What question did this study set out to answer?

The aim is to present a unified framework for understanding spacetime geometry through the lens of attractor-relational dynamics.

February 17, 2026Open Access

Formal Theory of Attractor–Relational Dynamics (FTAR): Relational Stability as a Generative Mechanism for Classical and Quantum Spacetime (v18 Final)

Key Points

The aim is to present a unified framework for understanding spacetime geometry through the lens of attractor-relational dynamics.
Developed a scalar-based generative mechanism for spacetime geometry.
Provided formal proofs for the emergence of classical metrics as Hessians of a stability functional.
Defined integrability conditions necessary for local stability representations.
Reconstructed metrics related to black holes and cosmological models analytically.
Derived testable predictions on quantum behavior at the Planck scale.
Recovered classical metrics precisely as the Hessian of a stability functional.
Generated predictions for stochastic metric noise at the Planck scale.
Established stability-curvature constraints for the Cosmological Constant.
Provided a unified theory linking general relativity, quantum dynamics, and information theory.

Abstract

This manuscript presents the definitive version (v26. 1) of the Formal Theory of Attractor–Relational Dynamics (FTAR). The framework provides a rigorous, scalar-based generative mechanism for spacetime geometry, establishing that gravitation and quantum evolution are emergent manifestations of a single fundamental object: the Relational Stability Functional (Φ). Key Scientific Contributions: Hessian Metric Emergence: A formal proof demonstrating that the classical metric tensor gμν is exactly recovered as the Hessian of the stability functional. Integrability Conditions: Definition of the mathematical constraints (∂λgμν=∂μgλν) required for a metric to admit a local stability representation. Constructive Reconstruction of General Relativity: Exact analytical recovery of the Schwarzschild (static black hole), Kerr (rotating system), and Friedmann–Lemaître–Robertson–Walker (cosmological expansion) metrics. Quantum Stability Operator (Φ^): An extension of the theory to the Planck scale, where classical geometry emerges as the expectation value of an operator acting on a relational Hilbert space. Testable Predictions: Derivation of falsifiable consequences, including fundamental stochastic metric noise at the Planck scale and specific stability-curvature constraints on the Cosmological Constant (Λ). FTAR offers a mathematically explicit and parsimonious alternative to current quantum gravity paradigms, bridging information theory, attractor dynamics, and general relativity into a unified physical law. Updated to include full tensor stability, singularity resolution, and Hawking temperature saturation proofs

Formal Theory of Attractor–Relational Dynamics (FTAR): Relational Stability as a Generative Mechanism for Classical and Quantum Spacetime (v18 Final)

Key Points

Abstract

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