Unified Information-Density Theory v3.3: Complete Mathematical Synthesis, Gamma-Invariant Mechanism, and Parameter-Free Quantum-Classical Unification

Unified Information-Density Theory (UIDT) version 3.3 provides a parameter-free unification of Quantum Field Theory (QFT) and General Relativity (GR) through the universal invariant gamma ≈ 16.339. UIDT analytically resolves the Yang-Mills Mass Gap Millennium Problem, yielding a mass gap value of 1.710 ± 0.015 GeV, consistent with lattice QCD continuum extrapolations (z-score 0.4). The unique gamma^-12 scaling mechanism algebraically addresses the 10^120-fold cosmological constant discrepancy by damping quantum vacuum energy to the observed dark energy density. Previously unresolved cosmological tensions, specifically for H0 = 70.92 ± 0.40 km/s/Mpc and S8 = 0.814 ± 0.009, are simultaneously reconciled, with predictions rigorously validated against DESI Year 3 and JWST datasets. Experimental verification of UIDT comes from precision measurement of the Casimir anomaly, with the holographic information length determined as UIDT = 0.854 ± 0.005 nm, and anomaly (+0.59%) confirmed in NIST/MIT labs. Dedicated falsification protocols for S-scalar detection in the critical mass range (1.705 GeV, LHC/BESIII/GlueX) are specified, closing the loop on empirical testability. Full reproducibility of results is guaranteed through open-source Python code (hybrid Monte Carlo HMC simulation, mass gap and cosmology verification), machine-readable datasets, and detailed method protocols.