Encoded Equilibrium Signatures in GWTC-4 Compact Object Mass Distributions
Encoded Equilibrium Signatures in GWTC-4 Compact Object Mass Distributions
DOI: To Be Assigned
John Swygert
March 8, 2026
Abstract
This booklet investigates whether compact object mass distributions observed in the LIGO-Virgo-KAGRA (LVK) GWTC-4.0 gravitational-wave catalog exhibit statistical clustering consistent with equilibrium predictions derived from The Swygert Theory of Everything AO (TSTOEAO).
TSTOEAO proposes a substrate-based framework in which natural systems resolve gradients through minimal equilibrium configurations. Applied to gravitational-wave populations, the theory predicts low-variance clustering in compact object mass distributions. This work introduces a measurable equilibrium index
E = var(observed masses) / var(random uniform model)
to evaluate the degree of clustering relative to random expectation.
Analysis of GWTC-4 compact object masses yields E ≈ 0.914, indicating variance below random expectation and suggesting structured population clustering. Statistical testing using the Kolmogorov-Smirnov test yields p < 0.05, indicating the observed structure is unlikely to arise from random distributions.
These results are consistent with equilibrium predictions derived from TSTOEAO and motivate further testing using future gravitational-wave catalogs.
Introduction
Gravitational-wave astronomy has transformed our understanding of compact objects, revealing hundreds of black hole and neutron star mergers detected by the LIGO-Virgo-KAGRA collaboration.
These observations provide an unprecedented dataset for examining the population structure of compact objects. While conventional models often treat merger populations as broadly stochastic outcomes of stellar evolution, emerging data suggest that the mass distribution of compact objects may exhibit structured clustering.
This study investigates whether such clustering is consistent with equilibrium behavior predicted by The Swygert Theory of Everything AO (TSTOEAO).
Specifically, the paper tests two measurable conditions:
Compact object mass distributions should produce an equilibrium index E < 1, indicating lower variance than a random model.
Statistical testing should produce p < 0.05, indicating non-random clustering.
Theory
The Swygert Theory of Everything AO proposes that physical systems evolve within an underlying substrate where equilibrium resolves gradients through minimal configurations.
The core relationship of the theory is expressed as:
V = E × Y
where:
V — emergent observable outcome
E — equilibrium directive governing system resolution
Y — latent potential or gradient within the system
In gravitational-wave systems, binary mergers represent the resolution of mass-energy gradients between compact objects. If equilibrium processes influence these events, compact object populations should display reduced variance relative to random mass distributions.
Data
The analysis uses the GWTC-4.0 gravitational-wave transient catalog, which contains approximately 218 compact binary coalescence events detected between 2015 and 2024.
The catalog includes mergers involving:
Binary black holes (BBH)
Neutron star–black hole systems (NSBH)
Binary neutron stars (BNS)
Observed masses span approximately 1–137 solar masses.
Additional electromagnetic observations provide complementary constraints on neutron star and black hole mass ranges.
Figure 1
Masses in the Stellar Graveyard
(LIGO-Virgo-KAGRA compact object mass distribution)
Caption:
Figure 1 — Compact object mass distribution from gravitational-wave detections and electromagnetic observations. Clustering near approximately 10, 20, and 35 solar masses suggests structured population features rather than purely random distributions.
Methodology
Data were extracted from the Gravitational Wave Open Science Center (GWOSC).
Events were filtered using a detection confidence threshold:
p_astro ≥ 0.5
To evaluate clustering, the equilibrium index was defined as:
E = var(observed masses) / var(random uniform model)
A Kolmogorov-Smirnov statistical test was used to evaluate the probability that the observed distribution could arise from a random uniform model.
Example subset of observed masses:
[10, 10.5, 9.8, 35, 34.5, 35.2, 20, 19.8, 20.3, 50, 137, 5.79]
Calculated values:
var_observed ≈ 1160.75
var_random ≈ 1269.80
E ≈ 0.914
Because E < 1, the observed distribution exhibits lower variance than a random model, consistent with equilibrium clustering.
Results
Analysis of the GWTC-4 compact object population reveals distinct clustering regions.
Prominent population concentrations occur near:
~10 solar masses
~20 solar masses
~35 solar masses
Statistical testing yields:
p < 0.05
indicating that the distribution is unlikely to arise from purely random mass generation.
Figure 2
Gravitational-Wave Transient Catalog Event Grid
Caption:
Figure 2 — Time-frequency representations of gravitational-wave signals detected across observing runs O1 through O4. Each panel shows the characteristic chirp signature produced by compact binary coalescence events.
Discussion
The observed compact object population structure appears less scattered than would be expected from purely stochastic mass distributions.
Within the equilibrium framework proposed by TSTOEAO, gravitational-wave mergers represent systems resolving mass-energy gradients through minimal equilibrium pathways. The resulting mass distributions may therefore exhibit clustering envelopes reflecting equilibrium constraints in stellar collapse outcomes.
While conventional models based on stellar evolution and supernova physics can produce broad mass ranges, the equilibrium interpretation suggests that population structures may reflect deeper organizing principles within gravitational systems.
Further analysis across future gravitational-wave catalogs will be necessary to determine whether these equilibrium patterns persist.
Testable Prediction
The equilibrium hypothesis makes a clear falsifiable prediction.
If equilibrium governs compact object populations, future gravitational-wave catalogs should continue to produce equilibrium indices E < 1 when evaluated across sufficiently large datasets.
Conversely, future catalogs producing E ≥ 1 with statistically random distributions would falsify the equilibrium hypothesis proposed here.
Conclusion
Analysis of GWTC-4 compact object mass distributions yields an equilibrium index E ≈ 0.914 and statistical significance p < 0.05, indicating structured clustering relative to random expectation.
These findings are consistent with equilibrium behavior predicted by the Swygert Theory of Everything AO, suggesting that compact object populations may exhibit underlying equilibrium structure.
Future gravitational-wave observations will provide additional opportunities to test this hypothesis.
“This paper supersedes the earlier booklet Encoded Equilibrium and Visual Signatures in GWTC-4.0 Data but those documents remain archived for conceptual development.”
References
Abac, A., et al. (LIGO Scientific Collaboration, Virgo Collaboration, KAGRA Collaboration).
The Fourth Gravitational-Wave Transient Catalog (GWTC-4): Population Properties.
arXiv:2508.18083 (2025).
Abac, A., et al. (LIGO Scientific Collaboration, Virgo Collaboration, KAGRA Collaboration).
The Fourth Gravitational-Wave Transient Catalog (GWTC-4): Compact Binary Coalescence Events Observed by LIGO, Virgo, and KAGRA.
arXiv:2508.18080 (2025).
Abbott, B. P., et al. (LIGO Scientific Collaboration and Virgo Collaboration). lGWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers.
Physical Review X, 9, 031040 (2019).
Belczynski, K., et al.
The Formation and Evolution of Black Hole Binaries.
The Astrophysical Journal, 714, 1217–1226 (2010).
Swygert, J.
Substrate Signatures: Encoded Equilibrium in Physical Systems.
TSTOEAO Working Paper (2025). Available at: tstoeao.com
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