{"id":"1af0df79-600b-4880-9c56-e63318aa27b0","arxiv_id":"2509.08298","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"GW231123 is claimed to be a 2G+2G hierarchical merger, but only under the NRSur7dq4 waveform; the conclusion flips with IMRPhenomXO4a.","lead":"The authors used a Bayesian comparison of hierarchical black-hole merger scenarios to argue that GW231123's two huge components are themselves products of earlier black-hole mergers, the 2G+2G scenario. The conclusion holds only for one gravitational-wave waveform model; with another model the event looks like a 2G+1G merger.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 2G+2G conclusion reverses under the IMRPhenomXO4a waveform model; the paper does not justify why NRSur7dq4 is preferred, so the central claim is not robust.","rationale":"The reader's weakest assumption identified the waveform-model dependence as the key vulnerability, and the paper's own Table I confirms that the conclusion flips under IMRPhenomXO4a. My independent read converges on the same concern: the central claim is not a robust finding but a conditional one. The prior odds, while approximate, are not the primary issue because the Bayes factor itself changes sign. The post-merger spin result is also prior-dominated, but that is a secondary weakness. The appropriate verdict remains CONDITIONAL, matching the reader's assessment. The paper should qualify the abstract, justify or marginalize over waveform choice, and provide code for reproducibility. No more severe flaw (e.g., a clear internal inconsistency) is apparent from the text, so a REJECT would be too strong.","tokens_in":14823,"tokens_out":7150,"duration_ms":81980,"concrete_test":"Compute the Bayesian evidence for the GW231123 data under the NRSur7dq4 and IMRPhenomXO4a waveform models themselves (i.e., the waveform-model Bayes factor) using the same PE priors. If IMRPhenomXO4a is favored or the evidence is inconclusive (log Bayes factor < 5), then the 2G+2G conclusion is not robust; if NRSur7dq4 is strongly favored, the conclusion still holds but only after explicitly marginalizing over waveform uncertainty. Alternatively, recompute the odds ratio using a third independent waveform model (e.g., SEOBNRv5PHM) with the same hierarchical priors to check convergence.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim that GW231123 is a 2G+2G merger with odds >10^3 rests entirely on the posterior obtained with the NRSur7dq4 waveform model. In Table I, the same analysis using IMRPhenomXO4a yields log B_{2G+1G}^{2G+2G} = −1.48, corresponding to odds 0.03, i.e., the 2G+1G scenario is favored. This reversal is driven by the drastically different mass posterior: with IMRPhenomXO4a the secondary mass is ~55 M_sun, which falls within the 1G mass distribution, whereas with NRSur7dq4 the secondary is ~111 M_sun, requiring a 2G origin. The paper acknowledges this sensitivity but does not provide a physical or statistical justification for preferring NRSur7dq4 over IMRPhenomXO4a for this unusually massive event. Absent such a justification, the headline claim is conditional on an arbitrary waveform choice, and the stated >10^3 odds are not a robust property of the data.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":15087,"tokens_out":6735,"duration_ms":75528,"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":[{"comment":"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.","section":"Abstract; §III A, Table I"},{"comment":"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.","section":"§II B, Eq. (2)"},{"comment":"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.","section":"§III B, Fig. 3"},{"comment":"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.","section":"§II B, after Eq. (3)"}],"minor_comments":[{"comment":"The conclusion quotes log Bayes factor 8.35 for 2G+2G versus 3G+2G, but Table I gives 8.38. Please correct the inconsistency.","section":"§IV, item (1)"},{"comment":"The dataset is denoted 'd^1' in one place and 'd' elsewhere. Use a single symbol, e.g., 'd', and remove the superscript.","section":"Eq. (1) and surrounding text"},{"comment":"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.","section":"Footnote 1"},{"comment":"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.","section":"Table I, IMRPhenomXO4a row"},{"comment":"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.","section":"Fig. 1 caption"}],"recommendation":"major_revision","confidential_remarks":"The paper has a genuinely interesting but currently conditional result. The most important issue is the waveform-model dependence: the abstract's headline odds ratio is contradicted by the IMRPhenomXO4a row in Table I. The authors are transparent about this, but the framing needs substantial revision, not just a caveat. I would encourage the editor to request that the authors either justify the waveform choice quantitatively or significantly soften the claim. The evidence-integral method also needs to be made concrete for reproducibility."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The headline claim—2G+2G favored over 2G+1G with odds >10^3—is not robust. The paper's own Table I shows the same comparison with IMRPhenomXO4a gives odds 0.03 in favor of 2G+1G. The authors acknowledge this and conclude that waveform choice is decisive, so the abstract overstates the case: it presents 2G+2G as favored without the NRSur7dq4 qualifier.\n\nThe paper does useful work. Applying the hierarchical-merger machinery to GW231123 and showing the conclusion flips with waveform choice is genuinely new. The authors are also honest: they flag that the post-merger spins near 0.7 are dominated by the input spin prior, and they engage with the competing scenarios (Pop III, primordial black holes, accretion, cosmic strings) instead of ignoring them.\n\nThe soft spots. The authors do not justify why NRSur7dq4 is the right waveform for this unusually massive, high-spin event. The secondary mass shifts from roughly 111 to 55 solar masses between waveforms, and that shift drives the model comparison. Without a physical or statistical reason to prefer one waveform, the central claim is conditional on an arbitrary choice. The evidence integral in Eq. 2 is not tied to a concrete numerical scheme, so the reported Bayes factors are hard to check. The exclusion of the 1G+2G case is dismissed in one sentence about mass difference, which is inadequate given that the secondary mass is waveform-dependent. The prior odds are proportional to retention probabilities—a reasonable choice, but unvalidated; in this case it matters little because the Bayes factors are extreme under both waveforms. And the ~0.7 remnant spins are prior-driven; the paper admits this, so it is a caveat, not a hidden circularity.\n\nWho this is for: people working on GW231123's origin and anyone studying how sensitive hierarchical-origin claims are to waveform and population-prior choices. It deserves a serious referee; the sensitivity finding is worth publishing. But the abstract and conclusions need rewording so the NRSur7dq4 dependence is upfront, and the evidence calculation needs more detail. I would cite it as a demonstration of waveform sensitivity, not as evidence for the 2G+2G scenario.","headline":"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.","tokens_in":15592,"tokens_out":3897,"would_cite":true,"duration_ms":39276,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["GW231123","hierarchical mergers","black hole mergers","gravitational waves","2G+2G","spin prior","pair-instability mass gap","waveform model"],"falsifier":"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).","tokens_in":14649,"feed_emoji":"🕳️","tokens_out":11282,"duration_ms":102348,"temperature":0.7,"pith_summary":"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.","feed_headline":"GW231123 likely came from two second-generation black holes","feed_subtitle":"Odds beat 2G+1G and 3G+2G by 10^4 and 10^8, but a rival waveform flips the verdict.","key_machinery":"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","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the GW231123 detection and the posterior masses and spins that all hypotheses are tested against.","marker":"[1]"},{"why":"Provides the NRSur7dq4 waveform model whose posterior yields the 2G+2G preference.","marker":"[45]"},{"why":"Defines the first-generation black-hole mass and spin population from which higher generations are built.","marker":"[36]"},{"why":"Gives the parametric population model with escape-speed cutoff used to synthesize 2G and 3G black-hole priors.","marker":"[37]"},{"why":"Extends the population model to current detector data and hierarchical-merger origin channels, informing the synthetic priors.","marker":"[38]"},{"why":"Motivates setting prior probabilities proportional to remnant retention probabilities for hierarchical mergers.","marker":"[16]"},{"why":"Supplies the retention-probability treatment that sets the prior odds among 2G+1G, 2G+2G, and 3G+2G.","marker":"[39]"},{"why":"Establishes the ~0.7 spin clustering expected for recycled merger remnants that the 2G/3G spin prior reflects.","marker":"[10]"},{"why":"Provides the IMRPhenomXO4a waveform whose alternative mass posterior reverses the model-comparison result.","marker":"[46]"}],"fun_headline_variants":["GW231123's odds favor second-gen pair over first-gen by 10^4","Spin prior and waveform decide GW231123's hierarchical origin","Second-gen merger wins for GW231123, but only with chosen prior","GW231123: odds 10^4 for 2G+2G, but waveform flips to 2G+1G","Hierarchical GW231123 likely 2G+2G, unless rival waveform used"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["GW231123's odds favor second-gen pair over first-gen by 10^4","Spin prior and waveform decide GW231123's hierarchical origin","Second-gen merger wins for GW231123, but only with chosen prior","GW231123: odds 10^4 for 2G+2G, but waveform flips to 2G+1G","Hierarchical GW231123 likely 2G+2G, unless rival waveform used"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000865,"raw_usage":{"total_tokens":3602,"prompt_tokens":776,"completion_tokens":2826,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":520,"completion_tokens_details":{"reasoning_tokens":2713}},"tokens_in":520,"tokens_out":2826,"duration_ms":23592,"temperature":1.0,"reasoning_tokens":2713,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T20:49:07.222247+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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).","supporting_citations":[],"review_version":1}