Emergence of the Mercury Perihelion Shift

The perihelion shift of Mercury is derived as a purely structural consequence of a closed quartic variational functional S[Ψ], without introducing spacetime geometry, gravitational interaction, or phenomenological corrections. The derivation follows a strictly constrained emergence procedure in which all admissible structures originate from the functional through a mandatory sequence: variational stationarity, Hes- sian construction, spectral decomposition, invariant extraction, domain emergence, operator induction, spectral hierarchy, and admissibility. Within this framework, the invariant set {L,E⋆, ν,Z3} is generated from the Hessian spectrum, with L = 1/4 and a twofold degeneracy structure {1, L,L}. The emergent domain induces an internal operator ΓD, whose spectrum denes a hier- archical organization B = {E⋆Lk}. The closure level k is determined structurally through compatibility constraints involving Z3 cyclicity, spectral stability, and res- olution scale ν, yielding k = 12 as the minimal stable depth. The perihelion shift arises from a second-order spectral coupling between adja- cent hierarchy levels, induced by Z3 degeneracy.