DOI: (to be assigned)
John Swygert
March 19, 2026
Abstract
This paper presents a formal definition of the Swygert Equilibrium Quotient (SEQ) as a dimensionless metric for quantifying coherence in systems undergoing violent re-equilibration. SEQ is constructed as a weighted composite of measurable observables, including stability persistence, angular alignment, spatial clustering, and gradient persistence. The formulation is independent of any specific theoretical interpretation and is fully compatible with established physics. Within TSTOEAO, SEQ is interpreted as a candidate proxy for constraint-driven selection processes, though this interpretation remains provisional. The metric is designed for direct application across experimental and simulated systems, enabling consistent comparison between magnetic cusp chambers, explosion-implosion environments, and high-energy collision data.
- Mathematical Formulation
The Swygert Equilibrium Quotient is defined as:
\text{SEQ} = w_1 S + w_2 A + w_3 C + w_4 P
where:
represents stability persistence over time,
represents angular or directional alignment,
represents clustering or spatial organization,
represents persistence of structured gradients,
and are normalized weighting coefficients such that:
\sum_i w_i = 1
- Observable Definitions
Each component is derived from measurable quantities:
- Stability persistence from time-resolved position or structural data.
- Angular alignment from directional correlation analysis.
- Clustering from statistical distribution metrics.
- Gradient persistence from field or force-mapping continuity.
- Normalization and Scaling
Each term is normalized to allow comparison across systems of different scale, ensuring that SEQ remains dimensionless and transferable between experimental regimes.
- Application Domains
SEQ is applicable to:
- Magnetic cusp compression systems and buoyancy experiments.
- Explosion and implosion remnant analysis.
- High-energy collision event topology and particle distributions.
- Simulated systems undergoing rapid constraint-driven transitions.
- Interpretation Framework
As a purely mathematical construct, SEQ serves as a comparative metric independent of theoretical interpretation. Within TSTOEAO, it is considered a candidate indicator of underlying constraint selection, but its utility does not depend on that framework.
- Statistical Implementation
SEQ values are evaluated across repeated trials to determine correlation with stability, repeatability, and energy minimization. Statistical significance testing is required to establish meaningful relationships between SEQ and observed outcomes.
- Falsifiability
The metric is weakened if it shows no consistent correlation with experimentally observed stability or coherence. It gains support if higher SEQ values reliably predict repeatable, low-energy configurations across independent systems and datasets.
Conclusion
The formalization of the Swygert Equilibrium Quotient provides a quantitative foundation for analyzing coherence in violent re-equilibration systems. By converting qualitative observations into measurable quantities, SEQ enables cross-domain comparison and rigorous testing. Whether or not it ultimately reflects deeper physical principles, it stands as a useful and testable tool for studying how ordered structures emerge from instability.
References
Swygert, John. “Violent Re-equilibration: Explosions and Implosions as Natural Laboratories.” Ivory Tower Journal (2026).
Swygert, John. “Magnetic Compression at the Repulsion Cusp.” Ivory Tower Journal (2026).