I watched this anime where each person summoned one monster with this device that was kind of gun-like. They would weave (or cut) signs into the air to make their monster perform a special attack.
If their monster died, the summoner would lose their memory from the point that they made the contract. When the monsters were summoned, they would be walking among paper doors from Japan.
The main character had this blue cat-man character that had a sword. This cat-man apparently was in the manga as well apparently. Also, I think the cat-man was voiced by the Japanese voice actor for Edward Elric in Fullmetal Alchemist.
The main character's summoned monster is a white tiger anthropomorphic character and I remember his sword being a big deal. Like they had to find a sign in order to make his sword bigger or something like that.
I watched this anime around the late 2000s or early 2010s. We had to find it on non-mainstream sites and I don't think it was ever dubbed, so it had a very Japanese name. Does anyone know what this anime is called and maybe a site where I could watch it?