Tricritical Universality Class from Minimal Structural Conditions: A Field-Theoretic Derivation of β = 1/4 for Coherence-Driven Organization

We derive a scalar field theory for coherence-driven organization from three minimal structural conditions—kinetic coupling to an environment, a Noethertype conservation law, and a self-bounding boundary condition—combined with four standard field-theoretic assumptions (locality, Lorentz invariance, U (1) gauge symmetry, renormalizability). The resulting Lagrangian is unique up to two real parameters. The theory introduces a topological parameter κ ∈ −1, +1 that governs the sign of the quartic self-coupling. At the critical point κ → 0, the quartic term vanishes identically, forcing stability onto the sextic term and placing coherencedriven transitions in the tricritical universality class. The mean-field critical exponent β = 1/4 follows directly from minimizing the effective free energy F ∼ r|ψ|² + w|ψ|⁶. This value is parameter-free: it cannot be tuned without abandoning the structural conditions that determine κ. The derivation identifies a broad class of organized systems—from protein folding to chemical oscillations to ecological transitions—whose order-parameter scaling should exhibit β = 1/4 near their coherence thresholds, consistent with the established tricritical phenomenology of He³ -He⁴ mixtures and metamagnets. The Higgs scalar sector and Ginzburg-Landau free energy emerge as domain-specific instances within the same two-parameter family, providing astructural explanation for their mathematical isomorphism. Aspects of this theoretical framework are subject to pending patent applications by Yunaverse, Inc.