Dark Matter Depletion into Cosmic Vacuum and Cosmic Energy Depletion into Dark Energy: A Structural Brane–String Framework Consistent with DESI

We present a unified structural brane–string framework (DCM/DSM) in which dark matter (DM) depletes into cosmic vacuum and dark energy through a continuous, regulated process. This model transforms the philosophical distinction between absolute entities (space, vacuum, cosmic energy) and their fragile traces (DM, dark energy) into concrete, testable mathematics. The core prediction is a depletion exponent δ that modifies the standard ΛCDM energy density for cold dark matter: ρDM(z) = ρDM,0(1 + z)3-δ. Using DESI DR2 BAO data and Planck 2015 constraints we obtain δ = 0.30 ± 0.07, which simultaneously explains: (i) the ∼ 1σ excess in the effective dark energy density ρX(z) reported by Wang & Freese, (ii) the S8 tension via a predicted suppression of fσ8(z) by ϵσ ≈ δ/3 ∼ 10%, and (iii) a mild evolution of the dark energy equation of state w(z) = -1 + wa z/(1 + z) with wa > 0. The same single parameter δ derived from BAO predicts the growth-rate suppression observed in DESI DR1 RSD measurements, with χ2 ΛCDM = 4.68 reduced to χ2 DCM = 2.33 (∆χ2 = 2.35). Thus, a single, structurally motivated depletion exponent offers a coherent explanation of three contemporary cosmological tensions. The paper concludes with a clear, reproducible numerical pipeline that can be applied to future DESI, Euclid, and Roman data.