The Note on the Ritual is a memo Travis Grady finds in Room 503 on the first floor of Riverside Motel in Silent Hill: Origins.
It refers to the rituals of the Order – in particular, the birth of God and the vessel which would be used to bring Her into the world: Alessa Gillespie.
Transcript[]
"...it is believed a being of
tremendous mental energy may
become a vessel capable of giving birth
to Samael, the God worshipped by this cult.
Samael's arrival will bring forth
Paradise on Earth.
(Something has been added in the
margin.)
Given that this vessel is to be molded
with 'suffering and pain', just what
kind of God and what kind of 'paradise'
would result?"