Sinpozium - slash con in Sydney

Basically the Hogwarts book of names would have every magical birth in the British Isles as far back as the Founding of Hogwarts. Depending on how much you want it to record it would be a great Ancestry Resource - I suspect it would record the child’s name birth date and parents. Maybe the birth entry is in green ink which is why the letters are written in green ink it’s an association confirming their name is still green in the book etc

I suspect it would also record the birth of squibs or all a parent would have to do is see if they are in the book instead they have to wait for the letter at eleven to be sure!

An interesting idea here would be for the a Squib entry to turn red when the hogwarts register finds them not magical enough at eleven to use a wand - it still keep track of their bloodline via the magic until they fully turn muggle way down the line and become fully untraceable - Muggles are brown but only show for two reasons in the book a muggle married a magical so a parent or a muggle child born to a magical parent already in the book basically it is a record of the full loss of magic to that squib branch of a bloodline.
Eg: Petunia is listed in the book as red but Dudley could be either red a squib like his mother or brown a full muggle like his father.

If the invitation to attend Hogwarts is refused a note of why is put next to the name and it turns another colour - if Muggleborn and parents refuse the Ministry probably binds their core so possibly blue ink marking them as made squib not natural.

So colour code
Green - magical core at birth
Green - enough magic to use wand at eleven so gets a letter
Red - not enough magic for wand at eleven so register turns entry red as squib
Blue - letter sent said no as either Home Schooled or going to other magical School
Purple - got the letter but a Muggleborn whose parents said no so the child’s core was bound and family obviated about magic to protect the statute
Brown - Muggle no magical core