Collective Membrane Modes in the U-Cell Model: A Self-Consistent Derivation of the Dark Matter Threshold Energy E_Λ, SR = 23. 9 eV

The dark matter threshold energy E_Λ, SR = 23. 9 eV is the highest-priority open problem in the U-Cell Model (UCM): currently introduced as a motivated ansatz, not derived from first principles (Paper 30). This paper introduces Route C: collective membrane oscillations. Each U-Cell is bounded by a membrane. When N membranes oscillate coherently, the collective mode frequency is suppressed by 1/√N relative to the Planck frequency. We show that the self-consistent condition: E_Λ, SR = EPlanck / √N, N = (rc, min / ℓPlanck) ², rc, min = ℏc / E_Λ, SR is satisfied exactly at E_Λ, SR = 23. 9 eV. The coherence length rc, min is simultaneously the size of the collective membrane mode and the minimum size of a stable sub-threshold (dark matter) excitation — a self-consistent fixed point. A deep structural connection is identified: the same membrane network that carries quantum entanglement correlations (Paper 31, Zenodo 19435808) also determines the dark matter threshold scale. This unifies two previously separate UCM features. The remaining open problem — independent selection of the fixed point by substrate dynamics — is explicitly declared. Part of the UCM preprint series (ORCID 0009-0005-5088-4339, records 19387201–19435808).