Pith. sign in

REVIEW 4 major objections 5 minor 16 cited by

The paper argues that GW231123 is best explained as a 2G+2G hierarchical merger — both observed black holes being remnants of earlier mergers — not as a 2G+1G or 3G+2G event.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

GW231123 is claimed to be a 2G+2G hierarchical merger, but only under the NRSur7dq4 waveform; the conclusion flips with IMRPhenomXO4a.

T0 review reviewed 2026-08-04 challenge →

load-bearing objection The 2G+2G claim for GW231123 reverses under the paper's own alternative waveform; read this as a useful sensitivity study, not a settled origin. the 4 major comments →

arxiv 2509.08298 v1 pith:7CARB4CO submitted 2025-09-10 astro-ph.HE astro-ph.GAastro-ph.SRgr-qc

The Hierarchical Merger Scenario for GW231123

Guo-Peng Li , Xi-Long Fan This is my paper
classification astro-ph.HE astro-ph.GAastro-ph.SRgr-qc
keywords GW231123hierarchical mergersblack hole mergersgravitational waves2G+2Gspin priorpair-instability mass gapwaveform model
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 reading

GW231123 is a detected black-hole merger with component masses near 137 and 103 solar masses and high spins, properties that ordinary stellar collapse struggles to produce. The paper asks whether it formed hierarchically, with one or both observed black holes being remnants of earlier mergers. Using Bayesian model comparison, it argues that the most likely channel is 2G+2G: both components are second-generation black holes. The implied progenitors are four first-generation black holes of roughly 75, 66, 64, and 59 solar masses, and the observed high spins match the ~0.7 spin expected of merger remnants. The paper also reports that this conclusion is waveform-dependent, since an alternative waveform model reverses the preference.

Core claim

On the paper's own terms, assuming GW231123 is hierarchical, the 2G+2G hypothesis is strongly preferred over 2G+1G and 3G+2G. With the NRSur7dq4 posterior, escape speed 100 km/s, and a 1G maximum mass of 85 solar masses, the odds ratios are 1.28×10^4 versus 2G+1G and 2.81×10^8 versus 3G+2G. The primary is then a remnant of ~75+66 solar-mass progenitors, and the secondary of ~64+59 solar-mass progenitors, with remnant spins peaking near 0.69. The paper stresses that this depends on an informed 0.7-peaked spin prior and on the waveform: with IMRPhenomXO4a the 2G+2G versus 2G+1G odds fall to 0.03, favoring 2G+1G.

What carries the argument

The central tool is the Bayesian odds ratio O_i^j = (p(d|H_i)/p(d|H_j))×(p(H_i)/p(H_j)), comparing the three hypotheses 2G+1G, 2G+2G, and 3G+2G. The evidence terms are built from generation-specific priors synthesized by a parametric population model that starts from the inferred 1G mass/spin distribution and adds a retention condition: a merger remnant participates in the next merger only if its kick velocity stays below the host escape speed. The prior odds are set proportional to the retention probabilities of the required earlier mergers. The GW231123 posterior from NRSur7dq4 provides the data term, and the mass-dependent overlap between that posterior and the mass distributions of 1G, 2

Load-bearing premise

The 2G+2G conclusion rests on the assumption that the NRSur7dq4 posterior for GW231123 is the correct one; the paper's own comparison shows that with the IMRPhenomXO4a waveform the 2G+2G hypothesis becomes only 3% as probable as 2G+1G.

What would settle it

A re-analysis of GW231123 with a waveform model validated for asymmetric, precessing, high-mass binaries, or with an additional detector's data, would settle the central claim by fixing the secondary mass: if the secondary is near 111 solar masses the 2G+2G scenario wins, while a secondary near 55 solar masses makes 2G+1G win (odds 0.03).

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

If this is right

  • If GW231123 is a 2G+2G event, ordinary hierarchical assembly in a low-escape-speed environment can place black holes in the pair-instability gap without invoking unusual stellar collapse physics.
  • The four inferred first-generation progenitors have masses consistent with standard stellar-collapse black holes, so an apparent upper-mass-gap event does not by itself require new formation physics.
  • The post-merger spins cluster near 0.69, which means parameter estimation for repeated-merger candidates should use an informed spin prior peaked near 0.7 instead of a uniform prior.
  • Waveform choice is decisive: replacing NRSur7dq4 with IMRPhenomXO4a changes the odds ratio for 2G+2G versus 2G+1G by six orders of magnitude and reverses the favored channel.
  • Higher escape speeds (300 km/s) weaken the preference for 2G+2G over 2G+1G but do not overturn it, while a lower 1G maximum mass strengthens the 2G+2G case.

Where Pith is reading between the lines

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

  • Inference: A decisive next step would be to rerun this comparison with a waveform model that is validated for asymmetric, precessing, high-mass systems; the discriminating observable is the secondary-mass posterior, since it moves from ~111 to ~55 solar masses between the two waveform models.
  • Inference: If high-generation black holes really spin near 0.7, a population-wide reanalysis of massive high-spin events with the informed prior could reclassify some previously reported events as hierarchical, a consequence the paper does not work out.
  • Inference: The reversal under IMRPhenomXO4a could also mean the true arrangement is not among the three channels tested; a 3G+1G or 4G+2G scenario might accommodate the asymmetric mass posterior that makes 2G+1G look better.
Share X Bluesky LinkedIn Reddit HN

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

4 major / 5 minor

Summary. The paper analyzes the very massive, high-spin gravitational-wave event GW231123 under the hypothesis of hierarchical black-hole mergers. It compares three formation scenarios—2G+1G, 2G+2G, and 3G+2G—by computing prior odds from retention probabilities and Bayes factors from population-level mass/spin priors, using the published LVK posterior distributions obtained with the NRSur7dq4 and IMRPhenomXO4a waveform models. Under NRSur7dq4 with V_esc = 100 km/s and M_max = 85 M_sun, the authors report odds of ~1.28e4 and ~2.8e8 favoring 2G+2G over 2G+1G and 3G+2G, and they infer a progenitor scenario with four 1G BHs. They also report that using IMRPhenomXO4a reverses the 2G+2G versus 2G+1G comparison (odds 0.03) and that the post-merger spin values are dominated by the assumed spin prior. The paper is transparent about these caveats, but the abstract and conclusions present the NRSur7dq4-based odds as the primary result.

Significance. If the central claim were robust, the paper would provide a concrete, testable progenitor scenario for GW231123 and strengthen the case that hierarchical mergers are observable in current LIGO-Virgo-KAGRA data. The methodology is clearly formulated, the paper makes use of publicly available LVK posterior samples, and the authors are commendably explicit about the waveform-model reversal and the prior-dominated nature of the inferred post-merger spins. However, the headline odds ratio of >O(10^3) is conditional on a single waveform model, and the paper does not supply a physical or statistical reason to prefer NRSur7dq4 over IMRPhenomXO4a for this unusually massive event. The evidentiary integral in Eq. (2) is also not connected to a concrete numerical scheme. These issues affect the load-bearing claim and therefore need to be addressed before the result can be considered robust.

major comments (4)
  1. [Abstract; §III A, Table I] The abstract's claim that 'odds ratios of >O(10^3)' favor the 2G+2G scenario is contradicted by the paper's own Table I: for IMRPhenomXO4a, log B_{2G+1G}^{2G+2G} = -1.48 and O_{2G+1G}^{2G+2G} = 0.03, i.e., the 2G+1G scenario is preferred. The text notes this reversal but does not justify why NRSur7dq4 should be trusted over IMRPhenomXO4a for this event. Because the conclusion reverses under an alternative waveform model used in the LVK analysis, the paper must either (i) provide a quantitative justification for preferring NRSur7dq4 (e.g., a waveform-model Bayes factor, goodness-of-fit comparison, or evidence that IMRPhenomXO4a is inadequate for such high masses) or (ii) reframe the abstract and conclusions as a conditional statement. A caveat in the text is not sufficient while the unqualified odds statement remains in the abstract.
  2. [§II B, Eq. (2)] The evidence p(d|H_i) is defined as an eight-dimensional integral over masses and spins, but the manuscript never states how this integral is evaluated numerically. The Bayes factors in Table I are the central quantitative result, and they depend on both the prior volume and the normalization of the likelihood over the integration domain. The authors should specify the estimator used (e.g., importance sampling, nested sampling, harmonic mean), how the LVK posterior samples are reweighted to compute p(d|H_i), the integration bounds, and convergence checks. Without this, the numbers in Table I are not reproducible and the model comparison cannot be independently verified.
  3. [§III B, Fig. 3] The paper states that the post-merger spin distributions of ~0.69 are 'dominated by the prior' and 'reflect the effect of the spin prior that clusters around 0.7.' This is an explicit admission that the quoted spin values are not data-driven measurements. Presenting these values as results in the text and in Fig. 3 without a clear separation between 'prior input' and 'posterior output' is misleading, especially because the abstract uses high spins as motivation. The authors should clearly mark these as prior-driven predictions and, ideally, quantify the information gain from the data or remove them from the set of inferred quantities.
  4. [§II B, after Eq. (3)] The dismissal of the 'primary=1G, secondary=2G' case is argued by saying that when the mass difference is 'relatively large' the probability can be ignored. This is not a valid criterion in general. The actual reason is that the primary-mass posterior from both waveform models lies above the assumed maximum 1G BH mass of 85 M_sun, so a 1G primary is excluded by construction. The paper should replace the hand-waving statement with this explicit argument and note that the exclusion depends on the chosen M_max value.
minor comments (5)
  1. [§IV, item (1)] The conclusion quotes log Bayes factor 8.35 for 2G+2G versus 3G+2G, but Table I gives 8.38. Please correct the inconsistency.
  2. [Eq. (1) and surrounding text] The dataset is denoted 'd^1' in one place and 'd' elsewhere. Use a single symbol, e.g., 'd', and remove the superscript.
  3. [Footnote 1] The Zenodo link is given without a description. Please state whether it contains the LVK posterior samples, the analysis code, or both, and provide a version/DOI reference.
  4. [Table I, IMRPhenomXO4a row] The '/' for the 3G+2G comparison is explained as computational cost, but the paper should state whether the 3G+2G evidence was not computed or whether an upper/lower bound was used. This affects the interpretation of the row.
  5. [Fig. 1 caption] The caption mentions a maximum 1G BH mass of ~85 M_sun, but Section III A also tests M_max = 65 M_sun. Consider adding the 65 M_sun truncation to the figure or explaining why only 85 M_sun is shown.

Circularity Check

1 steps flagged

One secondary result—post-merger spins near 0.7—is explicitly prior-dominated; the central 2G+2G vs 2G+1G comparison is an independent Bayesian calculation, not a circular reduction.

specific steps
  1. self definitional [Section III B (Progenitors of GW231123), after Figure 3]
    "The two progenitor mergers of GW231123 both show post-merger spin distributions sharply peaked near χ∼0.7, with 0.69+0.04−0.05 and 0.69+0.04−0.04, reflecting the effect of the spin prior that clusters around 0.7 [10]."

    The 2G population prior used in the analysis (Appendix A and Figure 1) is constructed so that high-generation BH spin distributions peak near χ~0.7–0.9. The posterior for the post-merger (2G) remnant spin is then dominated by this prior because the GW data constrain only the final binary spins of GW231123, not the spins of the hypothetical 2G remnants. The paper's own conclusion (3) states these spins are 'dominated by the prior.' Thus the claimed peak at 0.69 is a direct restatement of the assumed spin prior, not an inference from the data.

full rationale

The only clear circular step is the spin result in Section III B: the post-merger spins of ~0.7 are explicitly attributed to the spin prior that clusters at that value, making that particular 'prediction' equivalent to an input assumption by the paper's own admission. This is a supporting result, not the central claim. The central claim—that GW231123 is a 2G+2G merger with odds >10^3 over 2G+1G—is obtained by a hierarchical Bayesian evidence computation: the likelihood from the NRSur7dq4 posterior is integrated against hypothesis-specific priors synthesized from the GWTC-3 1G population and a kick/remnant model. That is an independent calculation, not a reduction to a fitted parameter or a self-citation theorem. The authors do cite their own earlier population models (refs. [37,38]) for the 2G/3G priors, but those are physical models with stated assumptions, not an unverified uniqueness claim, and the odds are not a pure restatement of the priors. The dramatic reversal under IMRPhenomXO4a is a robustness/correctness issue—the paper itself reports it—but it is not circularity, because the waveform choice is an external input, not something derived from the hypotheses being compared. On balance, the paper has one self-definitional supporting result while the central model comparison retains independent content, so the circularity score is 4.

Axiom & Free-Parameter Ledger

3 free parameters · 7 axioms · 0 invented entities

The paper adds no new entities. Its burden is carried by assumed population models, a hand-chosen escape speed and 1G mass cutoff, and a spin prior that predetermines the reported remnant-spin result. The prior odds themselves rest on a retention-probability proportionality that is not derived from rates.

free parameters (3)
  • escape speed V_esc = 100, 300 km/s (chosen)
    Host environment escape speed is not inferred; it sets the retention probability, prior odds, and the shape of higher-generation population priors.
  • maximum 1G BH mass M_max = 85, 65 M_sun (chosen)
    Truncation of the 1G mass distribution at the theorized pair-instability gap; varied by hand and strongly affects the odds ratios.
  • hierarchical remnant spin prior peak = chi ~ 0.7
    The 2G/3G spin distributions peak near 0.7 following Gerosa & Fishbach (2021); this input directly produces the claimed post-merger spin values.
axioms (7)
  • standard math Bayes theorem and marginal likelihood computation
    Used in Eqs. 1 and 2 to define odds ratios and evidences.
  • domain assumption GW231123 is a hierarchical merger
    The introduction states the analysis is done 'under the assumption that the event originates from the hierarchical merger scenario.' The paper does not test this against non-hierarchical channels.
  • domain assumption 2G/3G population model from Li et al. (2023) and Li & Fan (2025) is faithful
    The priors p(m,chi|NG) and retention probabilities come from the authors' own parametric model; its accuracy is assumed, not independently validated on new data.
  • ad hoc to paper Prior probability of each hypothesis is proportional to retention probability
    Eq. 4 sets p(H) proportional to products of f_ret; this is a modeling choice, not derived from merger rates or delay-time distributions.
  • domain assumption Delay times between subsequent mergers are negligible
    Section II C: delay times are neglected with a brief justification that they are negligible in low escape-speed environments; this affects hierarchical merger rates and prior odds.
  • ad hoc to paper The 1G+2G case with primary=1G, secondary=2G can be ignored
    Section II B argues this is negligible when the mass difference is large, but the NRSur7dq4 masses are 129 and 111 solar masses, not a large difference.
  • domain assumption GWTC-3 1G population with Mmax truncation
    The 1G mass and spin priors follow GWTC-3 [36] with a sharp cutoff at Mmax; the choice of Mmax directly affects the 2G and 3G distributions.

reviewed 2026-08-04 · how reviews work

0 comments
Cite this review

Pith. "Pith review of The Hierarchical Merger Scenario for GW231123." pith.science (2026). https://pith.science/paper/7CARB4CO

@misc{pith2026250908298,
  author       = {Pith},
  title        = {Pith review of: The Hierarchical Merger Scenario for GW231123},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7CARB4CO}},
  note         = {Machine review of arXiv:2509.08298}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

GW231123 exhibits exceedingly massive components and high spins, which challenges the formation of first-generation (1G) black holes from stellar collapse and implies that this event might originate from hierarchical mergers. Here we show that the \texttt{2G+2G} merger scenario for GW231123 is favored over a \texttt{2G+1G} (or \texttt{3G+2G}) merger, with odds ratios of $>$$\mathcal{O}(10^3)$. The primary (secondary) black hole is consistent with merging binary black holes with masses of $75^{+7}_{-7}\,M_\odot$ and $66^{+4}_{-10}\,M_\odot$ ($64^{+8}_{-10}\,M_\odot$ and $59^{+7}_{-9}\,M_\odot$; 90\% credible intervals), respectively. Our results reveal that the treatment of spin priors from the population level and waveform model choice are decisive in interpreting potential hierarchical gravitational-wave signals.

Figures

Figures reproduced from arXiv: 2509.08298 by Guo-peng Li, Xi-Long Fan.

Figure 1
Figure 1. Figure 1: FIG. 1. Probability density distributions of masses ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Probability density distributions (left) of kick veloc [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Posterior probability density distributions of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 16 Pith papers

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

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

    gr-qc 2026-04 unverdicted novelty 7.0

    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...

  2. Short Gravitational-Wave Transients as Probes of Cosmic Domain Walls

    gr-qc 2026-06 unverdicted novelty 6.0

    Two LIGO transients are consistent with domain wall signals from a shared scalar field but binary black hole models remain favored, with a morphological degeneracy identified.

  3. Across the Universe: GW231123 as a magnified and diffracted black hole merger

    astro-ph.GA 2025-12 conditional novelty 6.0

    GW231123's extreme mass and spins may be explained by a point-mass microlens embedded in a galaxy, reducing the inferred source mass to about 100-180 solar masses.

  4. A new group of low-spin $50-70M_\odot$ Black Holes and the high pair-instability mass cutoff

    astro-ph.HE 2025-10 conditional novelty 6.0

    GWTC-4.0 data shows low-spin black holes up to 70 solar masses, moving the low-spin cutoff to 68.5 solar masses and favoring a high pair-instability mass gap.

  5. A new group of low-spin $50-70M_\odot$ Black Holes and the high pair-instability mass cutoff

    astro-ph.HE 2025-10 conditional novelty 6.0

    GWTC-4.0 reveals low-spin black holes up to ~68.5 Msun, implying a higher pair-instability mass cutoff and a lower 12C(alpha,gamma)16O rate.

  6. Black Hole Binary Detection Landscape for the Laser Interferometer Lunar Antenna (LILA): Signal-to-Noise Calculations & Science Cases

    astro-ph.HE 2026-05 unverdicted novelty 5.0

    LILA can detect IMBH binaries at redshifts 20-30, IMRIs, and provide months-to-years early warnings with high-SNR events for gravity tests.

  7. 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...

  8. 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.

  9. Ringdown Analysis of GW250114 with Orthonormal Modes

    gr-qc 2026-05 unverdicted novelty 5.0

    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.

  10. Measuring Eccentricity and Addressing Waveform Systematics in GW231123

    gr-qc 2025-12 conditional novelty 5.0

    Reanalysis of GW231123 shows no significant eccentricity, with parameter estimate differences explained by waveform model disagreements at strong spin precession.

  11. GW231123: Overlapping Gravitational Wave Signals?

    gr-qc 2025-12 conditional novelty 5.0

    GW231123 data favors an overlapping two-signal model over a single merger with Bayes factors of 100-10000, mitigating waveform-dependent discrepancies and suggesting possible gravitational lensing.

  12. Searching for Electromagnetic Counterpart Candidates to GW231123

    astro-ph.HE 2025-11 conditional novelty 5.0

    A crossmatch of GW231123's localization with ZTF AGN-flare catalogs yields six unconfirmed optical flare candidates, with association claims driven largely by the event's high primary mass.

  13. Exploring Hierarchical Merger Scenarios for GW241011 and GW241110

    astro-ph.HE 2026-07 conditional novelty 4.5

    GW241011 and GW241110 favor 2G+1G hierarchical-merger models over a fiducial 1G+1G population, with mild AGN-disk preference and one weak optical flare candidate.

  14. Polarization Birefringence and Waveform Systematics in GW231123

    astro-ph.HE 2026-05 unverdicted novelty 4.0

    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...

  15. Remnant recoil and host environments of GWTC-4.0 binary black-hole mergers

    astro-ph.HE 2026-04 unverdicted novelty 4.0

    Five O4 gravitational-wave events prefer dynamical cluster formation; typical recoil kicks eject remnants from globular clusters but allow possible retention in nuclear star clusters, disfavoring efficient hierarchica...

  16. Considering lensing effect on gravitational wave signals from black holes in mass gap

    astro-ph.HE 2025-12 reject novelty 4.0

    Gravitational lensing could in principle explain apparent mass-gap black-hole mergers, but the required magnifications are μ≈12–39 for GW190521 and μ≈320–444 for GW231123 depending on assumptions—and the paper's abstr...

Reference graph

Works this paper leans on

54 extracted references · 6 canonical work pages · cited by 14 Pith papers · 2 internal anchors

  1. [1]

    The LIGO Scientific Collaboration, the Virgo Col- laboration, the KAGRA Collaboration, A. G. Abac, I. Abouelfettouh, F. Acernese, K. Ackley, C. Adam- cewicz, S. Adhicary, D. Adhikari, N. Adhikari, R. X. Ad- hikari, V. K. Adkins, S. Afroz, A. Agapito, D. Agarwal, M. Agathos, N. Aggarwal, S. Aggarwal, O. D. Aguiar, I. L. Ahrend, L. Aiello, A. Ain, P. Ajith,...

    Pith/arXiv arXiv 2025

  2. [2]

    Abbott, T

    R. Abbott, T. D. Abbott, S. Abraham, F. Acernese, K. Ackley, C. Adams, R. X. Adhikari, V. B. Adya, C. Af- feldt, M. Agathos, and et al., GW190521: A Binary Black Hole Merger with a Total Mass of 150 M ⊙, Phys. Rev. Lett.125, 101102 (2020), arXiv:2009.01075 [gr-qc]

    arXiv 2020

  3. [3]

    Mapelli, Formation Channels of Single and Binary Stellar-Mass Black Holes, inHandbook of Gravitational Wave Astronomy(2021) p

    M. Mapelli, Formation Channels of Single and Binary Stellar-Mass Black Holes, inHandbook of Gravitational Wave Astronomy(2021) p. 16

    work page 2021

  4. [4]

    Mandel and A

    I. Mandel and A. Farmer, Merging stellar-mass binary black holes, Phys. Rep.955, 1 (2022), arXiv:1806.05820 [astro-ph.HE]

    Pith/arXiv arXiv 2022

  5. [5]

    Li, Y.-Z

    Y.-J. Li, Y.-Z. Wang, S.-P. Tang, and Y.-Z. Fan, Re- solving the Stellar-Collapse and Hierarchical-Merger Ori- gins of the Coalescing Black Holes, Phys. Rev. Lett.133, 051401 (2024), arXiv:2303.02973 [astro-ph.HE]

    Pith/arXiv arXiv 2024

  6. [6]

    Antonini, I

    F. Antonini, I. M. Romero-Shaw, and T. Callister, Star Cluster Population of High Mass Black Hole Mergers in Gravitational Wave Data, Phys. Rev. Lett.134, 011401 (2025), arXiv:2406.19044 [astro-ph.HE]

    Pith/arXiv arXiv 2025

  7. [7]

    R. M. O’Leary, Y. Meiron, and B. Kocsis, Dynamical Formation Signatures of Black Hole Binaries in the First Detected Mergers by LIGO, Astrophys. J. Lett824, L12 (2016), arXiv:1602.02809 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  8. [8]

    Gerosa and E

    D. Gerosa and E. Berti, Are merging black holes born from stellar collapse or previous mergers?, Phys. Rev. D 95, 124046 (2017), arXiv:1703.06223 [gr-qc]

    Pith/arXiv arXiv 2017

  9. [9]

    Fishbach, D

    M. Fishbach, D. E. Holz, and B. Farr, Are LIGO’s Black Holes Made from Smaller Black Holes?, Astrophys. J. Lett840, L24 (2017), arXiv:1703.06869 [astro-ph.HE]

    Pith/arXiv arXiv 2017

  10. [10]

    Gerosa and M

    D. Gerosa and M. Fishbach, Hierarchical mergers of stellar-mass black holes and their gravitational- wave signatures, Nature Astronomy5, 749 (2021), arXiv:2105.03439 [astro-ph.HE]

    Pith/arXiv arXiv 2021

  11. [11]

    Arca Sedda, S

    M. Arca Sedda, S. Naoz, and B. Kocsis, Quiescent and Active Galactic Nuclei as Factories of Merging Compact Objects in the Era of Gravitational Wave Astronomy, Universe9, 138 (2023), arXiv:2302.14071 [astro-ph.GA]

    Pith/arXiv arXiv 2023

  12. [12]

    Antonini and M

    F. Antonini and M. Gieles, Merger rate of black hole binaries from globular clusters: Theoretical error bars and comparison to gravitational wave data from GWTC- 2, Phys. Rev. D102, 123016 (2020), arXiv:2009.01861 [astro-ph.HE]

    Pith/arXiv arXiv 2020

  13. [13]

    C. L. Rodriguez, M. Zevin, P. Amaro-Seoane, S. Chat- terjee, K. Kremer, F. A. Rasio, and C. S. Ye, Black holes: The next generation—repeated mergers in dense star clusters and their gravitational-wave properties, Phys. Rev. D100, 043027 (2019), arXiv:1906.10260 [astro- ph.HE]

    Pith/arXiv arXiv 2019

  14. [14]

    Mapelli, M

    M. Mapelli, M. Dall’Amico, Y. Bouffanais, N. Giacobbo, M. Arca Sedda, M. C. Artale, A. Ballone, U. N. Di Carlo, G. Iorio, F. Santoliquido, and S. Torniamenti, Hierarchi- cal black hole mergers in young, globular and nuclear star clusters: the effect of metallicity, spin and cluster properties, Mon. Not. R. Astron. Soc.505, 339 (2021), arXiv:2103.05016 [as...

    Pith/arXiv arXiv 2021

  15. [15]

    Kimball, C

    C. Kimball, C. Talbot, C. P. L. Berry, M. Zevin, 7 E. Thrane, V. Kalogera, R. Buscicchio, M. Car- ney, T. Dent, H. Middleton, E. Payne, J. Veitch, and D. Williams, Evidence for Hierarchical Black Hole Mergers in the Second LIGO-Virgo Gravitational Wave Catalog, Astrophys. J. Lett915, L35 (2021), arXiv:2011.05332 [astro-ph.HE]

    Pith/arXiv arXiv 2021

  16. [16]

    Li, Constraining hierarchical mergers of binary black holes detectable with LIGO-Virgo, Astron

    G.-P. Li, Constraining hierarchical mergers of binary black holes detectable with LIGO-Virgo, Astron. Astro- phys666, A194 (2022), arXiv:2208.11894 [astro-ph.HE]

    Pith/arXiv arXiv 2022

  17. [17]

    Arca Sedda, M

    M. Arca Sedda, M. Mapelli, M. Benacquista, and M. Spera, Isolated and dynamical black hole mergers with B-POP: the role of star formation and dynamics, star cluster evolution, natal kicks, mass and spins, and hi- erarchical mergers, Mon. Not. R. Astron. Soc.520, 5259 (2023), arXiv:2109.12119 [astro-ph.GA]

    Pith/arXiv arXiv 2023

  18. [18]

    Heger, C

    A. Heger, C. L. Fryer, S. E. Woosley, N. Langer, and D. H. Hartmann, How Massive Single Stars End Their Life, Astrophys. J.591, 288 (2003), arXiv:astro- ph/0212469 [astro-ph]

    arXiv 2003

  19. [19]

    S. E. Woosley, S. Blinnikov, and A. Heger, Pulsational pair instability as an explanation for the most lumi- nous supernovae, Nature (London)450, 390 (2007), arXiv:0710.3314 [astro-ph]

    Pith/arXiv arXiv 2007

  20. [20]

    Belczynski, A

    K. Belczynski, A. Heger, W. Gladysz, A. J. Ruiter, S. Woosley, G. Wiktorowicz, H. Y. Chen, T. Bu- lik, R. O’Shaughnessy, D. E. Holz, C. L. Fryer, and E. Berti, The effect of pair-instability mass loss on black-hole mergers, Astron. Astrophys594, A97 (2016), arXiv:1607.03116 [astro-ph.HE]

    Pith/arXiv arXiv 2016

  21. [21]

    Maga˜ na Hernandez and A

    I. Maga˜ na Hernandez and A. Palmese, Astrophysics in- formed Gaussian processes for gravitational-wave pop- ulations: Evidence for the onset of the pair-instability supernova mass gap, arXiv e-prints , arXiv:2508.19208 (2025), arXiv:2508.19208 [astro-ph.HE]

    Pith/arXiv arXiv 2025

  22. [22]

    Li, S.-P

    Y.-J. Li, S.-P. Tang, L.-Q. Xue, and Y.-Z. Fan, GW231123: a product of successive mergers from ∼10 stellar-mass black holes, arXiv e-prints , arXiv:2507.17551 (2025), arXiv:2507.17551 [astro- ph.HE]

    arXiv 2025

  23. [23]

    Delfavero, S

    V. Delfavero, S. Ray, H. E. Cook, K. Nathaniel, B. McKernan, K. E. S. Ford, J. Postiglione, E. McPike, and R. O’Shaughnessy, Prospects for the formation of GW231123 from the AGN channel, arXiv e-prints , arXiv:2508.13412 (2025), arXiv:2508.13412 [gr-qc]

    Pith/arXiv arXiv 2025

  24. [24]

    Tanikawa, S

    A. Tanikawa, S. Liu, W. Wu, M. S. Fujii, and L. Wang, GW231123 Formation from Population III Stars: Iso- lated Binary Evolution, arXiv e-prints , arXiv:2508.01135 (2025), arXiv:2508.01135 [astro-ph.SR]

    Pith/arXiv arXiv 2025

  25. [25]

    Bartos and Z

    I. Bartos and Z. Haiman, Accretion is All You Need: Black Hole Spin Alignment in Merger GW231123 Indicates Accretion Pathway, arXiv e-prints , arXiv:2508.08558 (2025), arXiv:2508.08558 [astro- ph.HE]

    arXiv 2025

  26. [26]

    Stegmann, A

    J. Stegmann, A. Olejak, and S. E. de Mink, Resolving Black Hole Family Issues Among the Massive Ances- tors of Very High-Spin Gravitational-Wave Events Like GW231123, arXiv e-prints , arXiv:2507.15967 (2025), arXiv:2507.15967 [astro-ph.HE]

    arXiv 2025

  27. [27]

    Gottlieb, B

    O. Gottlieb, B. D. Metzger, D. Issa, S. E. Li, M. Renzo, and M. Isi, Spinning into the Gap: Direct-Horizon Collapse as the Origin of GW231123 from End-to-End GRMHD Simulations, arXiv e-prints , arXiv:2508.15887 (2025), arXiv:2508.15887 [astro-ph.HE]

    arXiv 2025

  28. [28]

    Croon, J

    D. Croon, J. Sakstein, and D. Gerosa, Can stellar physics explain GW231123?, arXiv e-prints , arXiv:2508.10088 (2025), arXiv:2508.10088 [astro-ph.HE]

    arXiv 2025

  29. [29]

    S. A. Popa and S. E. de Mink, Very Massive, Rapidly Spinning Binary Black Hole Progenitors through Chemically Homogeneous Evolution – The Case of GW231123, arXiv e-prints , arXiv:2509.00154 (2025), arXiv:2509.00154 [astro-ph.HE]

    Pith/arXiv arXiv 2025

  30. [30]

    T. W. Baumgarte and S. L. Shapiro, Can ”premature collapse” form black holes in the upper and lower mass gaps?, (2025), arXiv:2509.04574 [astro-ph.HE]

    arXiv 2025

  31. [31]

    X. Shan, H. Yang, S. Mao, and O. A. Hannuksela, The degeneracy between microlensing wave effect and precession in strongly lensed gravitational wave, arXiv e-prints , arXiv:2508.21262 (2025), arXiv:2508.21262 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  32. [32]

    Yuan, Z.-C

    C. Yuan, Z.-C. Chen, and L. Liu, GW231123 Mass Gap Event and the Primordial Black Hole Scenario, arXiv e-prints , arXiv:2507.15701 (2025), arXiv:2507.15701 [astro-ph.CO]

    arXiv 2025

  33. [33]

    De Luca, G

    V. De Luca, G. Franciolini, and A. Riotto, GW231123: a Possible Primordial Black Hole Origin, arXiv e-prints , arXiv:2508.09965 (2025), arXiv:2508.09965 [astro- ph.CO]

    Pith/arXiv arXiv 2025

  34. [34]

    Nojiri and S

    S. Nojiri and S. D. Odintsov, Dynamical Black Hole in the accelerating Universe approaching the future singularity – Possible origin of (super-)massive black holes, arXiv e-prints , arXiv:2508.07524 (2025), arXiv:2508.07524 [gr- qc]

    arXiv 2025

  35. [35]

    Cuceu, M

    I. Cuceu, M. A. Bizouard, N. Christensen, and M. Sakel- lariadou, GW231123: Binary Black Hole Merger or Cos- mic String?, arXiv e-prints , arXiv:2507.20778 (2025), arXiv:2507.20778 [gr-qc]

    arXiv 2025

  36. [36]

    Abbott, T

    R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, N. Adhikari, R. X. Adhikari, V. B. Adya, C. Affeldt, D. Agarwal, and et al., Population of Merging Compact Binaries Inferred Using Gravitational Waves through GWTC-3, Physical Review X13, 011048 (2023), arXiv:2111.03634 [astro-ph.HE]

    Pith/arXiv arXiv 2023

  37. [37]

    Comparing hierarchical black hole mergers in star clusters and active galactic nuclei

    G.-P. Li, D.-B. Lin, and Y. Yuan, Comparing hierarchical black hole mergers in star clusters and active galactic nu- clei, Phys. Rev. D107, 063007 (2023), arXiv:2211.11150 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  38. [38]

    Li and X.-L

    G.-P. Li and X.-L. Fan, The Origin Channels of Hierarchical Binary Black Hole Mergers in the LIGO–Virgo–KAGRA O1, O2, and O3 Runs, Astrophys. J.981, 177 (2025), arXiv:2411.09195 [astro-ph.HE]

    Pith/arXiv arXiv 2025

  39. [39]

    Li and X.-L

    G.-P. Li and X.-L. Fan, The Nature of Gravitational Wave Events with Host Environment Escape Velocities, Astrophys. J.984, 63 (2025), arXiv:2502.11489 [astro- ph.HE]

    Pith/arXiv arXiv 2025

  40. [40]

    Dominik, K

    M. Dominik, K. Belczynski, C. Fryer, D. E. Holz, E. Berti, T. Bulik, I. Mandel, and R. O’Shaughnessy, Double Compact Objects. I. The Significance of the Com- mon Envelope on Merger Rates, Astrophys. J.759, 52 (2012), arXiv:1202.4901 [astro-ph.HE]

    Pith/arXiv arXiv 2012

  41. [41]

    Bartos, B

    I. Bartos, B. Kocsis, Z. Haiman, and S. M´ arka, Rapid and Bright Stellar-mass Binary Black Hole Mergers in Active Galactic Nuclei, Astrophys. J.835, 165 (2017), arXiv:1602.03831 [astro-ph.HE]

    Pith/arXiv arXiv 2017

  42. [42]

    U. N. Di Carlo, M. Mapelli, Y. Bouffanais, N. Giacobbo, F. Santoliquido, A. Bressan, M. Spera, and F. Haardt, Binary black holes in the pair instability mass gap, Mon. Not. R. Astron. Soc.497, 1043 (2020), arXiv:1911.01434 [astro-ph.HE]. 8

    Pith/arXiv arXiv 2020

  43. [43]

    Mapelli, F

    M. Mapelli, F. Santoliquido, Y. Bouffanais, M. A. Arca Sedda, M. C. Artale, and A. Ballone, Mass and Rate of Hierarchical Black Hole Mergers in Young, Globular and Nuclear Star Clusters, Symmetry13, 1678 (2021), arXiv:2007.15022 [astro-ph.HE]

    Pith/arXiv arXiv 2021

  44. [44]

    Antonini and F

    F. Antonini and F. A. Rasio, Merging Black Hole Binaries in Galactic Nuclei: Implications for Advanced-LIGO De- tections, Astrophys. J.831, 187 (2016), arXiv:1606.04889 [astro-ph.HE]

    Pith/arXiv arXiv 2016

  45. [45]

    Varma, S

    V. Varma, S. E. Field, M. A. Scheel, J. Blackman, D. Gerosa, L. C. Stein, L. E. Kidder, and H. P. Pfeiffer, Surrogate models for precessing binary black hole simu- lations with unequal masses, Physical Review Research 1, 033015 (2019), arXiv:1905.09300 [gr-qc]

    Pith/arXiv arXiv 2019

  46. [46]

    J. E. Thompson, E. Hamilton, L. London, S. Ghosh, P. Kolitsidou, C. Hoy, and M. Hannam, Phenomenolog- ical gravitational-wave model for precessing black-hole binaries with higher multipoles and asymmetries, Phys. Rev. D109, 063012 (2024), arXiv:2312.10025 [gr-qc]

    Pith/arXiv arXiv 2024

  47. [47]

    C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gom- mers, P. Virtanen, D. Cournapeau, E. Wieser, J. Tay- lor, S. Berg, N. J. Smith, R. Kern, M. Picus, S. Hoyer, M. H. van Kerkwijk, M. Brett, A. Haldane, J. F. del R ´ ıo, M. Wiebe, P. Peterson, P. G´ erard-Marchant, K. Shep- pard, T. Reddy, W. Weckesser, H. Abbasi, C. Gohlke, and T. E. Oliphant, Array...

    work page 2020

  48. [48]

    Virtanen, R

    P. Virtanen, R. Gommers, T. E. Oliphant, M. Haber- land, T. Reddy, D. Cournapeau, E. Burovski, P. Pe- terson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey, ˙I. Po- lat, Y. Feng, E. W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henr...

    2020

  49. [49]

    J. D. Hunter, Matplotlib: A 2D Graphics Environment, Computing in Science and Engineering9, 90 (2007)

    2007

  50. [50]

    Foreman-Mackey, D

    D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Good- man, emcee: The MCMC Hammer, Publ. Astron. Soc. Pac.125, 306 (2013), arXiv:1202.3665 [astro-ph.IM]

    Pith/arXiv arXiv 2013

  51. [51]

    Perez and B

    F. Perez and B. E. Granger, IPython: A System for Inter- active Scientific Computing, Computing in Science and Engineering9, 21 (2007)

    work page 2007

  52. [52]

    Foreman-Mackey, corner.py: Scatterplot matrices in Python, The Journal of Open Source Software1, 24 (2016)

    D. Foreman-Mackey, corner.py: Scatterplot matrices in Python, The Journal of Open Source Software1, 24 (2016)

    work page 2016

  53. [53]

    M. L. Waskom, seaborn: statistical data visualization, Journal of Open Source Software6, 3021 (2021)

    2021

  54. [54]

    Astropy Collaboration, A. M. Price-Whelan, P. L. Lim, N. Earl, N. Starkman, L. Bradley, D. L. Shupe, A. A. Patil, L. Corrales, C. E. Brasseur, M. N¨ othe, A. Do- nath, E. Tollerud, B. M. Morris, A. Ginsburg, E. Va- her, B. A. Weaver, J. Tocknell, W. Jamieson, M. H. van Kerkwijk, T. P. Robitaille, B. Merry, M. Bachetti, H. M. G¨ unther, T. L. Aldcroft, J. ...

    Pith/arXiv arXiv 2022

This paper was first reviewed by deepseek-v4-flash on August 4, 2026.