Temperature Dependence of the Constraint Network Sparse Rate γ(T): A Phenomenological Model for Chain Undertaking Decay

The constraint network sparse rate γ is a key parameter in Energy Ontology describing the natural decay rate of chain undertaking strength under thermal motion. This paper establishes a phenomenological Arrhenius-type model for the temperature dependence of γ: γ(T) = ν_D · exp(−E_bind/(k_B T)), where ν_D ≈ 10¹³ s⁻¹ is the Debye frequency and E_bind ≈ 0.16 eV is the equivalent binding energy of a chain, calibrated from the phase transition data of iron (melting point T_m = 1811 K, boiling point T_b = 3134 K). The model makes a directly testable prediction: in the femtosecond laser pump-probe experiment proposed in our companion paper on particle physics experimental equipment, the resonance peak width Γ of M-value oscillations is given by Γ = 2γ(T) and will follow an Arrhenius-type variation with temperature. By measuring the resonance peak width at different temperatures, the experimental value of E_bind can be extracted and independently compared with the known melting point of the target material. If the two are consistent, the γ(T) model receives independent experimental verification.