Emergence of Doubly Heavy Baryonic Structures from a Closed Quartic Variational Functional Reduction to the Livolsi Structural Constants L and E Star and Connection with CERN Observations

A closed quartic variational functional is introduced and developed as a self-contained generative framework in which physical structure, hierarchy, and energy scale emerge without external input, parameter tuning, or phenomenological assumptions. Starting from the exact functional definition, a complete variational derivation is carried out, leading to an explicit Hessian decomposition of the form H=E⋆TH = E^ TH=E⋆T. The spectrum of the normalized operator is uniquely determined as {1,L,L}\{1, L, L\}{1,L,L}, where LLL is a dimensionless structural constant. This spectral structure enforces a minimal cyclic closure with three components and leads to a Z3-stable configuration. From this structure, a natural asymmetry arises for L<1L < 1L<1, producing a clustered (2+1)(2+1)(2+1) configuration characterized by two dominant modes and one suppressed mode. The internal hierarchy is derived explicitly, yielding a ratio α/β∼1/Lα/β ~ 1/Lα/β∼1/L, which fixes the relative weight of the components without introducing free parameters. All physical observables, including the energy and mass spectrum, are shown to take the universal form Mn=E⋆fn(L)M_n = E^ f_n(L)Mn=E⋆fn(L), where E⋆E^⋆ is an emergent energy scale determined dynamically and related to an intrinsic coherence length. No external constants or mass parameters are introduced. The framework naturally reproduces the structural features of doubly heavy baryonic configurations, such as those observed at CERN in the LHCb experiment, including clustering, hierarchy, and energy scale. These results suggest that the observed heavy–heavy–light structures can be interpreted as direct realizations of internal solutions of the variational functional. The entire physical content of the system is therefore fully determined by two quantities only, the Livolsi structural constants (L,E⋆)(L, E^)(L,E⋆), establishing a closed, parameter-free, and internally consistent framework.