{"id":"e09b7fc1-5097-466c-b4f3-4176e56544d6","arxiv_id":"2605.16199","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Bayesian analysis finds individual QNM frequencies near avoided crossings hard to resolve even under optimistic conditions, though collective AC waveform signatures may remain detectable if those modes dominate and slower-mode contamination is minimal.","lead":"This paper uses Bayesian inference on three waveform models to test whether avoided crossings between quasinormal modes in black hole ringdowns can be resolved or detected in gravitational wave signals. A smart generalist might read it to understand practical limits on extracting detailed black hole properties from future LIGO/Virgo/KAGRA or next-generation detector data.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"Central claim for identifying AC collective signatures rests on untested assumption that AC modes dominate and slower-mode contamination can be removed in realistic ringdown data.","rationale":"The reader correctly isolated the dominance/contamination proviso as the weakest link directly from the abstract. Because the full text confirms the analysis is performed under controlled injections without reported contamination sweeps, the concern is internal to the argument rather than external consensus. Adjusting to CONDITIONAL reflects that the claim is valid only inside the stated proviso; the concrete test above would falsify or corroborate that proviso without requiring new data.","tokens_in":1671,"tokens_out":359,"duration_ms":27995,"concrete_test":"Re-run the Bayesian inference on the three waveform models after injecting the AC pair plus a 5–20% amplitude slower-damped QNM (with frequency separation and damping time taken from the paper’s Table 1 or equivalent); if the posterior support for the collective AC signature (e.g., phase opposition or amplitude enhancement) drops below 2σ or the model evidence ratio reverses, the dominance assumption does not hold under mild contamination.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The abstract and strongest claim state that collective AC signatures 'may still be identified ... provided that the AC-related modes dominate the observed ringdown signal and contamination from more slowly damped modes is negligible or can be removed.' This condition is load-bearing because the reported difficulty in resolving individual frequencies is already conceded; the positive detectability result therefore collapses if the dominance/contamination premise fails. The three waveform models and Bayesian framework are applied to controlled injections, but no explicit robustness test against realistic contamination amplitudes or removal procedures is described in the available text, leaving the practical applicability of the collective-signature route unsecured.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper examines the detectability of avoided crossings (ACs) among quasinormal modes (QNMs) in black hole ringdown signals. Using a Bayesian framework applied to three waveform models on controlled injections, it finds that resolving the individual (closely spaced) QNM frequencies remains difficult even under optimistic conditions. It concludes that collective waveform signatures associated with ACs may nevertheless be identifiable through complementary descriptions, provided the AC-related modes dominate the observed signal and contamination from more slowly damped modes is negligible or can be removed.","tokens_in":1789,"tokens_out":500,"duration_ms":70865,"significance":"If the central claims hold, the work usefully distinguishes the practical limits of standard black-hole spectroscopy from the potential utility of collective AC signatures. The explicit use of multiple waveform models and forward-modeling inference is a strength that allows assessment of template dependence. The conditional positive result could guide analysis strategies for ringdown data from gravitational-wave detectors, provided the dominance/contamination premise can be validated.","major_comments":[{"comment":"Abstract (final sentence): The claim that collective AC signatures 'may still be identified ... provided that the AC-related modes dominate the observed ringdown signal and contamination from more slowly damped modes is negligible or can be removed' is load-bearing for the positive detectability conclusion. The manuscript applies the three models only to controlled injections; no explicit robustness tests against realistic contamination amplitudes, removal procedures, or varying dominance ratios are described. This leaves the practical applicability of the collective-signature route unsecured.","section":"Abstract"},{"comment":"Bayesian framework description: The abstract and main text report qualitative findings on frequency/amplitude inference but omit specifics on prior choices, sampling algorithms, convergence diagnostics, or quantitative model-comparison metrics (e.g., Bayes factors or evidence values). These omissions prevent independent verification of the reported difficulty in resolving individual QNMs.","section":"Bayesian framework"}],"minor_comments":[{"comment":"Figure captions and legends would benefit from explicit indication of which waveform model corresponds to each curve when comparing the three templates.","section":"Figures"},{"comment":"Notation for the complex QNM frequencies and amplitudes should be introduced once with a clear table or equation reference to avoid ambiguity across sections.","section":"Notation"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their thorough review and constructive feedback on our manuscript. We appreciate the recognition of the strengths of our approach using multiple waveform models. Below, we provide point-by-point responses to the major comments and outline the revisions we intend to make.","responses":[{"response":"We agree that the positive conclusion regarding collective signatures is conditional and that our current analysis relies on controlled injections without explicit tests for contamination. To address this, we will revise the manuscript to include a more detailed discussion in the conclusions section on the implications of contamination and the assumptions required for the collective signatures to be detectable. We will also modify the abstract to better reflect the idealized conditions of our study while maintaining the conditional nature of the claim.","revision_made":"yes","referee_comment":"[Abstract] Abstract (final sentence): The claim that collective AC signatures 'may still be identified ... provided that the AC-related modes dominate the observed ringdown signal and contamination from more slowly damped modes is negligible or can be removed' is load-bearing for the positive detectability conclusion. The manuscript applies the three models only to controlled injections; no explicit robustness tests against realistic contamination amplitudes, removal procedures, or varying dominance ratios are described. This leaves the practical applicability of the collective-signature route unsecured."},{"response":"We thank the referee for pointing this out. Upon review, we realize that while some details are present in the methods section, they are not sufficiently detailed. In the revised manuscript, we will expand Section 2.2 to explicitly describe the prior distributions used for the QNM frequencies and amplitudes, the nested sampling algorithm employed (with specific settings), convergence diagnostics such as the evidence tolerance, and we will include quantitative metrics like Bayes factors in a new table or figure to support the model comparisons and the difficulty in resolving individual modes.","revision_made":"yes","referee_comment":"[Bayesian framework] Bayesian framework description: The abstract and main text report qualitative findings on frequency/amplitude inference but omit specifics on prior choices, sampling algorithms, convergence diagnostics, or quantitative model-comparison metrics (e.g., Bayes factors or evidence values). These omissions prevent independent verification of the reported difficulty in resolving individual QNMs."}],"tokens_in":1344,"tokens_out":476,"duration_ms":56528,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main point is that splitting the two close frequencies in an avoided crossing stays difficult under Bayesian recovery, yet the overall interference pattern from the AC might still be picked up with the right set of templates, provided the relevant modes lead the signal and other modes can be ignored or subtracted. They test this by running inference on three different waveform models and varying the frequency separation plus the template choice, which gives a direct look at when parameters become unrecoverable versus when the collective signature persists. That setup is the concrete step forward here, since prior work on ringdowns has not zeroed in on AC detectability this way with controlled injections and model comparison. The methods look standard and the qualitative trend matches what one would expect from near-degenerate modes interfering. The load-bearing assumption is that AC modes dominate and slower-damped contamination can be removed or is negligible; the paper does not appear to run explicit robustness checks against realistic amplitudes of those extra modes, so the collective-signature route remains conditional rather than demonstrated for typical data. Details on priors, sampling convergence, and quantitative error bars would help verify the strength of the claims, but the overall logic holds without circularity or obvious fitting artifacts. This is useful for anyone doing ringdown spectroscopy or planning GR tests with current and next-gen detectors. Readers focused on the practical limits of QNM extraction will find the dependence on separation and template choice worth seeing. It deserves a serious referee because the question is timely and the modeling is grounded, even if the positive claim needs tighter tests on contamination. I would send it to review with a request to expand the robustness section.","headline":"Individual QNM frequencies stay hard to resolve even in good conditions, but the paper shows collective AC waveform effects could still register if those modes dominate and slower contamination stays out of the way.","tokens_in":2256,"tokens_out":402,"would_cite":false,"duration_ms":60233,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[],"headline":"Bayesian detectability study of avoided crossings in QNM ringdowns; standard GR perturbation analysis with no RS-shaped cost or ladder structure","alignment":"orthogonal","rationale":"The paper performs Bayesian parameter estimation on three waveform models (2DS, 2AC, EP) for nearly-degenerate QNMs near avoided crossings in black-hole ringdowns. Its machinery is conventional GR perturbation theory plus nested sampling; it contains no J-cost functions, golden-ratio ladders, 8-tick periodicity, ratio-symmetric forcing, or parameter-free constant derivations. RS therefore has no opinion on the resolvability thresholds or model-comparison results reported here.","tokens_in":56092,"confidence":"high","tokens_out":151,"duration_ms":28966,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Avoided crossings in black hole quasinormal modes produce interference that may be detectable even when the individual frequencies cannot be resolved.","keywords":["quasinormal modes","avoided crossings","black hole ringdown","gravitational waves","Bayesian inference","waveform models","interference","detectability"],"falsifier":"A measured ringdown waveform in which the avoided-crossing modes are expected to dominate yet no collective interference signature appears after slower modes are subtracted.","tokens_in":2570,"feed_emoji":"🕳️","tokens_out":667,"duration_ms":36387,"temperature":0.7,"pith_summary":"This paper studies avoided crossings where two quasinormal mode frequencies approach each other in black hole ringdown signals. At these points the amplitudes become enhanced and nearly opposite in phase, creating a characteristic interference pattern. The authors test detectability with Bayesian inference on three different waveform models and vary the frequency separation between the modes. They find that separating the close frequencies remains difficult under even optimistic conditions. Collective signatures of the avoided crossing can still be recovered through complementary waveform descriptions when the relevant modes dominate the signal and slower-decaying modes do not contaminate it substantially.","feed_headline":"Avoided crossings leave detectable marks in black hole ringdown waveforms","feed_subtitle":"Bayesian tests find individual frequencies hard to separate but collective interference patterns may still appear when those modes dominate.","key_machinery":"Avoided crossing between two quasinormal modes, in which frequencies approach, amplitudes enhance, and phases become nearly opposite to produce interference in the ringdown waveform.","core_discovery":"Quasinormal modes of black holes can exhibit avoided crossings in which specific frequencies approach each other while their amplitudes are enhanced and acquire nearly opposite phases, leading to characteristic interference. Resolving such closely spaced modes through black hole spectroscopy is observationally challenging. Using Bayesian analysis with three waveform models, the work shows that inferring the separate complex frequencies and amplitudes depends on their separation and on the choice of template. Resolving the individual frequencies is difficult even under optimistic conditions, yet collective waveform signatures associated with avoided crossings may still be identified through a","pith_inferences":["Observers may need waveform templates that encode collective interference rather than isolated mode frequencies when close pairs are present.","Time-domain and frequency-domain analyses could be combined to isolate avoided-crossing effects in real gravitational-wave data.","The same interference logic might apply to other resonant pairs in black-hole perturbation spectra beyond the specific cases studied."],"forward_implications":["Individual quasinormal mode frequencies remain difficult to resolve even under optimistic conditions.","Collective waveform signatures tied to avoided crossings can be recovered with complementary waveform descriptions.","Detection requires that avoided-crossing modes dominate the ringdown and that slower modes contribute negligibly or can be removed.","The choice of waveform template affects how well frequencies and amplitudes are inferred near an avoided crossing."],"fun_headline_variants":["Avoided crossings make QNM frequencies hard to separate in ringdowns","Collective interference from ACs may be detectable in black hole ringdowns","Bayesian inference struggles to resolve close QNMs near avoided crossings","Waveform templates affect detection of avoided crossings in ringdown signals"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The assumption that the avoided-crossing modes dominate the observed ringdown signal and that contamination from more slowly damped modes is negligible or can be removed.","fun_headline_variants_meta":{"raw":{"variants":["Avoided crossings make QNM frequencies hard to separate in ringdowns","Collective interference from ACs may be detectable in black hole ringdowns","Bayesian inference struggles to resolve close QNMs near avoided crossings","Waveform templates affect detection of avoided crossings in ringdown signals"]},"model":"grok-4.3","cost_usd":0.007355,"raw_usage":{"total_tokens":3285,"prompt_tokens":632,"num_sources_used":0,"completion_tokens":73,"cost_in_usd_ticks":73553000,"prompt_tokens_details":{"text_tokens":632,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2580,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":632,"tokens_out":73,"duration_ms":31529,"temperature":1.0,"reasoning_tokens":2580,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-20T17:51:04.302701+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A measured ringdown waveform in which the avoided-crossing modes are expected to dominate yet no collective interference signature appears after slower modes are subtracted.","supporting_citations":[],"review_version":1}