Open Problem C3 (Critical)
The phonon ZPF calculation (§4.3.4) demonstrates that the ether mechanism produces vacuum energy at the correct order of magnitude with w = -1 (Theorem 4.2). However, exact matching \rho_{\text{ZPF}} = \rho_\Lambda requires a sound speed c_s = 4.8 \times 10^6 m/s that conflicts with CMB compatibility (§4.5.5).
The resolution treats \Lambda as the integration constant of the trace-free Einstein equation (Eqs. 4.143f–i), with the value determined by the full vacuum energy budget of the multi-component ether (Eq. 4.173c). Proposition 6.1 establishes that the ether must be multi-component; the transverse sector’s vacuum energy contribution is unknown.
Calculating this contribution — from the ether’s transverse microstructure, constrained by Proposition 6.1 and Corollary 6.2 to \ell_e \lesssim 3 nm — would simultaneously resolve C3 and determine the precise dark energy density.
This is a well-posed problem that unifies three previously separate questions: the dark energy value (C3), the EM cutoff (I1), and spin emergence (C2) — all requiring the specification of the ether’s multi-component order parameter.
Reference: Sections 4.3.4, 4.3.12, 4.5.5, 11.2
Difficulty: Very high