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Using a data-driven, model-agnostic reconstruction of 153 binary black-hole mergers, this paper finds a gap in secondary masses around 38-120 solar masses and a spin broadening above primary masses of about 45 solar masses.

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2026-08-04 18:31 UTC pith:7JTYC2A3

load-bearing objection Honest, well-hedged data-driven tour of GWTC-4; treat the headline features as visualization-level claims until they survive a nuisance-model robustness check. the 2 major comments →

arxiv 2509.09876 v1 pith:7JTYC2A3 submitted 2025-09-11 astro-ph.HE gr-qc

Trends in the Population of Binary Black Holes Following the Fourth Gravitational-Wave Transient Catalog: a Data-Driven Analysis

Nir Guttman , Ethan Payne , Paul D. Lasky , Eric Thrane This is my paper
classification astro-ph.HE gr-qc
keywords gravitational wavesbinary black holespopulation inferencepi-stroke formalismGWTC-4black hole mass gapblack hole spinspair-instability supernova
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 applies the pi-stroke formalism—a maximum-population-likelihood reconstruction that represents the underlying distribution as a weighted set of delta functions without choosing a parametric model—to the 153 binary black-hole mergers in the fourth Gravitational-Wave Transient Catalog. Its aim is to determine which features claimed by parametric population models are actually supported by the data and to surface features those models might mask. The main findings are a clear gap in the secondary black-hole mass distribution between roughly 38 and 120 solar masses, consistent with pair-instability supernova predictions, and a broadening of the effective inspiral spin distribution for primary masses above about 45 solar masses. The paper also finds support for spin magnitudes near 0.2 and 0.7, a possible correlation between the two component spins, and argues that the previously reported anti-correlation between effective spin and mass ratio is likely a projection artifact caused by misspecifying the joint mass distribution. If these results hold, they give population modelers concrete new targets and separate stable catalog features from model-dependent ones.

Core claim

On the paper's own terms, the central discovery: GWTC-4 data, reconstructed without a parametric population model, place essentially no probability on secondary black-hole masses between roughly 38 and 120 solar masses, while the primary mass distribution shows no comparable gap. In the (effective spin, primary mass) plane, the spin distribution is narrow near zero below about 45 solar masses and broadens above it. The paper also reports support for spin magnitudes near 0.2 and 0.7, a possible correlation between the two component spins, and a preference for aligned secondary spins, interpreting the high-mass broad-spin systems as likely second-generation black holes. It argues that the appa

What carries the argument

The pi-stroke formalism: the population distribution that maximizes the population likelihood over all possible distributions, guaranteed by a standard convexity theorem to be a weighted sum of delta functions (at most one per event). Delta locations and weights come from warm-started gradient descent with merging and pruning, so surviving components mark regions the data genuinely support. Nuisance parameters are marginalized by reweighting posterior samples with the previous catalog's best-fit population model (Eq. 15), and selection effects enter through a normalizing-flow fit to the injection campaign.

Load-bearing premise

The reconstruction reweights every event's posterior samples using the previous catalog's best-fit population model for all parameters it is not directly measuring; if that nuisance model is wrong, the inferred gap and spin broadening could be artifacts.

What would settle it

Re-run the pi-stroke reconstruction with the fourth catalog's population model used for the nuisance reweighting, or in three dimensions (m1, q, chi_eff): if the 38-120 solar-mass secondary gap fills in or the q–chi_eff anti-correlation persists with m1 explicitly included, the paper's central interpretation fails. A simpler check: with future catalog data, watch whether delta functions appear inside the claimed gap or whether the spin broadening threshold shifts.

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

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If this is right

  • A real secondary-mass gap with no primary gap points to a formation channel in which the heavier black hole is often a second-generation remnant, since such remnants can occupy the pair-instability gap while stellar-remnant companions cannot.
  • The broadening of effective spin above ~45 solar masses implies a mass-dependent spin transition that parametric models should build in; it also explains the apparent effective-spin/mass-ratio anti-correlation as a projection artifact.
  • Spin peaks near 0.2 and 0.7 and a possible correlation between the two spins suggest both components can be significantly spinning, challenging formation scenarios that allow only one spun-up black hole.
  • The released pi-stroke samples give a model-independent benchmark: theoretical predictions can be plotted against them, and in the large-N limit they converge to the true distribution, unlike maximum-likelihood event estimates.

Where Pith is reading between the lines

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

  • Editorial extension: re-running the same reconstruction with the fourth catalog's best-fit model (instead of the previous catalog's) for nuisance parameters would show whether the 38-120 solar-mass gap and the spin broadening shift; the paper does not perform this robustness check.
  • Editorial extension: the paper's own logic predicts that a three-dimensional pi-stroke reconstruction of (primary mass, mass ratio, effective spin) will make the apparent q–chi_eff anti-correlation vanish; this is a directly testable next step.
  • Editorial extension: the cosθ2 > 0 preference, if confirmed with a model that allows different tilt distributions for the two components, would implicate tidal alignment of the secondary before the second supernova.
  • Editorial extension: the apparent chi1–chi2 correlation could be a mixture of latent subpopulations rather than an intrinsic correlation; separating one-spin and two-spin subpopulations with a mixture model would settle it.

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 / 9 minor

Summary. This paper applies the pi-stroke (maximum population likelihood) formalism of Payne & Thrane (2023) to 153 binary black hole mergers from GWTC-4. Rather than assuming a parameterized population model, the method maximizes the population likelihood over distributions represented as weighted delta functions (Eq. 6), using a reweighting of LVK posterior samples (Eq. 15) in which all parameters except the one(s) of interest are assigned the GWTC-3 maximum-likelihood population model (Appendix B). One- and two-dimensional pi reconstructions are presented for masses, mass ratio, spin magnitudes, tilt angles, chi_eff, chi_p, and redshift. The headline findings are a secondary-mass gap at m2 ~ 38-120 M_sun (Figs. 1-2), a broadening of chi_eff for m1 >~ 45 M_sun (Fig. 11), an anti-correlation between chi_eff and q that the authors argue is a projection artifact of the m1-dependent broadening (Section 4.1), hints of chi ~ 0.2 and 0.7 spin subpopulations, a chi1-chi2 correlation, and a preference for cos(theta2) > 0. The paper is carefully hedged, repeatedly stating that pi features are not significance-tested and including internal consistency checks (e.g., the artificial chi_eff spike in the (chi_eff, z) analysis). A public data release of pi samples is provided.

Significance. Subject to the robustness concerns below, the paper would provide a useful cross-check of parameterized GWTC-4 population analyses using an independent, nonparametric reconstruction, corroborating the PISN-related secondary mass gap of Tong et al. (2025) and the high-mass chi_eff broadening of Antonini et al. (2025). Strengths include a transparent, well-documented pipeline (flowchart, Appendix D), public pi samples on Zenodo, a clear statement that features are not significance-tested, and an honest discussion of the mechanism by which the method can manufacture apparent correlations - the same logic used to dismiss the chi_eff-q anti-correlation as potentially spurious. The claim that the method is 'model-free' is, however, overstated: Eq. (15) requires a full population model for all nuisance parameters, and the robustness of the headline features to that model is asserted but not demonstrated. The incremental novelty over Payne & Thrane (2023) is moderate (new catalog, larger dataset, additional stability checks), but the corroboration and reframing of the chi_eff-q anti-correlation as a projection effect are valuable.

major comments (2)
  1. [Section 2.3, Eq. (15); Figs. 1-2 and 11] The headline features - the m2 gap (38-120 M_sun) and the chi_eff broadening above m1 ~ 45 M_sun - are produced by reweighting LVK posterior samples with the GWTC-3 maximum-likelihood nuisance model (Eq. 15, Appendix B). Section 2.3 asserts that results should be robust for 'qualitatively similar' nuisance models, but no test of this assertion is given. Section 4.1 uses misspecification of the joint mass distribution to dismiss the chi_eff-q anti-correlation as likely spurious, demonstrating that this pipeline can create apparent features from nuisance-model misspecification. The same mechanism could sculpt the m2 gap or the 45-M_sun transition; the latter is especially exposed because the assumed q(m1) nuisance model changes with m1. Please re-run the key reconstructions with at least two alternative nuisance models (e.g., GWTC-4 ML values; flat spin/uniform mass) and report whether the
  2. [Section 2.4, Stage 3; Fig. 2] The merge/discard thresholds in Stage 3 (5% of the hyper-diagonal; delta log L <= 0.05/sqrt(n)) are hand-tuned 'by trial and error' (footnote 2). Since the m2 gap is defined by the absence of components between two surviving edge components (Fig. 2), and the chi_eff broadening is read off from surviving component locations (Fig. 11), these thresholds directly determine the reported features. Please provide a sensitivity scan over the thresholds (e.g., 2-10% and 0.01-0.1/sqrt(n)) or quote the delta log L cost of inserting a component at m2 = 45 and 90 M_sun, so that the gap is shown to be data-driven rather than pruning-driven.
minor comments (9)
  1. [Abstract; Section 3.1] The abstract says 'a gap around 45 M_sun' but the analysis and Figs. 1-2 report a gap between approximately 38 and 120 M_sun. The abstract should quote the full range to avoid confusing the lower edge with the gap center.
  2. [Section 3.1] The text contains an orphan line 'kernel density estimation-based method' immediately after the sentence citing Sadiq et al. (2023). This appears to be a leftover fragment; delete it.
  3. [References] The citation 'Abac et al. 2025b, prx' is incomplete; the article title, arXiv identifier, or journal reference should be provided. Several other references are to arXiv preprints; please verify they are updated to the published versions where available.
  4. [Figures 1, 5, 7, 11, 12, 14] The two-dimensional figures encode delta-function weights by color but do not include a colorbar, making quantitative reading difficult. Adding a colorbar (or labeling the color scale) would improve interpretability.
  5. [Figure 1] The grey shading representing the parametric GWTC-4 maximum-likelihood model is difficult to discern against the white background; increasing contrast or overlaying contours would help the reader judge agreement.
  6. [Appendix B.1, Table 2] The text says f_U = 1/200 'corresponds approximately to the inverse of the number of events analyzed' (N = 153). The discrepancy is minor, but a one-line justification would avoid confusion.
  7. [Section 4.1] There is a typo in the sentence 'calculated assuming Power Law + Peak(Talbot & Thrane 2018) (See. Appendix B)' - 'See.' should be 'see' and the phrase is awkwardly placed. Also, the parenthesis around the citation is missing.
  8. [Figure 14 caption] The caption says the z distribution incorporates 'both the differential comoving volume and the merger-time delay, unlike Fig. 13,' but Fig. 13 shows a merger rate converted from a distribution. The distinction is confusing as stated; clarify what exactly differs between the two.
  9. [Section 3.1] Minor grammar: 'exhibits a excess near 10 M_sun' should be 'an excess'. Also, the phrase 'the data-driven estimate broadly tracks' in Section 3.3 could be clarified as referring to Fig. 13.

Circularity Check

0 steps flagged

No significant circularity: the pi reconstruction is a maximum-likelihood fit whose headline features are outputs, not inputs, and the nuisance model is deliberately taken from the earlier GWTC-3 catalog.

full rationale

The derivation chain is self-contained rather than circular. The pi distribution is defined in Eq. (5) as the argmax of the population likelihood, represented as a sum of delta functions in Eq. (6) via Carathéodory's theorem. The reweighting in Eq. (15) uses a uniform prior on the parameter of interest and a nuisance population model pi(eta|Lambda-hat) taken from the GWTC-3 maximum-likelihood fit. The paper explicitly adopts this earlier-catalog model to avoid circularity: 'To avoid circularity when analyzing GWTC-4 data and to enable a fair comparison with its parametric results, we adopt the GWTC-3 maximum-likelihood population model as an informed baseline.' The headline features—the m2 gap and the chi_eff broadening above m1 ~ 45 Msun—are read off from the optimized delta-function locations and weights; they are outputs of a likelihood fit, not inputs. The GWTC-3 nuisance model contains no secondary-mass gap and no mass-dependent spin broadening, so these features cannot be imported by construction. The paper also explicitly cautions that 'Different assumptions can, in principle, lead to different pi results' and that Bayesian inference is still required to assess significance, which is a limitation but not a circular reduction. Self-citations to Payne & Thrane (2023) for the formalism are standard methodology and are not used to force the conclusions; the method's earlier application to GWTC-3 provides independent, external grounding. Therefore no circular step is present.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The analysis rests on the adopted nuisance-parameter model (from GWTC-3), the selection-function estimate from found injections, and the pi-formalism's unproved convergence conjecture. There are no invented physical entities.

free parameters (5)
  • GWTC-3 Power Law + Peak mass hyperparameters = alpha=3.57, beta_q=0.63, m_min=5.30 Msun, m_max=88.69 Msun, lambda_peak=0.029, mu_m=34.60 Msun, sigma_m=3.53 Msun, delta
    Adopted from GWTC-3 maximum-likelihood model (Appendix B, Table 2) and used in Eq. (15) to weight posterior samples for the parameters of interest. The central claims depend on this nuisance model.
  • GWTC-3 spin model hyperparameters = mu_chi=0.23, sigma2_chi=0.033, zeta=0.97, sigma_t=1.18
    Adopted from GWTC-3 (Appendix B, Table 3); used for all spin-related reweightings.
  • Redshift evolution slope kappa = 3.46
    Adopted from GWTC-3 (Appendix B.3) for redshift reweighting.
  • Pruning merge/discard thresholds = merge distance 5% of hyper-diagonal; Delta-logL <= 0.05/sqrt(n)
    Determined by trial and error (Section 2.4 Stage 3); directly sets the number of delta functions and therefore the features visible in every pi plot.
  • Effective sample size threshold = 1% (with three events at 0.5-1%)
    Chosen threshold for acceptable reweighting efficiency (Section 2.3).
axioms (4)
  • standard math Caratheodory's theorem guarantees the discrete delta-function representation of the maximum population likelihood (Eq. 6).
    Justifies the discrete representation used throughout the pi formalism.
  • domain assumption Conjecture that the pi distribution converges to the true population distribution as the number of observations goes to infinity (Payne & Thrane 2023).
    Used to interpret pi samples as data-supported features; unproved and cited from prior work.
  • domain assumption The official GWTC-4 found injections provide a faithful, catalog-specific estimate of the selection function (Eq. 13).
    The selection correction depends on this empirical estimate; any bias propagates into the pi distributions.
  • domain assumption The normalizing-flow approximation of the detected-injection distribution f_det is accurate enough for the selection correction.
    The flow architecture (3 coupling layers, 16 knots) is a modeling choice whose error is not quantified.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of Trends in the Population of Binary Black Holes Following the Fourth Gravitational-Wave Transient Catalog: a Data-Driven Analysis." pith.science (2026). https://pith.science/paper/7JTYC2A3

@misc{pith2026250909876,
  author       = {Pith},
  title        = {Pith review of: Trends in the Population of Binary Black Holes Following the Fourth Gravitational-Wave Transient Catalog: a Data-Driven Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7JTYC2A3}},
  note         = {Machine review of arXiv:2509.09876}
}
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read the original abstract

Current population models of binary black hole distributions are difficult to interpret because standard population inferences hinge on modeling choices, which can mask or mimic real structure. The maximum population likelihood ``$\pistroke$ formalism'' provides a means to investigate and interpret features in the distribution of binary black holes using only data -- without specifying a population model. It tells us if features inferred from current population models are truly present in the data or if they arise from model misspecification. It also provides guidance for developing new models by highlighting previously unnoticed features. In this study, we utilize the $\pistroke$ formalism to examine the binary black hole population in the LIGO--Virgo--KAGRA (LVK) fourth Gravitational-Wave Transient Catalog (GWTC-4). Our analysis supports the existence of a gap around $45\,M_\odot$ in the secondary black hole mass distribution and identifies a widening in the distribution of the effective inspiral spin parameter $\chi_\text{eff}$ near this mass as recently reported by Tong et al. (2025). Similar to earlier studies, we find support for an anti-correlation between $\chi_\text{eff}$ and mass ratio. However, we argue that this may be a spurious correlation arising from misspecification of the joint distribution of black hole masses. Furthermore, we identify support for dimensionless black hole spin magnitudes at approximately $\chi \approx 0.2$ and $\chi\approx0.7$. The data support the existence of a correlation between the spin magnitudes $\chi_1$ and $\chi_2$, though subsequent study is required to determine if this feature is statistically significant. The accompanying data release includes $\pistroke$ samples, which can be used to compare theoretical predictions to LVK data and to assess assumptions in parameterised models.

Figures

Figures reproduced from arXiv: 2509.09876 by Eric Thrane, Ethan Payne, Nir Guttman, Paul D. Lasky.

Figure 2
Figure 2. Figure 2: The π– distribution for m2. The black mark￾ers and vertical lines denote the delta-function components, with heights proportional to the corresponding weights. The red bars show a histogram of these components. A clear gap is evident between approximately 38 M⊙ and 120 M⊙. The grey band indicates the 90% credible interval of the paramet￾ric GWTC-4 population model from Abac et al. (2025b). 25 50 75 100 125… view at source ↗
Figure 1
Figure 1. Figure 1: The π– distribution in the (m1, m2) plane. Red squares mark the delta-function components, with colour intensity proportional to their weights. The grey shad￾ing represents the maximum-likelihood fit of the parametric GWTC-4 population model (Abac et al. 2025b). A distinct secondary-mass gap appears for 38 M⊙ ≲ m2 ≲ 120 M⊙. Horizontal blue bands show the gap boundaries inferred by Tong et al. (2025). The o… view at source ↗
Figure 3
Figure 3. Figure 3: The π– distribution for m1. The distribution is consistent with the GWTC-4 parametric population model and exhibits a excess near 10 M⊙, and 35 M⊙. range (see, e.g., Woosley 2017; Farmer et al. 2019). We return to the implications of this hypothesis in Section 4. The primary-mass distribution m1 ( [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: , shows the π– distribution in the (χ1, χ2) plane. We are struck by the apparent correlation be￾tween χ1 and χ2. While a large range of spin values are supported by the data, there is no support for large χ1 when χ2 is small and vice versa. This result is con￾sistent with Adamcewicz et al. (2025), which suggests a χ1, χ2 correlation using a parameterized model. This result is surprising since conventional … view at source ↗
Figure 6
Figure 6. Figure 6: The π– distribution for spin magnitude χ1. The two-dimensional cosine tilt–angle distribution in [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The π– distribution in the (cos θ1, cos θ2) plane. 1.0 0.5 0.0 0.5 1.0 cos 1 0.2 0.4 0.6 ( c o s 1 ) [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The π– distribution for cos θ1. 1.0 0.5 0.0 0.5 1.0 cos 2 0.2 0.4 0.6 ( c o s 2 ) [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The π– distribution for cos θ2 [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: The π– distribution in the (χeff , m1) plane. The dashed horizontal line at m1 = 45 M⊙ marks the transi￾tion identified by Antonini et al. (2025); see also Tong et al. (2025). 0.25 0.00 0.25 0.50 0.75 1.00 eff 0.0 0.2 0.4 0.6 0.8 1.0 q [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: shows the one-dimensional π– reconstruction of the merger-rate evolution with redshift; the conver￾sion from a distribution to a rate is described in Ap￾ [PITH_FULL_IMAGE:figures/full_fig_p009_13.png] view at source ↗
Figure 12
Figure 12. Figure 12: The π– distribution in the (χeff , q) plane. 3.3. Redshift Properties [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: The π– distribution in the (χeff , z) plane. The dashed horizontal line at z = 0.3 marks the estimated spin￾transition redshift. Note that the z probability distribution shown here incorporates both the differential comoving vol￾ume and the merger-time delay, unlike [PITH_FULL_IMAGE:figures/full_fig_p010_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: summarizes the π–-optimization procedure described in Section 2.4 for constructing the maximum￾likelihood. Rectangles denote processing stages, diamonds denote decision tests, rounded rectangles denote the start/end states, and arrows indicate control flow, with symbols defined as follows: L is the population likelihood, ∆log L is the log-likelihood change, nδ the number of delta functions, and N the maxi… view at source ↗
Figure 16
Figure 16. Figure 16: One-dimensional π– distribution for χp (left) and χ2 (right), both consistent with GWTC-4 parametric model. Plotting conventions match those of [PITH_FULL_IMAGE:figures/full_fig_p017_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: The one-dimensional (blue) and two-dimensional (black and red) marginal π– distributions for m1 (left) and m2 (right). 0.0 0.2 0.4 0.6 0.8 1.0 1 0.0 0.1 0.2 0.3 0.4 ( 1 ) 0.0 0.2 0.4 0.6 0.8 1.0 2 0.0 0.2 0.4 0.6 0.8 ( 2 ) [PITH_FULL_IMAGE:figures/full_fig_p018_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: The one-dimensional (blue) and two-dimensional (black and red) marginal π– distributions for χ1 (left) and χ2 (right). Biscoveanu, S., Callister, T. A., Haster, C.-J., et al. 2022, The Astrophysical Journal Letters, 932, L19, doi: 10.3847/2041-8213/ac71a8 Buikema, A., et al. 2020, Phys. Rev. D, 102, 062003, doi: 10.1103/PhysRevD.102.062003 Callister, T. A., Essick, R., & Holz, D. E. 2024, Phys. Rev. D, 11… view at source ↗
Figure 19
Figure 19. Figure 19: The one-dimensional (blue) and two-dimensional (black and red) marginal π– distributions for cos θ1 (left) and cos θ2 (right). Edelman, B., Farr, B., & Doctor, Z. 2023, The Astrophysical Journal, 946, 16, doi: 10.3847/1538-4357/acb5ed Essick, R., et al. 2025, Compact Binary Coalescence Sensitivity Estimates with Injection Campaigns during the LIGO-Virgo-KAGRA Collaborations’ Fourth Observing Run. https://… view at source ↗

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Reference graph

Works this paper leans on

79 extracted references · 5 canonical work pages · cited by 9 Pith papers

  1. [1]

    G., Abouelfettouh, I., et al

    Abac, A. G., Abouelfettouh, I., et al. 2025 a , GW231123: a Binary Black Hole Merger with Total Mass 190-265 M_ . 2507.08219

    Pith/arXiv arXiv 2025

  2. [2]

    G., et al

    Abac, A. G., et al. 2025 b , prx

    2025

  3. [3]

    2021, Astrophys

    Abbott, R., et al. 2021, Astrophys. J. Lett., 913, L7

    2021

  4. [4]

    2023 a , Phys

    ---. 2023 a , Phys. Rev. X, 13, 011048

    2023

  5. [5]

    2023 b , Phys

    ---. 2023 b , Phys. Rev. X, 13, 041039, 10.1103/PhysRevX.13.041039

    doi:10.1103/physrevx.13.041039 2023

  6. [6]

    D., & Thrane, E

    Adamcewicz, C., Galaudage, S., Lasky, P. D., & Thrane, E. 2024, The Astrophysical Journal Letters, 964, L6, 10.3847/2041-8213/ad2df2

    doi:10.3847/2041-8213/ad2df2 2024

  7. [7]

    D., & Thrane, E

    Adamcewicz, C., Guttman, N., Lasky, P. D., & Thrane, E. 2025, Do both black holes spin in merging binaries? Evidence from GWTC-4 and astrophysical implications. 2509.04706

    arXiv 2025

  8. [8]

    2022, Monthly Notices of the Royal Astronomical Society, 517, 3928, 10.1093/mnras/stac2961

    Adamcewicz, C., & Thrane, E. 2022, Monthly Notices of the Royal Astronomical Society, 517, 3928, 10.1093/mnras/stac2961

    doi:10.1093/mnras/stac2961 2022

  9. [9]

    M., & Callister, T

    Antonini, F., Romero-Shaw, I. M., & Callister, T. 2025, Phys. Rev. Lett., 134, 011401, 10.1103/PhysRevLett.134.011401

    doi:10.1103/physrevlett.134.011401 2025

  10. [10]

    A., Doctor, Z., & Kalogera, V

    Banagiri, S., Callister, T. A., Doctor, Z., & Kalogera, V. 2025, Structure and Skewness of the Effective Inspiral Spin Distribution of Binary Black Hole Mergers. 2501.06712

    Pith/arXiv arXiv 2025

  11. [11]

    A., Haster, C.-J., et al

    Biscoveanu, S., Callister, T. A., Haster, C.-J., et al. 2022, The Astrophysical Journal Letters, 932, L19, 10.3847/2041-8213/ac71a8

    doi:10.3847/2041-8213/ac71a8 2022

  12. [12]

    2020, Phys

    Buikema, A., et al. 2020, Phys. Rev. D, 102, 062003, 10.1103/PhysRevD.102.062003

    doi:10.1103/physrevd.102.062003 2020

  13. [13]

    A., Essick, R., & Holz, D

    Callister, T. A., Essick, R., & Holz, D. E. 2024, Phys. Rev. D, 110, 123041, 10.1103/PhysRevD.110.123041

    work page doi:10.1103/physrevd.110.123041 2024

  14. [15]

    2024 b , Phys

    ---. 2024 b , Phys. Rev. X, 14, 021005, 10.1103/PhysRevX.14.021005

    doi:10.1103/physrevx.14.021005 2024

  15. [16]

    A., Haster, C.-J., Ng, K

    Callister, T. A., Haster, C.-J., Ng, K. K. Y., Vitale, S., & Farr, W. M. 2021, The Astrophysical Journal Letters, 922, L5, 10.3847/2041-8213/ac2ccc

    doi:10.3847/2041-8213/ac2ccc 2021

  16. [17]

    2025, Phys

    Capote, E., et al. 2025, Phys. Rev. D, 111, 062002, 10.1103/PhysRevD.111.062002

    doi:10.1103/physrevd.111.062002 2025

  17. [18]

    1911, Rendiconti del Circolo Matematico di Palermo (1884-1940), 32, 193

    Carath \'e odory, C. 1911, Rendiconti del Circolo Matematico di Palermo (1884-1940), 32, 193. https://api.semanticscholar.org/CorpusID:120032616

    1911

  18. [19]

    S., Collaboration, V., & Collaboration, K

    Collaboration, L. S., Collaboration, V., & Collaboration, K. 2025 a , GWTC-4.0: Data Quality Products for Transient Gravitational Wave Searches, v1, Zenodo, 10.5281/zenodo.16856919

    doi:10.5281/zenodo.16856919 2025

  19. [20]

    Collaboration, T. L. S., the Virgo Collaboration, & the KAGRA Collaboration. 2025 b , GWTC-4.0: Population Properties of Merging Compact Binaries. 2508.18083

    Pith/arXiv arXiv 2025

  20. [21]

    2001, Phys

    Damour, T. 2001, Phys. Rev. D, 64, 124013, 10.1103/PhysRevD.64.124013

    doi:10.1103/physrevd.64.124013 2001

  21. [22]

    2019, Neural Spline Flows

    Durkan, C., Bekasov, A., Murray, I., & Papamakarios, G. 2019, Neural Spline Flows. 1906.04032

    Pith/arXiv arXiv 2019

  22. [23]

    2023, The Astrophysical Journal, 946, 16, 10.3847/1538-4357/acb5ed

    Edelman, B., Farr, B., & Doctor, Z. 2023, The Astrophysical Journal, 946, 16, 10.3847/1538-4357/acb5ed

    doi:10.3847/1538-4357/acb5ed 2023

  23. [24]

    2025, Compact Binary Coalescence Sensitivity Estimates with Injection Campaigns during the LIGO-Virgo-KAGRA Collaborations' Fourth Observing Run

    Essick, R., et al. 2025, Compact Binary Coalescence Sensitivity Estimates with Injection Campaigns during the LIGO-Virgo-KAGRA Collaborations' Fourth Observing Run. 2508.10638

    arXiv 2025

  24. [25]

    M., Fishbach, M., & Holz, D

    Farah, A. M., Fishbach, M., & Holz, D. E. 2024, The Astrophysical Journal, 962, 69, 10.3847/1538-4357/ad0558

    doi:10.3847/1538-4357/ad0558 2024

  25. [26]

    E., Marchant, P., & Justham, S

    Farmer, R., Renzo, M., de Mink, S. E., Marchant, P., & Justham, S. 2019, The Astrophysical Journal, 887, 53, 10.3847/1538-4357/ab518b

    doi:10.3847/1538-4357/ab518b 2019

  26. [27]

    Fishbach, M., & Holz, D. E. 2020, The Astrophysical Journal Letters, 891, L27, 10.3847/2041-8213/ab7247

    doi:10.3847/2041-8213/ab7247 2020

  27. [28]

    E., & Farr, B

    Fishbach, M., Holz, D. E., & Farr, B. 2017, The Astrophysical Journal Letters, 840, L24, 10.3847/2041-8213/aa7045

    doi:10.3847/2041-8213/aa7045 2017

  28. [29]

    E., & Farr, W

    Fishbach, M., Holz, D. E., & Farr, W. M. 2018, The Astrophysical Journal Letters, 863, L41, 10.3847/2041-8213/aad800

    doi:10.3847/2041-8213/aad800 2018

  29. [30]

    2019, The Astrophysical Journal Letters, 881, L1, 10.3847/2041-8213/ab339b

    Fuller, J., & Ma, L. 2019, The Astrophysical Journal Letters, 881, L1, 10.3847/2041-8213/ab339b

    doi:10.3847/2041-8213/ab339b 2019

  30. [31]

    2023, Phys

    Ganapathy, D., et al. 2023, Phys. Rev. X, 13, 041021, 10.1103/PhysRevX.13.041021

    doi:10.1103/physrevx.13.041021 2023

  31. [32]

    2019, Phys

    Gerosa, D., & Berti, E. 2019, Phys. Rev. D, 100, 041301, 10.1103/PhysRevD.100.041301

    doi:10.1103/physrevd.100.041301 2019

  32. [33]

    2018, Phys

    Gerosa, D., Berti, E., O'Shaughnessy, R., et al. 2018, Phys. Rev. D, 98, 084036, 10.1103/PhysRevD.98.084036

    doi:10.1103/physrevd.98.084036 2018

  33. [34]

    2021, Nat

    Gerosa, D., & Fishbach, M. 2021, Nat. Astro., 8, 749

    2021

  34. [35]

    2013, Phys

    Gerosa, D., Kesden, M., Berti, E., O'Shaughnessy, R., & Sperhake, U. 2013, Phys. Rev. D, 87, 104028, 10.1103/PhysRevD.87.104028

    doi:10.1103/physrevd.87.104028 2013

  35. [36]

    2020, Phys

    Gerosa, D., Pratten, G., & Vecchio, A. 2020, Phys. Rev. D, 102, 103020, 10.1103/PhysRevD.102.103020

    work page doi:10.1103/physrevd.102.103020 2020

  36. [38]

    2024 b , The Astrophysical Journal, 976, 121, 10.3847/1538-4357/ad8572

    ---. 2024 b , The Astrophysical Journal, 976, 121, 10.3847/1538-4357/ad8572

    doi:10.3847/1538-4357/ad8572 2024

  37. [39]

    2023, Phys

    Golomb, J., & Talbot, C. 2023, Phys. Rev. D, 108, 103009, 10.1103/PhysRevD.108.103009

    doi:10.1103/physrevd.108.103009 2023

  38. [40]

    2025, pi stroke samples, Zenodo, 10.5281/zenodo.17096730

    Guttman, N. 2025, pi stroke samples, Zenodo, 10.5281/zenodo.17096730

    work page doi:10.5281/zenodo.17096730 2025

  39. [41]

    2025, Phys

    Heinzel, J., Mould, M., \'Alvarez-L\'opez, S., & Vitale, S. 2025, Phys. Rev. D, 111, 063043, 10.1103/PhysRevD.111.063043

    doi:10.1103/physrevd.111.063043 2025

  40. [42]

    D., van Son, L

    Hendriks, D. D., van Son, L. A. C., Renzo, M., Izzard, R. G., & Farmer, R. 2023, Monthly Notices of the Royal Astronomical Society, 526, 4130, 10.1093/mnras/stad2857

    doi:10.1093/mnras/stad2857 2023

  41. [43]

    2024, Hints of spin-magnitude correlations and a rapidly spinning subpopulation of binary black holes

    Hussain, A., Isi, M., & Zimmerman, A. 2024, Hints of spin-magnitude correlations and a rapidly spinning subpopulation of binary black holes. 2411.02252

    Pith/arXiv arXiv 2024

  42. [44]

    2024, Science, 385, 1318, 10.1126/science.ado8069

    Jia, W., et al. 2024, Science, 385, 1318, 10.1126/science.ado8069

    doi:10.1126/science.ado8069 2024

  43. [45]

    P., & Ba, J

    Kingma, D. P., & Ba, J. 2017, Adam: A Method for Stochastic Optimization. 1412.6980

    Pith/arXiv arXiv 2017

  44. [46]

    P., Salimans, T., Jozefowicz, R., et al

    Kingma, D. P., Salimans, T., Jozefowicz, R., et al. 2017, Improving Variational Inference with Inverse Autoregressive Flow. 1606.04934

    Pith/arXiv arXiv 2017

  45. [47]

    2022, A and A, 666, A194, 10.1051/0004-6361/202244257

    Li, Guo-Peng . 2022, A and A, 666, A194, 10.1051/0004-6361/202244257

    doi:10.1051/0004-6361/202244257 2022

  46. [48]

    LIGO Scientific Collaboration , & Virgo Collaboration . 2022, GWTC-2.1: Deep Extended Catalog of Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run - Parameter Estimation Data Release, v2, Zenodo, 10.5281/zenodo.6513631

    doi:10.5281/zenodo.6513631 2022

  47. [49]

    LIGO Scientific Collaboration , Virgo Collaboration , & KAGRA Collaboration . 2023, GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run — Parameter estimation data release, v2, Zenodo, 10.5281/zenodo.8177023

    doi:10.5281/zenodo.8177023 2023

  48. [50]

    2025, Classical and Quantum Gravity, 42, 045008, 10.1088/1361-6382/ad9c0e

    Lorenzo-Medina, A., & Dent, T. 2025, Classical and Quantum Gravity, 42, 045008, 10.1088/1361-6382/ad9c0e

    work page doi:10.1088/1361-6382/ad9c0e 2025

  49. [51]

    2022, Physics Reports, 955, 1, https://doi.org/10.1016/j.physrep.2022.01.003

    Mandel, I., & Farmer, A. 2022, Physics Reports, 955, 1, https://doi.org/10.1016/j.physrep.2022.01.003

    doi:10.1016/j.physrep.2022.01.003 2022

  50. [52]

    M., & Gair, J

    Mandel, I., Farr, W. M., & Gair, J. R. 2019, Monthly Notices of the Royal Astronomical Society, 486, 1086, 10.1093/mnras/stz896

    doi:10.1093/mnras/stz896 2019

  51. [53]

    J., Mohamed, S., & Lakshminarayanan, B

    Papamakarios, G., Nalisnick, E., Rezende, D. J., Mohamed, S., & Lakshminarayanan, B. 2021, Journal of Machine Learning Research, 22, 1. http://jmlr.org/papers/v22/19-1028.html

    2021

  52. [54]

    2018, Masked Autoregressive Flow for Density Estimation

    Papamakarios, G., Pavlakou, T., & Murray, I. 2018, Masked Autoregressive Flow for Density Estimation. 1705.07057

    Pith/arXiv arXiv 2018

  53. [55]

    D., Thrane, E., & Kissel, J

    Payne, E., Talbot, C., Lasky, P. D., Thrane, E., & Kissel, J. S. 2020, Phys. Rev. D, 102, 122004, 10.1103/PhysRevD.102.122004

    doi:10.1103/physrevd.102.122004 2020

  54. [56]

    2023, Phys

    Payne, E., & Thrane, E. 2023, Phys. Rev. Res., 5, 023013, 10.1103/PhysRevResearch.5.023013

    doi:10.1103/physrevresearch.5.023013 2023

  55. [57]

    L., Zevin, M., Amaro-Seoane, P., et al

    Rodriguez, C. L., Zevin, M., Amaro-Seoane, P., et al. 2019, Phys. Rev. D, 100, 043027, 10.1103/PhysRevD.100.043027

    doi:10.1103/physrevd.100.043027 2019

  56. [58]

    M., Thrane, E., & Lasky, P

    Romero-Shaw, I. M., Thrane, E., & Lasky, P. D. 2022, Pub. Astron. Soc. Aust., 39, E025

    2022

  57. [59]

    K., van Son, L

    Roy, S. K., van Son, L. A. C., & Farr, W. M. 2025, A Mid-Thirties Crisis: Dissecting the Properties of Gravitational Wave Sources Near the 35 Solar Mass Peak. 2507.01086

    arXiv 2025

  58. [60]

    2023, The Astrophysical Journal, 960, 65, 10.3847/1538-4357/ad0ce6

    Sadiq, J., Dent, T., & Gieles, M. 2023, The Astrophysical Journal, 960, 65, 10.3847/1538-4357/ad0ce6

    doi:10.3847/1538-4357/ad0ce6 2023

  59. [61]

    2025, Seeking Spinning Subpopulations of Black Hole Binaries via Iterative Density Estimation

    Sadiq, J., Dent, T., & Lorenzo-Medina, A. 2025, Seeking Spinning Subpopulations of Black Hole Binaries via Iterative Density Estimation. 2506.02250

    arXiv 2025

  60. [62]

    2015, Phys

    Schmidt, P., Ohme, F., & Hannam, M. 2015, Phys. Rev. D, 91, 024043, 10.1103/PhysRevD.91.024043

    doi:10.1103/physrevd.91.024043 2015

  61. [63]

    Scott, D. W. 1992, Multivariate Density Estimation: Theory, Practice and Visualization (New York: John Wiley and Sons), 10.1002/9780470316849

    doi:10.1002/9780470316849 1992

  62. [64]

    1986, Density Estimation for Statistics and Data Analysis

    Silverman, B. 1986, Density Estimation for Statistics and Data Analysis. (London: Chapman and Hall), 10.1007/978-1-4899-3324-9

    doi:10.1007/978-1-4899-3324-9 1986

  63. [65]

    Simpson, E. H. 2018, Journal of the Royal Statistical Society: Series B (Methodological), 13, 238, 10.1111/j.2517-6161.1951.tb00088.x

    arXiv 2018

  64. [66]

    2025, Classical and Quantum Gravity, 42, 085016, 10.1088/1361-6382/adc4b6

    Soni, S., et al. 2025, Classical and Quantum Gravity, 42, 085016, 10.1088/1361-6382/adc4b6

    doi:10.1088/1361-6382/adc4b6 2025

  65. [67]

    Stevenson, S., Berry, C. P. L., & Mandel, I. 2017, Monthly Notices of the Royal Astronomical Society, 471, 2801, 10.1093/mnras/stx1764

    doi:10.1093/mnras/stx1764 2017

  66. [68]

    2019, The Astrophysical Journal, 882, 121, 10.3847/1538-4357/ab3981

    Stevenson, S., Sampson, M., Powell, J., et al. 2019, The Astrophysical Journal, 882, 121, 10.3847/1538-4357/ab3981

    doi:10.3847/1538-4357/ab3981 2019

  67. [69]

    2017, Phys

    Talbot, C., & Thrane, E. 2017, Phys. Rev. D, 96, 023012, 10.1103/PhysRevD.96.023012

    doi:10.1103/physrevd.96.023012 2017

  68. [70]

    2018, The Astrophysical Journal, 856, 173, 10.3847/1538-4357/aab34c

    ---. 2018, The Astrophysical Journal, 856, 173, 10.3847/1538-4357/aab34c

    doi:10.3847/1538-4357/aab34c 2018

  69. [71]

    2022, The Astrophysical Journal, 927, 76, 10.3847/1538-4357/ac4bc0

    ---. 2022, The Astrophysical Journal, 927, 76, 10.3847/1538-4357/ac4bc0

    work page doi:10.3847/1538-4357/ac4bc0 2022

  70. [72]

    2019 a , Pub

    Thrane, E., & Talbot, C. 2019 a , Pub. Astron. Soc. Aust., 36, E010

    2019

  71. [73]

    2019 b , Publications of the Astronomical Society of Australia, 36, e010, 10.1017/pasa.2019.2

    ---. 2019 b , Publications of the Astronomical Society of Australia, 36, e010, 10.1017/pasa.2019.2

    doi:10.1017/pasa.2019.2 2019

  72. [74]

    2021, Classical and Quantum Gravity, 38, 155007, 10.1088/1361-6382/ac0b54

    Tiwari, V. 2021, Classical and Quantum Gravity, 38, 155007, 10.1088/1361-6382/ac0b54

    doi:10.1088/1361-6382/ac0b54 2021

  73. [75]

    2022, The Astrophysical Journal, 928, 155, 10.3847/1538-4357/ac589a

    ---. 2022, The Astrophysical Journal, 928, 155, 10.3847/1538-4357/ac589a

    doi:10.3847/1538-4357/ac589a 2022

  74. [76]

    2022, Phys

    Tong, H., Galaudage, S., & Thrane, E. 2022, Phys. Rev. D, 106, 103019, 10.1103/PhysRevD.106.103019

    doi:10.1103/physrevd.106.103019 2022

  75. [77]

    2025, Evidence of the pair instability gap in the distribution of black hole masses

    Tong, H., et al. 2025, Evidence of the pair instability gap in the distribution of black hole masses. 2509.04151

    Pith/arXiv arXiv 2025

  76. [78]

    M., & Taylor, S

    Vitale, S., Gerosa, D., Farr, W. M., & Taylor, S. R. 2020, Inferring the Properties of a Population of Compact Binaries in Presence of Selection Effects, ed. C. Bambi, S. Katsanevas, & K. D. Kokkotas (Singapore: Springer Singapore), 1

    2020

  77. [79]

    2022, flowjax Documentation

    Ward, D. 2022, flowjax Documentation. https://danielward27.github.io/flowjax/

    2022

  78. [80]

    Woosley, S. E. 2017, The Astrophysical Journal, 836, 244, 10.3847/1538-4357/836/2/244

    doi:10.3847/1538-4357/836/2/244 2017

  79. [81]

    2019, Phys

    Wysocki, D., Lange, J., & O'Shaughnessy, R. 2019, Phys. Rev. D, 100, 043012, 10.1103/PhysRevD.100.043012

    doi:10.1103/physrevd.100.043012 2019

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