# P21: [Proof Group E] MOIRE DE/DM PROOF — DUAL CYLINDER GEOMETRY

**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING

## Prompt

MOIRE DE/DM PROOF — DUAL CYLINDER GEOMETRY
Prove that dark energy and dark matter density fractions arise from the moire interference pattern of dual coaxial cylinders in the split-octonion geometry. Show: (a) the two cylinder radii are set by v+ and v-; (b) the beat frequency gives the DE scale Lambda; (c) the trapped nodes correspond to DM halos. Derive Omega_DM/Omega_DE ratio from cylinder geometry. Compare to Planck 2018. Assess whether 720/theta remnant is fully removed from v1.27.5. #SuperGrokTOE #DarkEnergy #DarkMatter #Moire