Universal Semantic Coupling: A Fifth Interaction Governing Structure Formation

We report the discovery of a universal dimensionless coupling  that governs information-geometric back-reaction in structured systems and measure its critical exponent  characterizing approach to semantic equilibrium.

Hamilton’s principle established that classical mechanics, optics, and thermodynamics are projections of a unified variational structure. We demonstrate this structure extends into information-geometric space through the Canonical Semantic Framework (CSF), which predicts that systems maintaining sustained structure operate near a semantic equilibrium manifold I ≈ 1, where I represents the ratio of information-geometric capacity to physical flux.

We test this framework in three radically different domains spanning ten orders of magnitude in timescale:

(1) Quantum feedback control: of superconducting qubits yields  with counterintuitive scalings inconsistent with standard control theory: optimal feedback gain  and recovery time . Crucially, Fisher information stabilizes 80% faster than state-space metrics , demonstrating top-down causation from information geometry to physical observables.

(2) Polymer rheology: using experimental xanthan gum frequency-sweep data across five formulations gives , invariant despite threefold variation in elastic modulus and salt concentration.

(3) Neural network grokking: dynamics reveal critical scaling  with R² > 0.98 as systems approach generalization, identifying I = 1 as a genuine critical manifold with mean-field-like exponent, the first measured semantic critical exponent.

The equilibrium couplings agree within 4% (combined ), while the critical exponent γ ≈ 0.73 defines a candidate universality class for semantic phase transitions. These systems span quantum coherent, classical dissipative, and computational regimes with no shared microscopic physics, yet exhibit identical information-geometric structure.

We propose semantic equilibrium as a fundamental organizing principle: long-lived structured systems maintain I ≈ 1 via back-reaction with characteristic coupling  and universal approach dynamics governed by exponent γ ≈ 0.7-0.8. This represents an effective organizing principle at the information-matter interface, operationally, a fifth interaction, beyond gravity and gauge forces, coupling information geometry to physical dynamics. The framework makes testable predictions for cold atoms, active matter, and cosmological structure formation.