ℝ∈Χ LUNATiCA is an original composition by Kai created for the maimai DX series, debuting in the BUDDiES PLUS update on August 2, 2024. It serves as the Perfect Challenge culmination track for Heaven Area 7 (天界ちほー7), following RondeauX of RagnaroQ as the previous challenge. This marks Kai's first solo original song written specifically for maimai, his prior contributions include the collaborative track U&iVERSE -銀河鸞翔- and a classical arrangement, True Love Song, neither of which was a standalone original commission in the same vein. The song's title incorporates mathematical and set-theory notation, ℝ (real numbers), ∈ (set membership), and Χ (the Greek letter chi), lending it a stark, symbolic aesthetic that echoes its mythological narrative. The in-game flavor text describes the origin of a demonic army: fallen gods and angels who lost their divinity, gathered under Lucifer's dominion. Formless negative emotions from across dimensions were given shape and purpose, finally uniting into a military force poised for war. Clocking in at a relentless 230 BPM and lasting 2 minutes and 32 seconds, the track delivers a pounding fusion of orchestral and electronic elements befitting its war-theme atmosphere. The MASTER chart (Level 14+, constant 14.8) was designed by BELiZHEL and contains 1,103 notes, with a dense concentration of 123 Slide and 76 Break notes demanding high stamina and precise timing. The EXPERT chart (Level 12+, constant 12.9) was designed by はっぴー. The music video was produced by あるし, with illustrations by 眠介 and michele.