Using WP comment system on static page

Dear smart friends,
I’m willing to use the awesome comment system of wordpress on a static page of my web site.
Since it’s outside of WP, I’m aware I have to include the call to WP header at the very start :

<?php
/* Don"t remove this line. */
require("./wp-blog-header.php");?>

I then have to modify it to point to my existing WP directory. So far so good.
Problem really starts when I want the comment part to appear… and work properly.
Comments refer to a unique post. So how can I create a fake (?) ID for the post that will not interfer with my existing WP database ?
Has anyone come up with a solution/how-to for this kind of weird request ?