Cryptic Dark Sectors from Noncommutative Geometry: Tree-Level Sequestering, Self-Interacting Dark Matter, and Evasion of Cosmological Bounds

We construct a phenomenologically viable Self-Interacting Dark Matter (SIDM) model within the noncommutative geometry (NCG) framework, based on the non‑Abelian dark algebra Adark=H4⊕H5Adark=H4⊕H5. The first‑order condition and the Disjointness Criterion of our companion paper force tree‑level sequestering from the Standard Model. In contrast to the obstructed Abelian dark sector, this algebra is automatically anomaly‑free and possesses a non‑degenerate intersection pairing. The Yukawa coupling between the dark matter candidate ΨΨ and the scalar mediator ΦΦ arises from an FOC‑allowed Dirac block. After spontaneous symmetry breaking SU(2)4×SU(2)5→SU(2)DSU(2)4×SU(2)5→SU(2)D, the neutral scalar drives velocity‑dependent self‑interactions with σT/m∼0.7 cm2/gσT/m∼0.7cm2/g, solving the cusp‑core problem. The model evades CMB bounds via rapid mediator decay into dark radiation and loop‑suppressed gravitational kinetic mixing ϵgrav∼10−36ϵgrav∼10−36. It predicts ΔNeff≈0.1ΔNeff≈0.1 and a direct detection cross section σSI∼10−110 cm2σSI∼10−110cm2, making the dark sector essentially invisible. Thermal freeze‑out fixes the Yukawa coupling yD≈0.057yD≈0.057. The quartic coupling is radiatively generated, while the light mediator mass requires a hierarchy protection addressed in Part 3.