This paper precisely calculates the critical density threshold ρc1 at which the constraint network transitions from the M≈0. 5 oscillation state to the M→0 free state, proceeding from the hydrogen atom ground-state wave function and the independently derived electron rest energy of 0. 511 MeV within Energy Ontology. The calculation path is as follows: the probability density distribution of the hydrogen atom ground-state electron is reinterpreted as the average flux density of M≈0. 5 oscillation-state energy trajectories in the constraint network; dividing the electron rest energy by the effective constraint volume yields ρc1 = 8. 233×10²⁹ MeV/m³ = 1. 319×10¹⁷ J/m³. This value lies between the sparse oscillation zone of the atomic shell and the dense sealing zone of the nucleus, consistent with the constraint network density distribution picture. This paper further performs an inverse verification of the hydrogen atom ionization energy—the Rydberg energy Rᵧ—using ρc1. The constraint gap energy = ρc1 × Vₑff × α² ≈ 27. 2 eV, which differs from the measured Rᵧ = 13. 6 eV by exactly a factor of 2. This factor corresponds precisely to the factor 2 in the origin relation α² = 2Rᵧ/ (mₑ c²) of Energy Ontology. ρc1, α, and Rᵧ form a self-consistent closed loop within the constraint network framework. This paper introduces no adjustable parameters and honestly labels the model dependence of the effective volume approximation.
Menggang Yu (Sat,) studied this question.
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