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REVIEW 2 major objections 4 minor 85 references

Stacking current binary-black-hole events gives only moderate evidence for the full (2,0) gravitational-wave mode; decisive detection is projected after roughly 166 events.

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T0 review · grok-4.5

2026-07-11 11:35 UTC pith:RWWPH3G3

load-bearing objection Solid cumulative search for the full (2,0) mode on O4 data; the stacked log10 B = 1.38 ± 0.79 and memory SNR ~0.9 are clean, while the N_events ~166 forecast is explicitly optimistic and systematics-limited. the 2 major comments →

arxiv 2607.04909 v1 pith:RWWPH3G3 submitted 2026-07-06 gr-qc

A stepping stone toward detecting gravitational wave memory: a cumulative analysis with the full (ell=2, m=0) spherical harmonic using events from GWTC-4.0 and GWTC-5.0

Maria Rossell\'o-Sastre , Sascha Husa , Yumeng Xu , Jorge Valencia , Joan Llobera-Querol , Antoni Ramos-Buades This is my paper
classification gr-qc
keywords gravitational-wave memory(2,0) modeBayesian model selectionIMRPhenomTHM_20GWTC-4.0SNR stackingbinary black holes
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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 subdominant (ℓ=2,m=0) spherical-harmonic mode—containing both its oscillatory ringdown piece and the permanent displacement memory—is already present in the binary-black-hole signals of GWTC-4.0 and a few loud GWTC-5.0 events. By comparing two otherwise identical waveform models, one with and one without that mode, the authors obtain a cumulative log-10 Bayes factor of 1.38 ± 0.79 for the full O4a catalog—moderate support that falls short of decisive. Stacking the mode’s signal-to-noise ratio yields a memory-only value near 0.9 after 7.5 months of O4a data, consistent with earlier forecasts. The authors argue that including the oscillatory contribution first strengthens the evidence relative to memory-only searches and therefore serves as a practical intermediate step toward a memory detection. Under the observed distribution of per-event Bayes factors they estimate that decisive evidence (log-10 B − 1σ ≥ 2) would require roughly 166 events, while cautioning that waveform systematics remain uncontrolled.

Core claim

For the 84 binary-black-hole events of GWTC-4.0 the stacked log-10 Bayes factor between the full-(2,0) model IMRPhenomTHM_20 and the model without that mode is 1.38 ± 0.79; under the fitted empirical distributions of the individual Bayes factors, decisive evidence is expected after N_events = 166^{+82}_{-55} detections at current sensitivity.

What carries the argument

Paired Bayesian model comparison of IMRPhenomTHM_20 (full (2,0) mode = oscillatory ringdown + displacement memory) versus IMRPhenomTHM (identical model without the mode), with per-event log-10 Bayes factors stacked under independence and validated by SNR stacking and high-SNR scaling relations.

Load-bearing premise

That the distribution of Bayes factors measured on the present GWTC-4.0 sample will continue to describe future detections, and that residual waveform modelling errors (especially the missing (3,±2) multipole) do not systematically bias those Bayes factors.

What would settle it

Accumulate a catalog of ~170 binary-black-hole events at O4/O5 sensitivity, recompute the stacked log-10 Bayes factor with the same two models (and with models that include the (3,±2) multipole), and check whether log-10 B − 1σ reaches or exceeds 2.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Decisive statistical evidence for the full (2,0) mode is expected before a clean detection of the memory component alone.
  • Controlling the presence of the full (2,0) mode supplies a practical intermediate step that also helps isolate systematics before memory-only searches.
  • Current individual events remain statistically consistent with either model; the (2,0) contribution is still too weak to shift recovered source parameters appreciably.
  • An optimistic total of ~166 events at present sensitivity would suffice for decisive evidence under the measured Bayes-factor distribution.

Where Pith is reading between the lines

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

  • Once the (2,0) mode is established, the same stacking pipeline can be re-run with the oscillatory piece subtracted to isolate the pure memory contribution and quantify how much extra catalog size it requires.
  • The mild preference already seen for the loudest events (especially GW230814_230901) suggests that a handful of future high-SNR, edge-on systems could accelerate the climb to decisive evidence faster than the average-event forecast.
  • Any future claim of memory detection that does not first demonstrate control of the full (2,0) mode will be vulnerable to the same systematics the authors flag for the missing higher multipoles.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The manuscript reanalyzes the 84 BBH events of GWTC-4.0 (plus six selected high-SNR GWTC-5.0 events) with the quasi-circular, non-precessing IMRPhenomTHM_20 model that includes both the oscillatory ringdown and displacement-memory pieces of the (2,0) mode. Bayesian model comparison against IMRPhenomTHM yields a stacked log10 B = 1.38 ± 0.79 for the GWTC-4.0 sample; the corresponding stacked memory SNR after ~7.5 months of O4a is 0.89^{+0.29}_{-0.11}. A single precessing candidate is also examined with IMRPhenomTPHM_20 and shows no additional support. From the empirical distribution of the per-event Bayes factors the authors forecast that decisive evidence (log10 B - 1σ ≥ 2) would require N_events = 166^{+82}_{-55} under the assumptions of the present analysis.

Significance. The work supplies the first systematic, catalog-level Bayesian assessment of the full (2,0) multipole (oscillatory + memory) rather than memory alone, using public O4 data, measured PSDs, calibration envelopes, and a carefully documented nested-sampling pipeline. The zero-noise NR and model injections that recover the expected high-SNR scaling of the Bayes factor, the explicit quadrature propagation of evidence uncertainties, and the transparent stacking of both Bayes factors and SNRs are concrete strengths. The cumulative numbers and the N_events forecast give the community a concrete, if optimistic, benchmark for when the (2,0) mode (and ultimately memory) may become detectable with second-generation detectors.

major comments (2)
  1. Sec. V D and the abstract: the optimistic forecast N_events = 166^{+82}_{-55} is obtained by fitting a Student-t (2.85 dof) and a skew-normal to the 84 GWTC-4.0 log10 B values and drawing 500 Monte-Carlo trajectories. The same section notes that the loudest event, GW230814_230901, drops from log10 B = 0.63 ± 0.09 (vs THM) to 0.18 ± 0.10 when compared with the multipole-complete IMRPhenomXHM. Because the stacking formulae (Eqs. 4.3–4.4) treat every event as i.i.d., a coherent bias of even ~0.1–0.2 in the high-SNR tail would shift the median N_events by tens of events. The independence and representativeness assumptions are therefore load-bearing for the central forecast, yet they are not stress-tested against a multipole-complete model for more than one event. A short additional comparison (or an explicit statement that the forecast is conditional on the present mode content) is needed be
  2. Sec. V A / Fig. 1 and Tab. III: the cumulative log10 B = 1.38 ± 0.79 is dominated by a handful of high-SNR events, most notably GW230814_230901. The paper already shows that this event’s Bayes factor is sensitive to the missing (3,±2) multipole. Without a quantitative assessment of how residual waveform systematics propagate into the stacked evidence, the claim that the catalog provides “moderate support” for the (2,0) mode remains provisional. At minimum the authors should recompute the stack after replacing or down-weighting the systematics-sensitive events, or clearly label the result as model-dependent.
minor comments (4)
  1. Fig. 1: the dual color-coding (fill = full SNR, edge = (2,0) SNR) is hard to read once printed in grayscale; a second panel or a different visual encoding would help.
  2. Eq. (4.7)–(4.8): the high-SNR scaling is validated only with zero-noise injections; a brief remark that real noise can flip the sign of O(1) Bayes factors (already noted in Sec. IV E) would strengthen the interpretation of the small measured values.
  3. Appendix A: the relative-runtime plot is useful but the absolute wall-clock times (color bar) are given only for ΔlnZ = 0.10; quoting the corresponding numbers for ΔlnZ = 0.05 would make the cost of the tighter threshold clearer.
  4. Throughout: a few typographical inconsistencies remain (“W A VEFORM”, occasional missing spaces around math mode). A final copy-edit pass would remove them.

Circularity Check

1 steps flagged

No load-bearing circularity: Bayes factors and SNR stacks are direct measurements on real data; the N_events forecast is an explicit empirical bootstrap from the observed distribution, not a tautological derivation.

specific steps
  1. self citation load bearing [Sec. III (waveform model) and abstract / Sec. V A (model comparison)]
    "As our signal model we use the quasi-circular, non-precessing IMRPhenomTHM_20 waveform model, which includes the oscillatory and displacement memory contributions. … To incorporate the memory effect in this analysis, we employ the phenomenological waveform model of the (ℓ=2,m=0) spherical harmonic mode … [24]. … Both the aligned-spin and the precessing models are implemented within IMRPhenomTHM and IMRPhenomTPHM, respectively, in the Python package phenomxpy [63]."

    The signal hypothesis H_20 is defined by the authors’ own prior papers that construct IMRPhenomTHM_20 / TPHM_20. While the subsequent Bayes-factor computation on real data is independent, the very existence of the mode content being tested rests on that self-citation chain; without it there is no H_20 to compare against H_∅. This is minor (normal model-building practice) and does not force the numerical value of the stacked log10 B.

full rationale

The central results (per-event and stacked log10 B = 1.38 ± 0.79, SNR stacking of the full (2,0)/memory/oscillatory pieces) are obtained by nested sampling of real GWOSC strain against two nested, previously calibrated waveform models (IMRPhenomTHM_20 vs IMRPhenomTHM) with fixed priors and measured PSDs; no free parameter is adjusted to force a positive stacked evidence. The N_events = 166^{+82}_{-55} figure is obtained by maximum-likelihood fitting of a Student-t (2.85 dof) and skew-normal to the same 84 observed (log10 B, σ) pairs, then drawing 500 Monte-Carlo trajectories until the cumulative reaches the Jeffreys threshold of 2 (Sec. V D). This is an ordinary empirical forecast under the stated i.i.d. and representativeness assumptions; the paper itself labels it “optimistic” and “based on the specific assumptions adopted in this work.” Self-citations supply the waveform models and the prior PE pipeline, but those models are NR-calibrated and the data analysis is independent of the citations. No equation reduces by construction to its own input, no uniqueness theorem is imported to forbid alternatives, and no ansatz is smuggled in. Residual waveform systematics (missing (3,±2)) are a correctness risk, not circularity. Score 1 only for the minor self-citation of the authors’ own (2,0) models that define the signal hypothesis being tested.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 0 invented entities

The analysis rests on standard Bayesian model comparison, public LVK data products, and previously published phenomenological waveform models. The only free parameters introduced for the forecast are the shape parameters of the empirical distributions fitted to the observed log B and σ(log B). No new physical entities are postulated.

free parameters (2)
  • Student-t degrees of freedom for log10 B distribution = 2.85
    Fitted by maximum likelihood to the 84 GWTC-4.0 Bayes factors; used to generate the Monte-Carlo realizations that produce N_events = 166^{+82}_{-55}.
  • skew-normal shape parameter for σ(log10 B) = 8.33
    Fitted to the observed evidence uncertainties; controls the width of the cumulative-error band in the forecast.
axioms (3)
  • domain assumption Events are statistically independent so that log Bayes factors add.
    Stated explicitly before Eq. (4.3); standard for LVK catalog stacking but ignores possible common calibration or noise systematics.
  • domain assumption IMRPhenomTHM_20 accurately captures the (2,0) mode (oscillatory + memory) for quasi-circular, non-precessing binaries up to mass ratio 10.
    Taken from the authors’ prior calibration paper; residual systematics (especially missing (3,±2)) are acknowledged but not quantified for the full catalog.
  • standard math Jeffreys scale thresholds (log10 B ≥ 2 decisive) remain the appropriate decision criterion.
    Adopted without modification in Sec. IV A and used to set the forecast threshold.

pith-pipeline@v1.1.0-grok45 · 29711 in / 2682 out tokens · 25438 ms · 2026-07-11T11:35:38.923213+00:00 · methodology

0 comments
read the original abstract

We perform Bayesian model selection to test for the presence of the $(\ell=2,m=0)$ spherical harmonic mode in gravitational wave events that have previously been identified as binary black hole mergers. As our signal model we use the quasi-circular, non-precessing IMRPhenomTHM_20 waveform model, which includes the oscillatory and displacement memory contributions. Including the oscillatory component of the (2,0) mode increases the signal-to-noise ratio and evidence for this mode, compared to testing only for the presence of gravitational wave memory. Our analysis thus constitutes a natural stepping stone toward detecting gravitational wave memory. We perform our analysis for the binary black hole signals identified in the GWTC-4.0 catalog, and for selected GWTC-5.0 events. In our Bayesian model comparison we find a cumulative $\log_{10}\mathcal{B}=1.38\pm0.79$ in favor of the presence of the (2,0) mode for the GWTC-4.0 catalog. We also stack the signal-to-noise ratio of the full (2,0) mode and of its individual contributions, obtaining results consistent with previous studies and reaching $\mathrm{SNR}_{\mathrm{memory}} = 0.89^{+0.29}_{-0.11}$ after approximately 7.5 months of O4a observations. In addition, we study the precessing candidate GW241127_061008, and find no additional evidence for the (2,0) mode when precession is included in IMRPhenomTPHM_20. Overall, our results provide an assessment of the observational support for the (2,0) mode in current gravitational wave data and allow us to discuss prospects for its future detection. We find that decisive statistical evidence will likely require a larger catalog, with an optimistic estimated number of events of $N_{\mathrm{events}} = 166^{+82}_{-55}$, based on the specific assumptions adopted in this work. We also expect that decisive evidence will require a more extensive waveform systematics study.

Figures

Figures reproduced from arXiv: 2607.04909 by Antoni Ramos-Buades, Joan Llobera-Querol, Jorge Valencia, Maria Rossell\'o-Sastre, Sascha Husa, Yumeng Xu.

Figure 1
Figure 1. Figure 1: FIG. 1. Log-10 Bayes factors for each individual event in increasing SNR of the [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Cumulative sum of log-10 Bayes factors as a function of the [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Posterior distributions of the SNR of the [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Cumulative sum of the SNR of the [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Posterior distributions for the event GW241127_061008. The [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Distribution of the number of events required for the cumu [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Relative runtime difference between the runs performed with [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Corner plot for the NR injection with SXS:BBH:2497, recovering with [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Posterior distributions for the events listed in Tab. [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Whitened waveforms for GW230814_230901 (only detected in L1) and GW250114_082203 (detected in both L1 and H1). The gray [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

85 extracted references · 57 linked inside Pith

  1. [1]

    twisting-up

    are expected to enable detections in individual events. In contrast, the detection of spin memory is likely to still rely on stacking even in these advanced scenarios [50]. In a recent work [51], the authors use hierarchical Bayesian inference on the GWTC-5.0 catalog of BBH observations to constrain the memory enhancement factor across the popula- tion, f...

    2000

  2. [2]

    We choose a non-equal mass simulation so that all the modes in the model have a non-zero contribution to the waveform

    Numerical relativity injection First we perform a zero-noise NR injection using a quasi-circular, non-precessing, waveform from the Simu- lating eXtreme Spacetimes (SXS) public Catalog [74–76], SXS:BBH:2497 (Q=2, χ 1 =χ 2 =0,N orbits =20 ). We choose a non-equal mass simulation so that all the modes in the model have a non-zero contribution to the wavefor...

  3. [3]

    Model injections Furthermore, to assess the correct scaling of the Bayes fac- tor with the SNR in the PE runs that have been performed in this work, we perform two zero-noise model injections: one at considerably high SNR and one at lower SNR, to check the scaling of the Bayes factor as a function of the SNR in- troduced in Sec. IVC. We choose model rathe...

    doi:10.13039/501100011033 2024

  4. [4]

    J.N.Goldberg,A.J.Macfarlane,E.T.Newman,F.Rohrlich,and E. C. G. Sudarshan, Journal of Mathematical Physics8, 2155 (1967)

    1967

  5. [5]

    Schmidt, M

    P. Schmidt, M. Hannam, S. Husa, and P. Ajith, Phys. Rev. D84, 024046 (2011)

    2011

  6. [6]

    Mills and S

    C. Mills and S. Fairhurst, Phys. Rev. D103, 024042 (2021), arXiv:2007.04313 [gr-qc]

    Pith/arXiv arXiv 2021

  7. [7]

    Calderón Bustillo, S

    J. Calderón Bustillo, S. Husa, A. M. Sintes, and M. Pürrer, Phys. Rev. D93, 084019 (2016), arXiv:1511.02060 [gr-qc]

    Pith/arXiv arXiv 2016

  8. [8]

    F. H. Shaik, J. Lange, S. E. Field, R. O’Shaughnessy, V. Varma, L. E. Kidder, H. P. Pfeiffer, and D. Wysocki, Phys. Rev. D101, 124054 (2020), arXiv:1911.02693 [gr-qc]

    Pith/arXiv arXiv 2020

  9. [9]

    P. B. Graff, A. Buonanno, and B. S. Sathyaprakash, Phys. Rev. D92, 022002 (2015), arXiv:1504.04766 [gr-qc]

    Pith/arXiv arXiv 2015

  10. [10]

    J.CalderónBustillo,S.H.W.Leong,T.Dietrich,andP.D.Lasky, Astrophys. J. Lett.912, L10 (2021), arXiv:2006.11525 [gr-qc]

    Pith/arXiv arXiv 2021

  11. [11]

    Calderón Bustillo, S

    J. Calderón Bustillo, S. H. W. Leong, and K. Chandra, Nature Astron.9, 1530 (2025), arXiv:2211.03465 [gr-qc]

    arXiv 2025

  12. [12]

    TheLIGOScientificCollaboration,ClassicalandQuantumGrav- ity32, 074001 (2015)

    2015

  13. [13]

    Virgo Collaboration, Classical and Quantum Gravity32, 024001 (2014)

    2014

  14. [14]

    KAGRA Collaboration, Progress of Theoreti- cal and Experimental Physics2021, 05A101 (2020), https://academic.oup.com/ptep/article- pdf/2021/5/05A101/37974994/ptaa125.pdf

    2020

  15. [15]

    Abbottet al

    R. Abbottet al. (LIGO Scientific, Virgo), Phys. Rev. D102, 043015 (2020), arXiv:2004.08342 [astro-ph.HE]

    Pith/arXiv arXiv 2020

  16. [16]

    C. Hoy, C. Mills, and S. Fairhurst, Phys. Rev. D106, 023019 (2022), arXiv:2111.10455 [gr-qc]

    Pith/arXiv arXiv 2022

  17. [17]

    R.Abbott etal.(LIGOScientific,Virgo),Astrophys.J.Lett.896, L44 (2020), arXiv:2006.12611 [astro-ph.HE]

    Pith/arXiv arXiv 2020

  18. [18]

    M.Favata,Astrophys.J.Lett.696,L159(2009),arXiv:0902.3660 [astro-ph.SR]

    Pith/arXiv arXiv 2009

  19. [19]

    Favata, Class

    M. Favata, Class. Quant. Grav.27, 084036 (2010), arXiv:1003.3486 [gr-qc]

    Pith/arXiv arXiv 2010

  20. [20]

    Mitman, J

    K. Mitman, J. Moxon, M. A. Scheel, S. A. Teukolsky, M. Boyle, N.Deppe,L.E.Kidder,andW.Throwe,Phys.Rev.D102,104007 (2020), arXiv:2007.11562 [gr-qc]

    Pith/arXiv arXiv 2020

  21. [21]

    Y. B. Zel’dovich and A. G. Polnarev, Astronomicheskii Zhurnal 51, 30 (1974)

    1974

  22. [22]

    Blanchet and T

    L. Blanchet and T. Damour, Phys. Rev. D46, 4304 (1992)

    1992

  23. [23]

    Christodoulou, Phys

    D. Christodoulou, Phys. Rev. Lett.67, 1486 (1991)

    1991

  24. [24]

    Y. Xu, M. Rosselló-Sastre, S. Tiwari, M. Ebersold, E. Z. Hamil- ton, C. García-Quirós, H. Estellés, and S. Husa, Phys. Rev. D 109, 123034 (2024), arXiv:2403.00441 [gr-qc]

    Pith/arXiv arXiv 2024

  25. [25]

    Gasparotto, R

    S. Gasparotto, R. Vicente, D. Blas, A. C. Jenkins, and E. Ba- rausse, Phys. Rev. D107, 124033 (2023), arXiv:2301.13228 [gr-qc]

    Pith/arXiv arXiv 2023

  26. [26]

    Calderón Bustillo, N

    J. Calderón Bustillo, N. Sanchis-Gual, A. Torres-Forné, J. A. Font, A. Vajpeyi, R. Smith, C. Herdeiro, E. Radu, and S. H. W. Leong, Phys. Rev. Lett.126, 081101 (2021), arXiv:2009.05376 [gr-qc]

    Pith/arXiv arXiv 2021

  27. [27]

    Rosselló-Sastre, S

    M. Rosselló-Sastre, S. Husa, and S. Bera, Phys. Rev. D110, 084074 (2024), arXiv:2405.17302 [gr-qc]

    Pith/arXiv arXiv 2024

  28. [28]

    A. G. Abacet al. (LIGO Scientific, KAGRA, Virgo), Astrophys. J. Lett.995, L18 (2025), arXiv:2508.18080 [gr-qc]

    Pith/arXiv arXiv 2025

  29. [29]

    A. G. Abacet al. (LIGO Scientific, KAGRA, Virgo), Astrophys. J. Lett.1004, L21 (2025), arXiv:2508.18081 [gr-qc]

    Pith/arXiv arXiv 2025

  30. [30]

    A. G. Abacet al. (LIGO Scientific, Virgo, KAGRA), Astrophys. J. Lett.1004, L22 (2025), arXiv:2508.18082 [gr-qc]

    Pith/arXiv arXiv 2025

  31. [31]

    L. S. Collaboration, V. Collaboration, and K. Collaboration, 10.5281/zenodo.17014085 (2025)

    doi:10.5281/zenodo.17014085 2025

  32. [32]

    Soniet al

    S. Soniet al. (LIGO), Class. Quant. Grav.42, 085016 (2025), arXiv:2409.02831 [astro-ph.IM]

    arXiv 2025

  33. [33]

    A. G. Abacet al. (LIGO Scientific, Virgo, KAGRA), (2026), arXiv:2605.27223 [gr-qc]

    Pith/arXiv arXiv 2026

  34. [34]

    LIGOScientific,Virgo,andKAGRA, (2026),arXiv:2605.27224 [gr-qc]

    Pith/arXiv arXiv 2026

  35. [35]

    LIGOScientific,Virgo,andKAGRA, (2026),arXiv:2605.27225 [gr-qc]

    Pith/arXiv arXiv 2026

  36. [36]

    LIGOScientific,Virgo,andKAGRA, (2026),arXiv:2605.27227 [astro-ph.CO]

    Pith/arXiv arXiv 2026

  37. [37]

    LIGOScientific,Virgo,andKAGRA, (2026),arXiv:2605.27226 [astro-ph.HE]

    Pith/arXiv arXiv 2026

  38. [38]

    Xuet al., (2025), arXiv:2512.19513 [gr-qc]

    Y. Xuet al., (2025), arXiv:2512.19513 [gr-qc]

    arXiv 2025

  39. [39]

    A. G. Abacetal. (LIGO Scientific, Virgo, KAGRA), Phys. Rev. Lett.135, 111403 (2025), arXiv:2509.08054 [gr-qc]

    Pith/arXiv arXiv 2025

  40. [40]

    A. G. Abacet al. (LIGO Scientific, Virgo, KAGRA), Astrophys. J. Lett.993, L21 (2025), arXiv:2510.26931 [astro-ph.HE]

    arXiv 2025

  41. [41]

    Estelles, A

    H. Estelles, A. Ramos-Buades, S. Husa, C. Garcia-Quiros, M.Colleoni,L.Haegel,andR.Jaume,Phys.Rev.D103,124060 (2021), arXiv:2004.08302 [gr-qc]

    Pith/arXiv arXiv 2021

  42. [42]

    Estelles, S

    H. Estelles, S. Husa, M. Colleoni, D. Keitel, M. Mateu-Lucena, C.Garcia-Quiros,A.Ramos-Buades,andA.Borchers,Phys.Rev. D105, 084039 (2022), arXiv:2012.11923 [gr-qc]

    Pith/arXiv arXiv 2022

  43. [43]

    Estellés, M

    H. Estellés, M. Colleoni, C. García-Quirós, 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]

    Pith/arXiv arXiv 2022

  44. [44]

    Rosselló-Sastre and S

    M. Rosselló-Sastre and S. Husa, Phys. Rev. D112, 124059 (2025)

    2025

  45. [45]

    Khera, B

    N. Khera, B. Krishnan, A. Ashtekar, and T. De Lorenzo, Phys. Rev. D103, 044012 (2021), arXiv:2009.06351 [gr-qc]

    Pith/arXiv arXiv 2021

  46. [46]

    Hübner, C

    M. Hübner, C. Talbot, P. D. Lasky, and E. Thrane, Phys. Rev. D 101, 023011 (2020), arXiv:1911.12496 [astro-ph.HE]

    Pith/arXiv arXiv 2020

  47. [47]

    Z.-C.Zhao,X.Liu,Z.Cao,andX.He,Phys.Rev.D104,064056 (2021), arXiv:2111.13882 [gr-qc]

    Pith/arXiv arXiv 2021

  48. [48]

    Hübner, P

    M. Hübner, P. Lasky, and E. Thrane, Phys. Rev. D104, 023004 (2021), arXiv:2105.02879 [gr-qc]

    Pith/arXiv arXiv 2021

  49. [49]

    S. Y. Cheung, P. D. Lasky, and E. Thrane, Class. Quant. Grav. 41, 115010 (2024), arXiv:2404.11919 [gr-qc]

    Pith/arXiv arXiv 2024

  50. [50]

    P.D.Lasky,E.Thrane,Y.Levin,J.Blackman,andY.Chen,Phys. Rev. Lett.117, 061102 (2016), arXiv:1605.01415 [astro-ph.HE]

    Pith/arXiv arXiv 2016

  51. [51]

    O. M. Boersma, D. A. Nichols, and P. Schmidt, Phys. Rev. D 101, 083026 (2020), arXiv:2002.01821 [astro-ph.HE]

    Pith/arXiv arXiv 2020

  52. [52]

    Reitze et al., Bull

    D. Reitze et al., Bull. Am. Astron. Soc.51, 035 (2019), arXiv:1907.04833 [astro-ph.IM]

    Pith/arXiv arXiv 2019

  53. [53]

    A.M.GrantandD.A.Nichols,Phys.Rev.D107,064056(2023), [Erratum: Phys.Rev.D 108, 029901 (2023)], arXiv:2210.16266 [gr-qc]

    Pith/arXiv arXiv 2023

  54. [54]

    Mitman, M

    K. Mitman, M. Isi, and W. M. Farr, (2026), arXiv:2605.27500 [gr-qc]

    Pith/arXiv arXiv 2026

  55. [55]

    Chen et al., Phys

    Y. Chen et al., Phys. Rev. D110, 064049 (2024), arXiv:2405.06197 [gr-qc]

    Pith/arXiv arXiv 2024

  56. [56]

    M.Colpi etal.(LISA), (2024),arXiv:2402.07571[astro-ph.CO]

    Pith/arXiv arXiv 2024

  57. [57]

    Inchauspé, S

    H. Inchauspé, S. Gasparotto, D. Blas, L. Heisenberg, 18 J. Zosso, and S. Tiwari, Phys. Rev. D111, 044044 (2025), arXiv:2406.09228 [gr-qc]

    Pith/arXiv arXiv 2025

  58. [58]

    Cogez, S

    A. Cogez, S. Gasparotto, J. Zosso, H. Inchauspé, C. Pitte, L. Magaña Zertuche, A. Petiteau, and M. Besancon, (2026), arXiv:2601.23230 [gr-qc]

    Pith/arXiv arXiv 2026

  59. [59]

    Zosso, L

    J. Zosso, L. Magaña Zertuche, S. Gasparotto, A. Cogez, H. In- chauspé, and M. Jacobs, (2026), arXiv:2601.23019 [gr-qc]

    Pith/arXiv arXiv 2026

  60. [60]

    Agazieet al

    G. Agazieet al. (NANOGrav), Astrophys. J.963, 61 (2024), arXiv:2307.13797 [gr-qc]

    Pith/arXiv arXiv 2024

  61. [61]

    S. M. Tomson et al. 10.3847/2041-8213/ae2912 (2025), arXiv:2512.14650 [gr-qc]

    Pith/arXiv arXiv doi:10.3847/2041-8213/ae2912 2041

  62. [62]

    Husa, and M

    M.d.L.Planas,A.Ramos-Buades,C.Garcia-Quiros,H.Estelles, S. Husa, and M. Haney, (2025), arXiv:2503.13062 [gr-qc]

    arXiv 2025

  63. [63]

    Schmidt, F

    P. Schmidt, F. Ohme, and M. Hannam, Phys. Rev. D91, 024043 (2015), arXiv:1408.1810 [gr-qc]

    Pith/arXiv arXiv 2015

  64. [64]

    Ashtekar, T

    A. Ashtekar, T. De Lorenzo, and N. Khera, Gen. Rel. Grav.52, 107 (2020), arXiv:1906.00913 [gr-qc]

    Pith/arXiv arXiv 2020

  65. [65]

    Compère, R

    G. Compère, R. Oliveri, and A. Seraj, JHEP10, 116, [Erratum: JHEP 06, 045 (2024)], arXiv:1912.03164 [gr-qc]

    Pith/arXiv arXiv 2024

  66. [66]

    García-Quirós, S

    C. García-Quirós, S. Tiwari, and S. Babak, Phys. Rev. D112, 064017 (2025)

    2025

  67. [67]

    A. G. Abacetal.(LIGO Scientific, Virgo, KAGRA),1004, 232 (2025), arXiv:2508.18079 [gr-qc]

    Pith/arXiv arXiv 2025

  68. [68]

    D. M. Macleod, J. S. Areeda, S. B. Coughlin, T. J. Massinger, and A. L. Urban, SoftwareX13, 100657 (2021)

    2021

  69. [69]

    Ashton et al., Astrophys

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

    Pith/arXiv arXiv 2019

  70. [70]

    Valencia, R

    J. Valencia, R. Tenorio, M. Rosselló-Sastre, and S. Husa, Phys. Rev. D110, 124026 (2024), arXiv:2406.16636 [gr-qc]

    Pith/arXiv arXiv 2024

  71. [71]

    Y. Xu, M. Rossello-Sastre, J. Valencia, A. Ramos Buades, J. Llobera Querol, and F. A. Ramis Vidal, Pe automator: v0.20.3 (2025)

    2025

  72. [72]

    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]

    Pith/arXiv arXiv 2019

  73. [73]

    Jeffreys,The Theory of Probability(Oxford University Press, Oxford, 1998)

    H. Jeffreys,The Theory of Probability(Oxford University Press, Oxford, 1998)

    1998

  74. [74]

    Del Pozzo, K

    W. Del Pozzo, K. Grover, I. Mandel, and A. Vecchio, Class. Quant. Grav.31, 205006 (2014), arXiv:1408.2356 [gr-qc]

    Pith/arXiv arXiv 2014

  75. [75]

    B. J. Owen, Phys. Rev. D53, 6749 (1996), arXiv:gr-qc/9511032

    Pith/arXiv arXiv 1996

  76. [76]

    J. S. Speagle, Monthly Notices of the Royal Astronomical Soci- ety493, 3132 (2020), https://academic.oup.com/mnras/article- pdf/493/3/3132/32890730/staa278.pdf

    2020

  77. [77]

    Simulating eXtreme Spacetimes (SXS) Collaboration, SpEC: Spectral Einstein Code, https://www.black-holes.org/ code/SpEC.html

  78. [78]

    Boyle et al., Class

    M. Boyle et al., Class. Quant. Grav.36, 195006 (2019), arXiv:1904.04831 [gr-qc]

    Pith/arXiv arXiv 2019

  79. [79]

    M. A. Scheelet al., Class. Quant. Grav.42, 195017 (2025), arXiv:2505.13378 [gr-qc]

    arXiv 2025

  80. [80]

    A.G.Abac etal.(LIGOScientific,Virgo,KAGRA)10.1103/gzrj- mwv3 (2026), arXiv:2605.11703 [gr-qc]

    Pith/arXiv arXiv doi:10.1103/gzrj- 2026

Showing first 80 references.