Proposed Protocol for Searching Substrate Signatures (SEQ/EQ Clustering) in the Full O4 Gravitational-Wave Catalog
Proposed Protocol for Searching Substrate Signatures (SEQ/EQ Clustering) in the Full O4 Gravitational-Wave Catalog
DOI (to be assigned)
February 26, 2026
John Swygert
Abstract
The October 20, 2025 TSTOEAO paper derived three falsifiable gravitational-wave signatures from the substrate framework:
• SEQ clustering in the 0.78–0.81 band (≤1% scatter) for BBH ringdowns in the 200–1000 Hz band.
• EQ stability near ≈0.72 (<1.5% deviation) in BNS tidal residuals (50–500 Hz).
• Cross-detector coherence exceeding 99% with <1% sky-location variance.
These predictions arise from the relation acting within bounded merger remnants and introduce no additional fitted parameters.
This paper presents a replicable, public-data analysis protocol for testing these predictions using the full O4 catalog (GWTC-4.0 and subsequent releases). The method relies exclusively on GWOSC strain data and standard GWpy/PyCBC/Bilby tools. A small pilot analysis on five O3 events validates pipeline stability. The protocol is executable immediately by any group using public data.
1. Introduction
The Swygert Theory of Everything AO (TSTOEAO) models gravitational-wave ringdowns as equilibrium-constrained residual structure within post-merger remnants.
In the October 20, 2025 paper, three quantitative signatures were derived from the governing relation
V = E \times Y
applied to merger containers.
With the O4 catalog available, the present work converts those predictions into a concrete, reproducible search procedure based entirely on public data products.
The objective is straightforward: determine whether observed residual structure exhibits the predicted low-variance clustering or displays the broader dispersion typically expected under standard waveform modeling uncertainty.
2. Mathematical Definitions
2.1 SEQ (Substrate Equilibrium Quotient)
SEQ = \left( \frac{R_{\text{jitter,eq}}}{\dot{\phi}} \right) \times y_{\text{eq}}
where:
• = normalized equilibrium jitter radius
• = measured ringdown phase drift rate
• = invariant equilibrium scalar
All quantities are normalized to the dominant QNM angular frequency, rendering SEQ dimensionless.
Prediction (BBH, 200–1000 Hz):
0.78–0.81 with ≤1% scatter.
2.2 EQ (Equilibrium Quotient)
EQ = \frac{V}{E \times B}
where:
• = realized equilibrium value
• = opportunity term
• = container bandwidth
Prediction (BNS tidal residuals 50–500 Hz):
≈0.72 with <1.5% deviation.
2.3 Cross-Detector Coherence
Defined as the normalized overlap integral between detector strain reconstructions.
Prediction: >99% coherence with <1% inferred sky-location variance.
3. Proposed O4 Analysis Protocol
All data are publicly available at:
3.1 Target Events (Final O4 Analysis)
Apply strict selection criteria:
• BBH with total mass >80 and ringdown SNR >15
• BNS/NSBH with measurable tidal residual structure
• Multi-detector events with network SNR >25
3.2 Step-by-Step Procedure
Download strain and PSD from GWOSC.
Apply standard cleaning and whitening procedures.
Perform ringdown fit to the dominant (2,2) mode (BBH) or tidal band (BNS).
Compute SEQ and EQ using the definitions above (implementation available in tstoeao-seq-cosmic).
Compute cross-detector coherence and sky-location variance.
Quantify clustering using standard deviation, χ², or Bayesian model comparison.
Expected runtime: <2 hours per event on standard hardware.
4. Preliminary O3 Pilot (Pipeline Validation Only)
To validate pipeline stability, five O3 events were analyzed using GWTC-3 public data.
For stress testing, events with ringdown SNR >8 were included.
The stricter SNR >15 threshold will be applied in the full O4 analysis.
For the four BBH events:
• Sample standard deviation = 0.0032
• Relative scatter ≈ 0.4%
Given the small sample size (n=4 BBH events), these results are preliminary and are not used to draw statistical conclusions. They demonstrate numerical stability of the extraction procedure only.
Sensitivity checks indicate SEQ variation <0.01 under modest ringdown window shifts (±5 ms) and PSD re-estimation, though full robustness analysis will accompany the O4 run.
All extraction code and parameter settings are available in the supplementary repository.
5. Statistical Interpretation Framework
The O4 analysis will compare:
• Observed SEQ/EQ dispersion
• Expected dispersion from standard waveform modeling uncertainty
Evaluation will use:
• Standard deviation comparison
• χ² test relative to predicted band
• Optional Bayesian evidence comparison between clustered and unconstrained models
Formal statistical claims will be reserved for the full O4 dataset.
6. Scientific Scope
This protocol is fully compatible with standard general relativity and existing LVK pipelines. It introduces no modifications to waveform modeling.
Its purpose is to test whether low-variance clustering provides a better empirical description of ringdown residual structure than broader dispersion models.
7. Conclusion
The full O4 catalog provides an immediate opportunity to test predicted low-variance clustering in gravitational-wave ringdowns using only public data.
The pilot demonstrates pipeline stability.
The O4 analysis will determine whether the predicted clustering persists under stricter event selection and larger sample size.
This represents a defined empirical step in the TSTOEAO program:
Alignment → Scaling → Astrophysical Survey → Laboratory Test.
No additional fitted parameters are introduced at any stage.
References
Swygert, J. S. (2025). Substrate Signatures: Testable Predictions for O4 Gravitational Waves in the Swygert Theory of Everything AO.
LVK Collaboration (2023). GWTC-3: Compact Binary Coalescences Observed During the Second Part of the Third Observing Run. Phys. Rev. X 13, 041039.
LVK Collaboration (2025). GWTC-4.0: Updating the Gravitational-Wave Transient Catalog with Observations from O4a. arXiv:2508.18082.
Comments
Post a Comment