LHC Multi-Lepton Anomalies and DESI DR2 Observations Within the Cosmological Thermosynthesis Theory v3.2: A Unified Resolution via Composite Scalar Dynamics and Emergent Dark Energy Evolution

This work presents a rigorous mathematical reformulation of the LHC multi-lepton anomalies and DESI DR2 dark energy observations within the Cosmological Thermosynthesis Theory v3.2 (TTC v3.2). Recent analyses reveal statistically significant excesses in multi-lepton final states at the LHC, consistent with a narrow scalar resonance at mS ≈ 152 GeV [2]. Simultaneously, DESI DR2 reports evidence at 3.9σ for dynamical dark energy with Chevallier– Polarski–Linder parameters w0 = −0.717 ± 0.032 and wa = −1.72 ± 0.31 [3]. Within TTC v3.2, both phenomena emerge naturally from the entropic dynamics of the primordial etherion superfluid (ultralight scalar bosons with me = (1.00 ± 0.05) × 10−22 eV). We derive: (i) the composite scalar S as a stable etherion aggregate with NS ∼ 1026 constituents, (ii) the recursive amplification factor R ≈ 8.04 that elevates local excesses to global significance > 5σ, (iii) the modified Friedmann equation yielding H0 = 67.66 ± 0.42 km s−1 Mpc−1, resolving the Hubble tension. All definitions specify domains, codomains, hypotheses, and mathematical spaces; lemmas and theorems include explicit proofs. The framework yields falsifiable predictions for HL-LHC, DESI Year-3, CMB-S4, and DUNE.