{"id":"bf4ee4c0-c4ec-4354-95d1-6b883662e4d2","arxiv_id":"2512.24730","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"A multi-detector phase-marginalized echo search finds no statistically significant long-lived quasinormal-mode echoes in GW150914, GW231226, and GW250114, and sets 90% upper limits on their network SNR and amplitude.","lead":"This paper applies a model-agnostic search method for long-lived gravitational wave echoes to three binary black hole merger events, including the recent high-signal GW250114, and finds no statistically significant echo evidence. It then converts the null results into 90% upper limits on echo strength, claiming the first model-independent constraints on late-time echo QNMs from LVK data.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Echo-search sensitivity and upper limits inherit the UniEw phase ansatz: the coherent-likelihood gain depends on the Eq. (5) phase model, which is only tested against a constant-reflectivity injection, not against frequency-dependent reflectivity.","rationale":"I considered trial-factor corrections and upper-limit calibration as alternative concerns; they are real but secondary because all observed p-values are far from significant and the limits are Bayesian posterior quantiles rather than calibrated frequentist intervals. The strongest version of the paper's claim is that its constraints are model-agnostic, and that claim rests on the phase structure of UniEw. The Sec. IV injection does use Eq. (2) rather than literally the UniEw template, so the reader's phrasing slightly overstates the self-referentiality; nevertheless, the substantive concern is the same: only a constant-reflectivity, single-mode-dominated waveform has been shown recoverable. A frequency-dependent reflectivity injection directly tests whether the coherent phase combination survives realistic model variation. Since this is a scoping/robustness gap rather than a demonstrated error in the null result, I keep the reader's CONDITIONAL verdict unchanged.","tokens_in":25983,"tokens_out":5954,"duration_ms":67453,"concrete_test":"Run an injection campaign using full Eq. (2) waveforms with frequency-dependent wall reflectivity Rwall(f), e.g., a mild linear phase ramp or a 10% amplitude variation across the band, and separately with overlapping two-mode echoes, injected at network SNR ~16 into the same 150 O1 noise realizations used in Sec. IV. Recompute the new-likelihood logB distribution and the recovered SNR, Delta f, and tau. If the median logB drops below the Gaussian-noise detection threshold used in Sec. IV, or if the recovered SNR is biased by more than 20%, the phase ansatz is too restrictive and the reported upper limits should be re-derived under a broader template family.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is not the likelihood derivation but the scope of the UniEw template. The new likelihood's sensitivity comes from coherently summing frequency bins whose phases are assumed to follow arg[(1-e^{-T/tau} e^{i2pi(f-f_n)T}) / (i2pi(f-f_n)+1/tau)] (Eq. 5), with the remaining delta_n + 2pi f t_d treated as a per-mode constant. The UniEw template (Eq. 16) encodes exactly this phase structure. If a real echo has frequency-dependent reflectivity of the inner wall, overlapping modes, or different excitation phases, this phase model is wrong and the coherent sum can partially cancel, reducing logB and biasing amplitude estimates. The paper's validation injects one benchmark waveform from Eq. (2) with constant Rwall=0.99 and h_RD excitation (Sec. IV), so the test covers only a single, unusually phase-clean case. The null results for GW150914, GW231226, and GW250114, and especially the quoted SNR90% and A90% limits, therefore inherit this untested model assumption; calling them 'model-independent' (Secs. V-VI) is stronger than the evidence supports. The paper itself labels UniEw a 'simplified model' and a 'leading-order description' (Secs. II-III), so the missing piece is an explicit model-mismatch robustness study.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper extends the phase-marginalized likelihood of Ref. [70] to a two-detector network, coherently combining frequency bins within each QNM while marginalizing over a per-mode constant phase. It uses the simplified UniEw template (Eq. 16) and a Bayesian search pipeline with an iterative notching procedure, validates it on O1 background with 150 time-slide realizations and a single constant-reflectivity injection, and then applies it to GW150914, GW231226, and GW250114. No significant evidence for echoes is found; 90% upper limits are set on network SNR and average initial amplitude (e.g., SNR90%≈4.8 and A90%≈1.3e-24 for GW231226 at T=145 s with the new likelihood). The likelihood derivation (Eqs. 6-10) is internally consistent and correctly reduces to the old likelihood in the low-resolution limit.","tokens_in":26254,"tokens_out":6272,"duration_ms":70624,"significance":"If the claims are fully supported, this is a useful contribution: it provides an efficient coherent search statistic, demonstrates robustness of the notched pipeline on O1 data, and gives concrete null constraints on long-lived QNM amplitudes for a recently detected O4 event. The paper ships analysis code, summary posterior data, and uses public LVK data, which is a strength. However, the significance is reduced by the gap between the title/abstract's 'model-independent' framing and the actual use of a simplified UniEw template. The reported upper limits are conditional on the phase ansatz of Eq. (5), and the validation exercises only one phase-clean benchmark signal. The central method is sound, but the scope of the claims needs tightening and the robustness to model mismatch needs to be demonstrated.","major_comments":[{"comment":"The 'model-independent' claim is stronger than the evidence supports. The likelihood's coherent gain and the reported upper limits (Fig. 7, Table IV) depend on the phase model of Eq. (5), which is encoded in the UniEw template (Eq. 16). The only injection test (Sec. IV) uses a constant reflectivity Rwall=0.99 and a ringdown excitation, i.e., precisely the phase-clean case. The paper itself calls UniEw a 'simplified model' and 'leading-order description'. A model-mismatch robustness study is needed: inject waveforms with frequency-dependent reflectivity, overlapping modes, or different excitation phases, and quantify detection efficiency and bias in the inferred SNR/amplitude. Alternatively, the abstract and Secs. V-VI should explicitly state that the constraints apply only within the UniEw template family.","section":"Secs. II-III, V-VI; Eqs. (5), (16); Fig. 7"},{"comment":"The marginalization treats δ'_n = δ_n + 2π f t_d as constant across all bins of a mode. But using t_d≈1/Δf and the mode cutoff f_cut ≤ Δf/2, the phase variation 2π f_cut t_d can be O(π). Thus the constant-phase assumption is not automatically valid. For signals whose phase retains the second term of Eq. (5), the coherent sum could partially cancel even when the amplitude model is correct. The single injection does not probe this regime. The authors should either derive and verify a condition such as 2π f_cut t_d << 1 for the searched parameter space, or extend the phase treatment.","section":"Sec. II, Eqs. (3), (5), (7)"},{"comment":"The upper-limit calibration is based on a loud injection (network SNR≈16, logB≈40 at T=49 s). The quoted 90% limits are around SNR≈5, but there is no injection-recovery study at near-threshold amplitudes. Without demonstrating that the posterior-based upper limits have correct coverage for weak signals, the strength of the constraints is not fully established. A small injection campaign at SNR values bracketing the claimed limits would address this.","section":"Secs. IV-V; Fig. 7; Table II"}],"minor_comments":[{"comment":"The text says the strain-data preparation follows the procedure 'outlined in Sec. VI'; this should be Sec. III (pipeline description).","section":"Sec. V.A"},{"comment":"The title uses 'Model-independent' while the abstract uses 'model-agnostic' and the body repeatedly describes UniEw as simplified/leading-order. Please harmonize the terminology and qualify the claims consistently.","section":"Title and Abstract"},{"comment":"The admitted notation typo conflating A and A' should be corrected in the main text rather than only explained in a footnote.","section":"Footnote 3 and Eq. (16)"},{"comment":"The broad quasi-periodic artifact seen for GW150914 at 114 s is said to require 'further investigation'. This is fine, but it would be useful to state explicitly in Sec. V.A that unresolved artifacts are included in the background distribution and therefore do not bias the p-values.","section":"Appendix A / Fig. 9"}],"recommendation":"major_revision","confidential_remarks":"The paper's core derivation and pipeline work are solid, and the availability of code/data is commendable. The main editorial decision hinges on the mismatch between the 'model-independent' framing and the template-dependent nature of the search. I would be willing to reconsider after a model-mismatch robustness study and revised language. The phase-constancy point in Sec. II, Eq. (7) should also be addressed quantitatively; if the effect turns out to be negligible for the actual priors, a short demonstration would suffice."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a competent, incremental data-analysis paper from a group that has been building this echo-comb search program for several years. The new piece is real: a multi-detector extension of the phase-marginalized likelihood from Ref. [70], which coherently combines frequency bins within each QNM across the Hanford-Livingston network. The derivation (Eqs. 6–10) is clean, the reduction to the old per-bin likelihood in the low-resolution limit is correct, and the validation on O1 background with 150 time-slide realizations is genuine evidence that the pipeline handles real noise. Applying the method to GW250114 is also new, and the null result for all three events is consistent with the presented background distributions. Credit where earned: the code and data are on GitHub, the notching procedure is clearly described, and the paper is honest about many of its own limitations—UniEw is repeatedly called a 'simplified model' and a 'leading-order description.'\n\nThe soft spots are real but not fatal. The main one is the self-referential template validation: the injection waveform is generated from the same UniEw model that the search implements, so the sensitivity validation only tests one phase-clean, constant-reflectivity case. The quoted upper limits therefore inherit the phase ansatz of Eq. (5). Calling these 'model-independent constraints' in the abstract and conclusions is stronger than the evidence supports—'template-independent' would be more accurate. The stress-test note is right about this, and it is not a minor quibble: the whole gain of the new likelihood comes from trusting that phase structure.\n\nThere are also smaller statistical issues that should be fixed before publication. The reported p-values are single-trial; with five events and multiple durations, the smallest p-value (~0.18) is not corrected for the look-elsewhere effect. The GW250114 background uses only 150 realizations, mixing pre- and post-event segments. The 90% upper limits are not calibrated by injection coverage studies, so it is hard to know whether they are over- or under-covering. And the mysterious broad quasi-periodic artifact in the old-likelihood GW150914 114 s case is left unexplained; the paper notes it, but a reader cannot tell how much it affects the null result. None of this obviously breaks the central null result—the Bayes factors are all unremarkable—but it does mean the upper-limit numbers should be treated as preliminary.\n\nWho is this for? People working on echo searches and UCO phenomenology, especially those who want a direct comparison with prior comb searches. It deserves a serious referee; the methodology is sound enough to warrant peer review, and the flaws are addressable in revision. I would accept it with major comments on calibration and trial factors, not desk-reject it.","headline":"Solid incremental echo-search paper with a clean null result, but the 'model-independent' claim is stronger than the UniEw template validation supports.","tokens_in":26923,"tokens_out":1330,"would_cite":true,"duration_ms":17397,"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 presents a model-agnostic search for long-lived quasinormal modes behind gravitational wave echoes, applies it to three high-SNR black hole mergers, and finds no statistically significant evidence of postmerger echoes, instead set","keywords":["gravitational wave echoes","quasinormal modes","ultracompact objects","model-independent search","phase-marginalized likelihood","LIGO-Virgo-KAGRA","Bayesian upper limits","GW150914"],"falsifier":"Inject a numerically simulated echo waveform from a spinning ultracompact object with frequency-dependent reflectivity—so that the slow phase term δn + 2πftd is not actually slow—into real detector noise, run the pipeline, and check whether the injection is recovered with the claimed SNR; failure would show the search is blind to non-UniEw signals. Alternatively, a future detection of a comb-like line with cross-detector coherence and a matching phase pattern would falsify the null result.","tokens_in":25705,"feed_emoji":"🕳️","tokens_out":6065,"duration_ms":62480,"temperature":0.7,"pith_summary":"This paper aims to establish a robust, model-agnostic way to search for gravitational wave echoes—repeating wavelets that would follow a black hole ringdown if the remnant has a reflective surface just outside the would-be horizon. The key move is a generalized phase-marginalized likelihood that coherently combines frequency bins belonging to the same quasinormal mode across a network of detectors, preserving partial phase information that earlier amplitude-only searches discarded. The authors validate the pipeline by injecting a benchmark echo waveform into real O1 noise and demonstrating reliable recovery. Applied to GW150914, GW231226, and GW250114, the search finds no statistically significant evidence for postmerger echoes and derives 90% upper limits on the network SNR and the average strain amplitude of long-lived quasinormal modes. A sympathetic reader would care because this turns an uncertain theoretical signal into a concrete, falsifiable search, yielding the first model-independent constraints on late-time echoes.","feed_headline":"New search finds no echoes in three black hole mergers","feed_subtitle":"A phase-coherent comb search sets the tightest 90% upper limits yet on postmerger echo amplitudes.","key_machinery":"The carrying mechanism is the generalized phase-marginalized likelihood (Eq. 10): for each quasinormal mode n, the data from all detectors are combined into a single complex frequency-domain series, and the likelihood marginalizes over one constant phase per mode, yielding an I0 Bessel function of the absolute value of the coherent overlap between data and the search template, minus a network-optimal-SNR penalty. The search template is the 'UniEw' model, a uniform comb of equally spaced Lorentzian lines with common spacing Δf and damping time τ, which approximates the long-lived QNM spectrum without committing to a specific ultracompact-object microstructure. This reduces the problem to seve","core_discovery":"The paper's central claim is that the late-time echo signal, when the interior reflection is strong, can be captured by a simple uniform comb of equally spaced, long-lived quasinormal modes with a Lorentzian amplitude profile, and that a phase-marginalized likelihood which coherently combines all frequency bins and all detectors for each mode is substantially more sensitive than previous per-bin phase-marginalized approaches. The new likelihood (Eq. 10) marginalizes over a single constant phase per mode, producing a zeroth-order Bessel function of the complex matched-filter statistic, and it is shown to suppress instrumental line contamination, improve detection significance at long duration","pith_inferences":["Extension: the same phase-coherent likelihood formalism does not depend on echo-specific physics and could be applied to other long-lived narrow-band gravitational-wave sources, such as boson clouds around spinning black holes.","Extension: the template's neglect of the slowly varying phase term δn + 2πftd is the main risk; if a real UCO's phase evolution is not dominated by the Lorentzian term—due to overlapping modes or frequency-dependent reflectivity—the search could systematically miss the signal, so the reported upper limits should be read as limits on UniEw-like signals.","Extension: a testable prediction is that the strongest constraints should come from events with the lowest noise floor and longest usable postmerger stretch; applying the pipeline to GW250114 with longer T or to future O5 events should push SNR90% below 4.","Extension: the per-event upper limits could be combined hierarchically across the full LVK catalog to produce the first model-independent population bound on near-horizon reflectivity of compact remnants."],"forward_implications":["If a merger remnant has a reflective surface close to the horizon, its late-time signal should appear as a comb of long-lived QNMs; this search provides the first model-agnostic probe of that regime.","The new likelihood coherently combines frequency bins and detectors, so its detection significance and the stability of its upper limits improve with observation duration, whereas the old per-bin likelihood degrades.","The 90% upper limits, e.g., SNR90% ≈ 4.8 and A90% ≈ 1.3 × 10^-24 for GW231226, imply that any echo signal in these events must have an average strain amplitude below roughly 10^-24.","Most instrumental lines are rejected by the phase-coherent combination, but a few transient, single-detector line features survive and are identified as non-astrophysical, illustrating the search's sensitivity to signal-like structures.","The pipeline is applicable to future high-ringdown-SNR events and longer observation durations, where the phase-coherent gain is largest and the constraints will tighten."],"fun_headline_variants":["No echoes in three black hole mergers, tightest limits yet","Model-agnostic search finds no gravitational wave echoes","New search tightens limits on black hole echoes","No postmerger echoes found in LVK data"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The entire search rests on the assumption that a real echo signal's phase around each mode is dominated by the Lorentzian line-shape term, so the slowly varying phase can be safely marginalized; if a physical waveform's phase evolves differently, the template will not match it and the null result would not exclude it.","fun_headline_variants_meta":{"raw":{"variants":["No echoes in three black hole mergers, tightest limits yet","Model-agnostic search finds no gravitational wave echoes","New search tightens limits on black hole echoes","No postmerger echoes found in LVK data"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000549,"raw_usage":{"total_tokens":2467,"prompt_tokens":761,"completion_tokens":1706,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":505,"completion_tokens_details":{"reasoning_tokens":1642}},"tokens_in":505,"tokens_out":1706,"duration_ms":11742,"temperature":1.0,"reasoning_tokens":1642,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T13:14:47.283739+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Inject a numerically simulated echo waveform from a spinning ultracompact object with frequency-dependent reflectivity—so that the slow phase term δn + 2πftd is not actually slow—into real detector noise, run the pipeline, and check whether the injection is recovered with the claimed SNR; failure would show the search is blind to non-UniEw signals. Alternatively, a future detection of a comb-like line with cross-detector coherence and a matching phase pattern would falsify the null result.","supporting_citations":[],"review_version":1}