What if dark energy is simply the energy of temporal vibrations that cannot find the √2 channel? In the fractal-spectral framework, the universe is a hierarchy of temporal vibrations connected by a transport tower with geometrically spaced frequencies ωₙ = ω₀ (√2) ⁿ. This tower enables multi-scale energy transport through the noncollision-octave mechanism. But the tower is discrete — it samples only ~1/ (Q ln√2) of all possible vibrational modes, where Q is the resonance quality factor. The remaining modes — the vast majority — vibrate and create local temporal gradients but cannot transport energy between scales. They are trapped. These trapped modes have three properties that make them dark energy. Their energy is predominantly potential (from the virial theorem applied to V ∝ τ^√2, the kinetic-to-potential ratio is √2/2 −1 and wₐ −1 with wₐ < 0 (testable by DESI Year 3–5, Euclid, LSST) ; no dark energy clustering at any scale (sound speed cₛ² ≈ 1) ; and a scale-dependent dark sector fraction measurable through weak lensing vs BAO/CMB comparison. If w₀ = −1 exactly with precision < 0. 01, or if dark energy clustering is detected, the trapped-mode mechanism is ruled out.
Thierry Marechal (2026) studied this question.