A Graviton Core is a device mentioned by L-elf in episode 22 when he analyzed the Moon crater that he and Haruto became stranded in after their rescue from a Dorssian Kirschbaum.
L-elf concluded that a graviton core detonated long ago, forming the crater and apparently leaving behind tetraquark radiation that completely impeded the radio signals of their SOS attempts.
Speculation[]
A graviton core implies that in the world of Valvrave, people have discovered and can manipulate gravitons, which would explain how artificial gravity operates for the modules of Dyson Spheres.