What question did this study set out to answer?

This research aims to classify closure regimes in closed classical gravity through symmetry considerations.

February 9, 2026Open Access

The Regime Trichotomy Theorem

Key Points

This research aims to classify closure regimes in closed classical gravity through symmetry considerations.
Proved a theorem regarding closure regimes
Analyzed symmetry-exhausted closure
Classified based on covariance and functional freedom
Identified exactly three distinct closure regimes
Established that no fourth closure regime exists
Demonstrated independence from field equations and matter content

Abstract

The theorem proves that closed classical gravity in three spatial dimensions admits exactly three symmetry-exhausted closure regimes and no fourth. The result is a structural classification based on classical covariance, finite quadratic closure, and exhaustion of functional freedom under symmetry, and is independent of field equations, matter content, or phenomenology.

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Cite This Study

Simon F. Gates (Sat,) studied this question.

synapsesocial.com/papers/69897a35f0ec2af6756e89d8 https://doi.org/https://doi.org/10.5281/zenodo.18515675