A Minimal Structural Unification of Quantum Field Theory and Gravity with Exact Vacuum Stability

This paper presents a complete structural unification of quantum field theory (QFT) and general relativity (GR) based on a single, dimension-one scalar mediation field that dynamically regulates the gravitational coupling while preserving the exact probabilistic structure of quantum mechanics.

The unified framework satisfies all major consistency requirements for a viable QFT–GR theory:

• Exact recovery of classical Einstein gravity
• Exact recovery of flat-space quantum field theory
• Structural elimination of the cosmological constant to all orders
• Rigidity of the Born probability rule and Hilbert-space geometry
• Non-perturbative preservation of the Yang–Mills mass gap
• Absence of higher-curvature ghosts, extra dimensions, or vacuum fine-tuning

At the physical fixed point, the scalar field vanishes dynamically, enforcing:

• Zero effective cosmological constant
• Exact Newton coupling
• No fifth forces or equivalence-principle violations
• Standard gravitational-wave propagation
• Conventional cosmological perturbation behavior

The scalar field propagates as an exactly massless conformal mode in flat spacetime and acquires only curvature-induced effective mass in weakly curved backgrounds, ensuring both ultraviolet and infrared stability. The full operator algebra of the theory is shown to be renormalization-closed and non-extendable without violating at least one core physical constraint.

This work integrates and completes the following previously established structural results:

• The Structural Origin of the Born Rule: Rigidity of the Quantum Probability Exponent
DOI: https://doi.org/10.5281/zenodo.17864384

• Cosmological Constant Problem via Spectral Thermodynamic Invariance
DOI: https://doi.org/10.5281/zenodo.17550178

• Unconditional Dual Resolution of the Yang–Mills Mass Gap via the RP–Dirac Spectral Bridge
DOI: https://doi.org/10.5281/zenodo.17555872

Together, these results establish a single, isolated renormalization-group fixed point simultaneously enforcing:

• Zero vacuum energy
• Exact quantum probability structure
• Stable non-Abelian confinement
• Exact recovery of GR and QFT

The resulting theory defines a minimal, local, covariant, and dynamically complete bridge between quantum theory and spacetime geometry, without introducing higher-curvature terms, new particle species, or phenomenological tuning.

Earlier pillars of the framework established:

• a universal recursion law for lawful systems (The Tier-0 Framework and the Everything Equation), DOI: https://doi.org/10.5281/zenodo.17813117

• a complete operator-theoretic resolution of the quantum measurement problem, DOI: https://doi.org/10.5281/zenodo.17823241

• the Law of Endogenous Constraint governing the internal balance of admissible fields, DOI: https://doi.org/10.5281/zenodo.17823404

• semantic completeness beyond Gödel-type limitations, DOI: https://doi.org/10.5281/zenodo.17826373

• geometric rigidity and exponential stability of physical law under curvature flow (The Kappa Law), DOI: https://doi.org/10.5281/zenodo.17851714

  and 

• a fully constructive spectral realization of the fixed law in quantum gravity. DOI: https://doi.org/10.5281/zenodo.17538401