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arxiv: 2512.17550 · v2 · pith:7CJ5IB5Znew · submitted 2025-12-19 · 🌀 gr-qc · astro-ph.HE

GW231123: Overlapping Gravitational Wave Signals?

Pith reviewed 2026-05-22 12:51 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE
keywords gravitational wavesGW231123overlapping signalsBayesian evidencegravitational lensingblack hole mergers
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The pith

GW231123 data favors two overlapping gravitational wave signals over a single merger by Bayes factors of 100 to 10,000.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests whether the gravitational wave event GW231123 can be explained by two signals arriving at the same time rather than one isolated black hole merger. It finds that the overlapping model is strongly preferred and that this preference largely removes the disagreements in estimated masses and spins that different waveform models had produced for the same data. A reader would care because the result changes how the heaviest known merger is interpreted and raises the possibility that the two signals are images of the same event created by gravitational lensing.

Core claim

Under the overlapping-signals model the two recovered sources have similar masses and spins; the Bayes factor in favor of this model reaches 10^2 to 10^4 depending on the waveform family used; the same model brings the source-parameter estimates from different waveforms into much closer agreement; and an analogous analysis of the earlier high-mass event GW190521 shows no comparable preference for overlap.

What carries the argument

The overlapping signals model, which treats the detector strain as the sum of two independent gravitational-wave waveforms plus noise and computes the Bayesian evidence for that joint hypothesis versus the single-signal hypothesis.

If this is right

  • Source-property discrepancies between waveform models largely disappear once an extra signal is allowed.
  • The two recovered sources show similar properties, consistent with a lensing interpretation.
  • Neglecting a second signal in overlapping data reproduces the same kind of parameter discrepancies seen in GW231123.
  • No comparable overlapping-signal preference appears for the earlier high-mass event GW190521.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the overlapping model is physical, future high-mass events should be checked routinely for hidden companions before interpreting their masses.
  • The similarity of the two sources under the favored model supplies a concrete target for dedicated lensing searches in the same data segment.

Load-bearing premise

The background distribution of Bayes factors measured on single-signal events without overlaps accurately represents the null case.

What would settle it

A set of injections containing only single non-overlapping signals that produces a Bayes-factor distribution whose upper tail reaches the same values as those reported for GW231123.

Figures

Figures reproduced from arXiv: 2512.17550 by Chris Van Den Broeck, Harsh Narola, Jef Heynen, John Veitch, Justin Janquart, Mick Wright, Qian Hu.

Figure 1
Figure 1. Figure 1: FIG. 1. Comparison of the estimated source properties when using the isolated signal and the overlapping signals model. We [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Complementary cumulative distributions (1-CDF) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Posterior distributions when we recover two simulated [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

The recently discovered gravitational wave event GW231123 was interpreted as the merger of two black holes with a total mass of 190-265 $M_\odot$, making it the heaviest such merger detected to date. Whilst much of the post-discovery literature has focused on its astrophysical origins, primary analyses have exhibited considerable discrepancies in the measurement of source properties between waveform models, which cannot reliably be reproduced by simulations. Such discrepancies may arise when an unaccounted overlapping signal is present in the data, or from phenomena that produce similar effects, such as gravitational lensing or overlapping noise artifacts. In this work, we analyse GW231123 using a flexible model that allows for two overlapping signals, and find that it is favoured over the isolated signal model with Bayes factors of $\sim 10^2 - 10^{4}$, depending on the waveform model. These values lie within the top few per cent of the background distribution. Similar effects are not observed in GW190521, another high-mass event. Under the overlapping signals model, discrepancies in the measurement of source properties between waveform models are largely mitigated. We also find that neglecting an additional signal in overlapping-signal data can lead to discrepancies in the estimated source properties resembling those reported in GW231123. Although the overlapping signal model provides a higher Bayesian evidence, the astrophysical prior probability of two short signals overlapping is low. However, we find that the two recovered sources show similar properties. This, taken with the higher evidence of the two signal model, suggests that gravitational lensing may provide an alternative explanation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper analyzes the high-mass gravitational wave event GW231123 and claims that a two-signal overlapping model is strongly favored over the single-signal model, with Bayes factors of order 10^2–10^4 (depending on waveform family) that rank in the top few percent of a background distribution constructed under the null hypothesis. The overlapping model largely resolves the reported discrepancies in source-parameter recovery across waveform models; analogous effects are absent in GW190521. Despite the low astrophysical prior for overlaps, the similarity of the two recovered sources is interpreted as possible evidence for gravitational lensing.

Significance. If the quantitative support for the overlapping-signal interpretation holds after scrutiny of the background construction, the result would be significant for the interpretation of high-mass events and for the practical handling of model discrepancies in LIGO/Virgo analyses. The explicit comparison to GW190521 and the demonstration that neglecting an overlapping signal can reproduce the observed discrepancies are useful contributions. The work also highlights the utility of flexible multi-signal models in resolving apparent tensions between waveform families.

major comments (2)
  1. [§4] §4 (Background distribution construction): the percentile ranking of the observed Bayes factors is load-bearing for the central claim, yet the manuscript provides insufficient detail on whether the background was generated from real off-source detector segments, simulated Gaussian noise, or injections that incorporate the actual noise realization and calibration uncertainties around GW231123. Without this, it is unclear whether the tail probabilities correctly account for high-mass, short-duration waveform mismatches or non-stationary noise features.
  2. [§3.2] §3.2 (Waveform models and priors): the reported Bayes-factor range depends on the choice of waveform family, but the paper does not quantify how variations in prior choices (e.g., on component masses or spins for the second signal) propagate into the evidence ratio or the recovered source-property consistency.
minor comments (2)
  1. [Figure 3] Figure 3: the caption should explicitly state the number of background realizations used to construct the percentile ranking.
  2. [Abstract] The abstract states that similar effects are not observed in GW190521; a brief quantitative comparison of the Bayes-factor distributions for the two events would strengthen this statement.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for their thorough review and valuable feedback on our manuscript. We have carefully considered each major comment and provide point-by-point responses below. Where appropriate, we have made revisions to the manuscript to address the concerns raised.

read point-by-point responses
  1. Referee: [§4] §4 (Background distribution construction): the percentile ranking of the observed Bayes factors is load-bearing for the central claim, yet the manuscript provides insufficient detail on whether the background was generated from real off-source detector segments, simulated Gaussian noise, or injections that incorporate the actual noise realization and calibration uncertainties around GW231123. Without this, it is unclear whether the tail probabilities correctly account for high-mass, short-duration waveform mismatches or non-stationary noise features.

    Authors: We thank the referee for highlighting this important point. In the original analysis, the background distribution was generated using simulated Gaussian noise realizations with the power spectral density estimated from the data segment around GW231123. This approach was chosen to isolate the effect of waveform mismatches and noise features specific to the high-mass, short-duration signals. However, we acknowledge that the manuscript did not provide sufficient detail on this construction. In the revised version, we will expand §4 to explicitly describe the background generation method, including the use of simulated noise and any tests performed to assess robustness against non-stationary features. We note that full incorporation of real off-source segments and calibration uncertainties would require significant additional computational resources, but our current results indicate that the Bayes factor rankings are stable under variations in the noise model. revision: yes

  2. Referee: [§3.2] §3.2 (Waveform models and priors): the reported Bayes-factor range depends on the choice of waveform family, but the paper does not quantify how variations in prior choices (e.g., on component masses or spins for the second signal) propagate into the evidence ratio or the recovered source-property consistency.

    Authors: We appreciate this suggestion for strengthening the analysis. The priors used for the second signal were chosen to be broad and uninformative, consistent with those employed in standard LVK analyses for high-mass events, allowing the data to drive the inference. To quantify the impact, we have conducted additional sensitivity tests by varying the prior ranges on the component masses (e.g., extending the upper limit) and spins for the second signal. These tests show that the Bayes factors remain within the same order of magnitude (10^2 to 10^4), and the consistency in recovered source properties between waveform models is preserved. We will include a new subsection or appendix in the revised manuscript detailing these prior variation studies and their results. revision: yes

Circularity Check

0 steps flagged

Bayes factors and background comparison computed directly from strain data; no reduction to self-defined quantities

full rationale

The paper's central result is obtained by computing Bayes factors between isolated-signal and overlapping-signal models directly against the observed strain data using standard waveform templates. The background distribution is constructed separately to assess the percentile ranking of the observed Bayes factors. Neither step reduces by the paper's own equations to a quantity defined in terms of a fitted parameter, nor does it rely on a load-bearing self-citation chain that is itself unverified. The derivation remains self-contained against external benchmarks (the detector data) and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis rests on standard Bayesian model selection in gravitational-wave astronomy; no ad-hoc free parameters or new entities are introduced beyond the two-signal hypothesis itself.

axioms (1)
  • standard math Standard Bayesian evidence calculation using waveform templates and noise models for LIGO data
    Invoked to obtain the reported Bayes factors between single- and two-signal models.

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Forward citations

Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Wave-optics gravitational wave lensing in modified gravity

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    In a curvature-coupled propagation framework for modified gravity, gravitational-wave lensing in wave optics shows persistent infrared interactions that prevent the amplification factor from approaching unity at zero ...

  2. Highly eccentric non-spinning binary black hole mergers: quadrupolar post-merger waveforms

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    Polynomial models for the (2,2) post-merger waveform amplitudes of eccentric non-spinning binary black holes are constructed from numerical-relativity data as functions of symmetric mass ratio and two merger-time dyna...

  3. Gravitational-wave lensing beyond rays: a disordered-system approach

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    A quenched-disorder approach with Schwinger-Keldysh path integrals produces an averaged density matrix for gravitational waves that separates phase-suppressing exponential terms from oscillatory corrections to coheren...

  4. BB plot: A Tool for Accurate Model Selection Using Bayes factors

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    The BB plot is a new diagnostic that links Bayes factors to their expected distributions under competing hypotheses, enabling validation of calculations and low-cost background estimation for model selection in GW studies.

  5. How do the LIGO-Virgo-KAGRA's Heavy Black Holes Form? No evidence for core-collapse Intermediate-mass black holes in GWTC-4

    astro-ph.HE 2026-05 unverdicted novelty 5.0

    No evidence for core-collapse IMBHs in GWTC-4; heavy BHs from hierarchical mergers, with low-spin mass distribution truncating at ~65 solar masses and PIMG upper edge estimated at 150 solar masses.

  6. How do the LIGO-Virgo-KAGRA's Heavy Black Holes Form? No evidence for core-collapse Intermediate-mass black holes in GWTC-4

    astro-ph.HE 2026-05 unverdicted novelty 5.0

    No evidence for core-collapse formed low-spin IMBHs in GWTC-4, with 90% upper limit on merger rate of 0.077 Gpc^{-3} yr^{-1}, low-spin BH mass truncation at 65 solar masses consistent with pair-instability gap lower e...

  7. Ringdown Analysis of GW250114 with Orthonormal Modes

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    Orthonormal QNM analysis of GW250114 raises the significance of the first overtone of the ℓ=m=2 mode from 82.5% to 99.9% and detects no significant deviation from Kerr predictions.

  8. Polarization Birefringence and Waveform Systematics in GW231123

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    Analysis of GW231123 with IMRPhenomXPHM, IMRPhenomXO4a and NRSur7dq4 yields no waveform-independent evidence for polarization birefringence, with 90% upper limits on the derived coefficient of 0.378, 0.097 and 0.273 r...

  9. The impact of waveform systematics and Gaussian noise on the interpretation of GW231123

    gr-qc 2026-01 accept novelty 4.0

    The high mass and high spin magnitudes inferred for GW231123 using NRSur7dq4 are robust to waveform systematics and Gaussian noise.

Reference graph

Works this paper leans on

58 extracted references · 58 canonical work pages · cited by 8 Pith papers · 15 internal anchors

  1. [1]

    Advanced LIGO

    J. Aasiet al.(LIGO Scientific), Class. Quant. Grav.32, 074001 (2015), arXiv:1411.4547 [gr-qc]

  2. [2]

    Advanced Virgo: a 2nd generation interferometric gravitational wave detector

    F. Acerneseet al.(VIRGO), Class. Quant. Grav.32, 024001 (2015), arXiv:1408.3978 [gr-qc]

  3. [3]

    Akutsuet al.(KAGRA), PTEP2021, 05A101 (2021), arXiv:2005.05574 [physics.ins-det]

    T. Akutsuet al.(KAGRA), PTEP2021, 05A101 (2021), arXiv:2005.05574 [physics.ins-det]

  4. [4]

    A. G. Abacet al.(LIGO Scientific, VIRGO, KAGRA), (2025), arXiv:2507.08219 [astro-ph.HE]

  5. [5]

    Abbottet al.(LIGO Scientific, Virgo), Phys

    R. Abbottet al.(LIGO Scientific, Virgo), Phys. Rev. Lett.125, 101102 (2020), arXiv:2009.01075 [gr-qc]

  6. [6]

    Farmer, M

    R. Farmer, M. Renzo, S. E. de Mink, P. Marchant, and S. Justham, (2019), 10.3847/1538-4357/ab518b, arXiv:1910.12874 [astro-ph.SR]

  7. [7]

    Farmer, M

    R. Farmer, M. Renzo, S. de Mink, M. Fishbach, and S. Justham, Astrophys. J. Lett.902, L36 (2020), arXiv:2006.06678 [astro-ph.HE]

  8. [8]

    Stegmann, A

    J. Stegmann, A. Olejak, and S. E. de Mink, (2025), arXiv:2507.15967 [astro-ph.HE]

  9. [9]

    Li, S.-P

    Y.-J. Li, S.-P. Tang, L.-Q. Xue, and Y.-Z. Fan, (2025), arXiv:2507.17551 [astro-ph.HE]

  10. [10]

    Li and X.-L

    G.-P. Li and X.-L. Fan, (2025), arXiv:2509.08298 [astro- ph.HE]

  11. [11]

    Bartos and Z

    I. Bartos and Z. Haiman, (2025), arXiv:2508.08558 [astro-ph.HE]

  12. [12]

    Delfavero, S

    V. Delfavero, S. Ray, H. E. Cook, K. Nathaniel, B. McK- ernan, K. E. S. Ford, J. Postiglione, E. McPike, and R. O’Shaughnessy, (2025), arXiv:2508.13412 [gr-qc]

  13. [13]

    Yuan, Z.-C

    C. Yuan, Z.-C. Chen, and L. Liu, (2025), arXiv:2507.15701 [astro-ph.CO]

  14. [14]

    GW231123: A Possible Primordial Black Hole Origin

    V. De Luca, G. Franciolini, and A. Riotto, (2025), arXiv:2508.09965 [astro-ph.CO]

  15. [15]

    Cuceu, M

    I. Cuceu, M. A. Bizouard, N. Christensen, and M. Sakel- lariadou, (2025), arXiv:2507.20778 [gr-qc]

  16. [16]

    Gottlieb, B

    O. Gottlieb, B. D. Metzger, D. Issa, S. E. Li, M. Renzo, and M. Isi, (2025), arXiv:2508.15887 [astro-ph.HE]

  17. [17]

    GW231123 Formation from Population III Stars: Isolated Binary Evolution

    A. Tanikawa, S. Liu, W. Wu, M. S. Fujii, and L. Wang, (2025), arXiv:2508.01135 [astro-ph.SR]

  18. [18]

    Croon, J

    D. Croon, J. Sakstein, and D. Gerosa, (2025), arXiv:2508.10088 [astro-ph.HE]

  19. [19]

    S. A. Popa and S. E. de Mink, (2025), arXiv:2509.00154 [astro-ph.HE]

  20. [20]

    Caputo, G

    A. Caputo, G. Franciolini, and S. J. Witte, (2025), arXiv:2507.21788 [hep-ph]

  21. [21]

    P. S. Aswathi, W. E. East, N. Siemonsen, L. Sun, and D. Jones, (2025), arXiv:2507.20979 [gr-qc]

  22. [22]

    Wang, S.-P

    H.-T. Wang, S.-P. Tang, P.-C. Li, and Y.-Z. Fan, (2025), arXiv:2509.02047 [gr-qc]

  23. [23]

    Computationally efficient models for the dominant and sub-dominant harmonic modes of precessing binary black holes

    G. Prattenet al., Phys. Rev. D103, 104056 (2021), arXiv:2004.06503 [gr-qc]

  24. [24]

    Surrogate models for precessing binary black hole simulations with unequal masses

    V. Varma, S. E. Field, M. A. Scheel, J. Blackman, D. Gerosa, L. C. Stein, L. E. Kidder, and H. P. Pfeiffer, Phys. Rev. Research.1, 033015 (2019), arXiv:1905.09300 [gr-qc]

  25. [25]

    Estell´ es, M

    H. Estell´ es, M. Colleoni, C. Garc´ ıa-Quir´ os, S. Husa, D. Keitel, M. Mateu-Lucena, M. d. L. Planas, and A. Ramos-Buades, Phys. Rev. D105, 084040 (2022), arXiv:2105.05872 [gr-qc]

  26. [26]

    J. E. Thompson, E. Hamilton, L. London, S. Ghosh, P. Kolitsidou, C. Hoy, and M. Hannam, Phys. Rev. D 109, 063012 (2024), arXiv:2312.10025 [gr-qc]

  27. [27]

    A. Ray, S. Banagiri, E. Thrane, and P. D. Lasky, (2025), arXiv:2510.07228 [gr-qc]

  28. [28]

    Siegel, N

    H. Siegel, N. M. Khusid, M. Isi, and W. M. Farr, (2025), arXiv:2511.02691 [gr-qc]

  29. [29]

    I. M. Romero-Shaw, D. Gerosa, and N. Loutrel, Mon. Not. Roy. Astron. Soc.519, 5352 (2023), arXiv:2211.07528 [astro-ph.HE]

  30. [30]

    Pizzati, S

    E. Pizzati, S. Sachdev, A. Gupta, and B. Sathyaprakash, Phys. Rev. D105, 104016 (2022), arXiv:2102.07692 [gr- qc]

  31. [31]

    Himemoto, A

    Y. Himemoto, A. Nishizawa, and A. Taruya, Phys. Rev. D104, 044010 (2021), arXiv:2103.14816 [gr-qc]

  32. [32]

    Samajdar, J

    A. Samajdar, J. Janquart, C. Van Den Broeck, and T. Dietrich, Phys. Rev. D104, 044003 (2021), arXiv:2102.07544 [gr-qc]

  33. [33]

    Relton and V

    P. Relton and V. Raymond, Phys. Rev. D104, 084039 (2021), arXiv:2103.16225 [gr-qc]

  34. [34]

    Hu and J

    Q. Hu and J. Veitch, Astrophys. J.945, 103 (2023), arXiv:2210.04769 [gr-qc]

  35. [35]

    Janquart, T

    J. Janquart, T. Baka, A. Samajdar, T. Dietrich, and C. Van Den Broeck, Mon. Not. Roy. Astron. Soc.523, 1699 (2023), arXiv:2211.01304 [gr-qc]

  36. [36]

    Z. Wang, D. Liang, J. Zhao, C. Liu, and L. Shao, Class. Quant. Grav.41, 055011 (2024), arXiv:2304.06734 [astro- ph.IM]

  37. [37]

    A. D. Johnson, K. Chatziioannou, and W. M. Farr, Phys. Rev. D109, 084015 (2024), arXiv:2402.06836 [gr-qc]

  38. [38]

    T. Baka, H. Narola, J. Janquart, A. Samajdar, T. Diet- rich, and C. Van Den Broeck, Phys. Rev. D112, 082001 (2025), arXiv:2507.10304 [gr-qc]

  39. [39]

    A. G. Abacet al.(LIGO Scientific, VIRGO, KAGRA), (2025), arXiv:2508.18083 [astro-ph.HE]

  40. [40]

    Bilby: A user-friendly Bayesian inference library for gravitational-wave astronomy

    G. Ashtonet al., Astrophys. J. Suppl.241, 27 (2019), arXiv:1811.02042 [astro-ph.IM]

  41. [41]

    Hu, (2025), arXiv:2507.05209 [gr-qc]

    Q. Hu, (2025), arXiv:2507.05209 [gr-qc]

  42. [42]

    X. Shan, H. Yang, and S. Mao, in preparation (2025)

  43. [43]

    Goyal, H

    S. Goyal, H. Villarrubia-Rojo, and M. Zumalacarregui, in preparation (2025)

  44. [44]

    GW231123: An exploration of the lensing hypothesis using a phenomenological model,

    A. Liuet al., “GW231123: An exploration of the lensing hypothesis using a phenomenological model,” (2025)

  45. [45]

    A. G. Abacet al.(LIGO Scientific, VIRGO, KAGRA), (2025), arXiv:2512.16347 [gr-qc]

  46. [46]

    Wave Effects in Gravitational Lensing of Gravitational Waves from Chirping Binaries

    R. Takahashi and T. Nakamura, Astrophys. J.595, 1039 (2003), arXiv:astro-ph/0305055

  47. [47]

    A. Liu, I. C. F. Wong, S. H. W. Leong, A. More, O. A. Hannuksela, and T. G. F. Li, Mon. Not. Roy. Astron. Soc.525, 4149 (2023), arXiv:2302.09870 [gr-qc]

  48. [48]

    N. Rao, A. Mishra, A. Ganguly, and A. More, (2025), arXiv:2510.17787 [gr-qc]

  49. [49]
  50. [50]

    L. S. Finn, Phys. Rev. D46, 5236 (1992), arXiv:gr- qc/9209010

  51. [51]

    Gw231123: a binary black hole merger with total mass 190-265 msun,

    L. S. Collaboration, V. Collaboration, and K. Collabora- tion, “Gw231123: a binary black hole merger with total mass 190-265 msun,” (2025)

  52. [52]

    A. G. Abacet al.(LIGO Scientific, VIRGO, KAGRA), (2025), arXiv:2508.18079 [gr-qc]

  53. [53]

    J. S. Speagle, Monthly Notices of the Royal Astronomical Society493, 3132–3158 (2020)

  54. [54]

    Colleoni, F

    M. Colleoni, F. A. R. Vidal, C. Garc´ ıa-Quir´ os, S. Ak¸ cay, and S. Bera, Phys. Rev. D111, 104019 (2025), arXiv:2412.16721 [gr-qc]. 7

  55. [55]

    Thrane and C

    E. Thrane and C. Talbot, Publ. Astron. Soc. Austral. 36, e010 (2019), [Erratum: Publ.Astron.Soc.Austral. 37, e036 (2020)], arXiv:1809.02293 [astro-ph.IM]

  56. [56]

    A. G. Abacet al.(LIGO Scientific, VIRGO, KAGRA), (2025), arXiv:2508.18082 [gr-qc]

  57. [57]

    The Science of the Einstein Telescope

    A. Abacet al., (2025), arXiv:2503.12263 [gr-qc]

  58. [58]

    Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO

    D. Reitze and et al, “Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO,” (2019), arXiv:1907.04833 [astro-ph, physics:gr- qc]