Macroscopic Decoherence as Deterministic Topological Phase-Locking: A Holographic Projection of the SU(175) Gauge Group on C_60 Fullerenes

This paper rigorously redefines macroscopic decoherence—historically attributed to probabilistic wave-function collapse and observer intervention—as an absolute deterministic thermodynamic discharge governed by algebraic topology and non-Abelian gauge field theory.The 174 effective vibrational degrees of freedom of a C_60 fullerene form a 174-dimensional maximal torus T^174 phase space, subjected to a spontaneous Cartan projection SU(175) → U(1)^174 at the critical topological threshold. We demonstrate that the evaporation of 15,225 non-commutative positive roots during this symmetry breaking couples with the quadratic Casimir invariant C_2 to establish the Topological Landauer Limit (Λ_ROA). The system’s intrinsic topological torsion, mathematically immortalized as the linking number γ of the first Chern class, is discharged through a pure algebraic holographic topological cross-section (A_topo) derived via the Weyl Integration Formula. By substituting the empirical data from the University of Vienna’s 2004 fullerene thermal emission experiment into our Topo Thermodynamic Discharge Equation, we achieve perfect numerical convergence. When the thermodynamic emission rate exceeds the Stefan-Boltzmann limit, and the time of flight(t_flight) crosses the intrinsic critical time (∆t_crit), the wave-function visibility undergoes a deterministic phase-locking, proving that statistics is merely a probabilistic mask hiding geometric collapse.