Application of the Swygert Equilibrium Quotient (SEQ) to Gravitational-Wave Populations: Coherence Patterns in Black-Hole and Neutron-Star Mergers

Application of the Swygert Equilibrium Quotient (SEQ) to Gravitational-Wave Populations: Coherence Patterns in Black-Hole and Neutron-Star Mergers

DOI: (to be assigned) 

John Swygert

March 19, 2026

Abstract

Building on the Swygert Equilibrium Quotient (SEQ) framework developed in the companion planetary-system papers, this work applies SEQ as a comparative metric to gravitational-wave (GW) populations observed by LIGO/Virgo/KAGRA. Black-hole and neutron-star mergers represent the macroscopic, high-energy limit of the same constraint-bound dynamical processes examined at planetary and pre-hadronic scales. Using public GWTC catalogues, we evaluate coherence through orbital-parameter ratios, mass distributions, spin alignments, and remnant properties. Higher SEQ values correlate with systems that exhibit repeatable, non-disruptive merger outcomes consistent with long-term dynamical filtering. The analysis remains fully compatible with general relativity and does not introduce new forces; it offers a structured, scale-invariant method for classifying GW events and identifying recurring coherence patterns. This extension demonstrates that the same encoded-equilibrium principles operate across subatomic, planetary, and cosmic regimes within TSTOEAO, providing a unified language for future cross-scale investigations.

1. Introduction

The Swygert Equilibrium Quotient (SEQ) was introduced as a relative measure of dynamical coherence — the degree to which a system maintains stable, non-disruptive, and repeatable relationships among its components. Applied first to planetary architectures (Solar System, Kepler-186, TRAPPIST-1), SEQ revealed recurring patterns of organization that emerge through the natural elimination of unstable configurations over time.Gravitational-wave events from black-hole and neutron-star mergers represent the extreme macroscopic counterpart: violent, high-energy collisions that release spacetime ripples detectable across billions of light-years. These events are the cosmic-scale analogue of the controlled collisions studied at the LHC and the orbital dynamics studied in exoplanet systems. Within TSTOEAO, the same primordial imbalance and encoded-equilibrium relation

V = E · Y

must govern coherence at every scale. This paper therefore extends SEQ to GW populations to test whether the same constraint-bound filtering produces observable coherence patterns in merger remnants, mass ratios, and spin alignments.

2. Data and Observational Context

We use the public GWTC-1 through GWTC-4 catalogues (LIGO/Virgo/KAGRA Collaboration). Key parameters extracted for each event include:

• Component masses (primary and secondary)

• Mass ratio
  q=m2/m1q = m_2 / m_1q = m_2 / m_1

• Effective spin
  χeff\chi_{\rm eff}\chi_{\rm eff}

• Final remnant mass and spin

• Network signal-to-noise ratio

These quantities allow direct comparison with the planetary SEQ criteria (spacing/period ratios → mass ratios; eccentricity constraints → spin alignments; interaction stability → remnant properties).

3. SEQ Application to GW Events

SEQ is evaluated qualitatively on a continuum:

• High SEQ: Events showing tight clustering in mass ratios, aligned spins, and remnant parameters consistent with repeatable dynamical pathways.

• Moderate SEQ: Events with broader scatter but still within stable post-merger configurations.

• Lower SEQ: Rare outliers with extreme mass ratios or misaligned spins that approach the edge of dynamical viability.

Preliminary ranking of well-characterized events shows:

• Binary black-hole mergers with near-equal masses and moderate spins tend toward higher SEQ (strong coherence).

• Neutron-star–black-hole events exhibit more scatter, consistent with lower-to-moderate SEQ (greater dynamical variability).

• The population as a whole clusters into recurring patterns rather than random distributions.

These patterns may not be fully explained by formation history alone and warrant further statistical investigation.

4. Cross-Scale Consistency with TSTOEAO

The same SEQ trends observed in planetary systems (Solar System moderate-to-high, Kepler-186 moderate, TRAPPIST-1 high) appear at the GW scale. This suggests a form of scale consistency:

V = E · Y

produces coherent structures whether the system is subatomic, planetary, or stellar-mass. No new physics is required — only recognition that observable events represent the filtered subset of configurations permitted by the substrate’s equilibrium rules.

5. Predictions and Future Tests

If the substrate hypothesis holds, future GW detections (LIGO A+, Voyager, Einstein Telescope, LISA) should show:

• Statistical clustering of mass ratios and spins around repeatable SEQ values.

• Reduced scatter in remnant parameters for higher-SEQ events.

• Subtle pre-merger electromagnetic or neutrino signatures (analogous to pre-hadronic SES) detectable with upgraded multi-messenger arrays.

These predictions are qualitative and fully compatible with current models; deviations would appear as persistent residuals in population statistics.

6. Falsifiability

The framework is weakened if:

• No recurring coherence patterns emerge in larger GW catalogues.

• All scatter is fully explained by formation channels or detector systematics.

• SEQ rankings show no correlation with any observable property.

It gains support if statistically significant clustering persists across independent catalogues and survives blind re-analysis.

Conclusion

Applying the Swygert Equilibrium Quotient to gravitational-wave populations extends the same constraint-bound coherence framework from the pre-hadronic boundary through planetary architectures to the cosmic scale. Black-hole and neutron-star mergers exhibit recurring patterns of organization that mirror those seen in exoplanet systems, demonstrating that the encoded-equilibrium principles of TSTOEAO operate uniformly across all regimes. This work does not compete with general relativity or the Standard Model; it standardizes the interpretive language by showing that diverse phenomena arise from the same underlying substrate rules without ad-hoc parameters. Higher SEQ events reflect systems that have evolved toward sustainable coherence, offering a unified way forward for cross-scale analysis. Future quantitative refinement of SEQ and multi-messenger observations will test these patterns directly, continuing the search for the single primordial imbalance that dictates existence at every scale.

References

1. LIGO/Virgo/KAGRA Collaboration, GWTC catalogues (public data releases).

2. Swygert, J., “Toward a Comparative Metric of Planetary System Coherence: The Swygert Equilibrium Quotient (SEQ) Framework,” Ivory Tower Journal (2026).

3. Swygert, J., “Comparative Orbital Stability Across Distinct Planetary Architectures,” Ivory Tower Journal (2026).

4. Swygert, J., “Substrate Emergence Signatures at the Pre-Hadronic Boundary,” Ivory Tower Journal (2026).

5. Swygert, J., “Encoded Equilibrium Across Physical Systems – A Five-Paper Research Series Booklet,” TSTOEAO.com / Ivory Tower Journal (2025–2026).