...
 </buyer-shipping-address>
 <order-total currency="GBP">...</order-total>
 <fulfillment-order-state>NEW</fulfillment-order-state>
 <financial-order-state>REVIEWING</financial-order-state>
</new-order-notification>

I can then use the secret to match the orders up to the details I'd stored in the database previously.