{"id":"93bbb0b8-ebbc-44ef-ab6f-ce3fbbeb6f3b","arxiv_id":"2412.05962","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"An improved multisynchrosqueezing transform is reported to reconstruct simulated supernova gravitational waves out to 317 kpc with the Einstein Telescope, versus 186 kpc for the short-time Fourier transform.","lead":"This paper applies an existing time-frequency analysis method, the improved multisynchrosqueezing transform, to reconstruct simulated gravitational wave signals from core-collapse supernovae in detector noise. It reports that with the Einstein Telescope the method recovers simulated signals at up to 317 kpc, compared to 186 kpc for the standard short-time Fourier transform, but the extraction step is underspecified.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The IMSST-vs-STFT comparison is undefined: by Eq. (14), the full-frequency integral of the IMSST representation is identical to the STFT reconstruction in Eq. (3), so the reported 317 kpc vs 186 kpc difference requires an unstated coefficient-selection rule.","rationale":"The reader's weakest_assumption is the same concern I would raise: Eq. (14) makes IMSST and STFT reconstruction identical under full-frequency integration, so the central comparison depends on an unstated selection step. This is an internal inconsistency, not a disagreement with external consensus, because the relevant equation is in the paper itself. The concern is load-bearing: the only quantitative evidence for IMSST superiority is the 317 kpc versus 186 kpc difference, and that difference cannot be derived from the published algorithm. The proposed test would settle it by checking whether the reconstruction as written collapses to STFT. If the authors disclose a selection rule, the claim might become testable, but as presented it is not. I therefore agree with the reader's REJECT verdict; no adjustment is needed.","tokens_in":15648,"tokens_out":5799,"duration_ms":55456,"concrete_test":"Obtain the authors' reconstruction code and parameters, or implement the Section 3 pipeline directly with waveforms M1, M2, N1, N2, the same whitened ET noise realizations, and the Gaussian window of Eq. (10). Compute match-versus-distance curves for IMSST using Eq. (14) and for STFT using Eq. (3). The equations imply the curves coincide; if they do, the claimed 317 kpc vs 186 kpc separation cannot be produced by the stated method. If the authors provide a coefficient-selection rule, re-run the comparison with that rule and verify whether 317 kpc and 186 kpc are reproduced.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2.2 defines the IMSST reconstruction as Eq. (14): s(τ) = (2πg(0))^{-1}∫ Ts[N](τ,ω)dω. Substituting Eq. (12), Ts[N](τ,η) = ∫ G(τ,ω) δ(η - ω_R^{[N]}(τ,ω)) dω, the η-integral collapses to ∫ G(τ,ω) dω because the reassignment delta integrates to unity. This is exactly the STFT reconstruction in Eq. (3), with the same prefactor and the same window. For identical input and window, the IMSST and STFT waveforms reconstructed by these equations are numerically identical. Therefore Fig. 5's different match-score curves, and the 317 kpc vs 186 kpc maximum distances, cannot arise from the stated method. A difference could only come from an unspecified post-processing step, such as selecting coefficients on a ridge, applying a time-frequency mask, or thresholding before inversion. The paper never states such a rule in Section 2 or Section 3.4, so the central claim is not reproducible and the headline improvement is not supported by the equations given. Secondary inconsistencies (FAPR values in Section 3.4 text vs Fig. 6 caption and Discussion; 4170 vs 4192 dataset count) reinforce that the numerical results lack an auditable trail, but the Eq. (14) identity is the load-bearing defect.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper applies the improved multisynchrosqueezing transform (IMSST) to reconstruct simulated core-collapse supernova gravitational-wave signals in aLIGO and Einstein Telescope noise, using the match score to quantify reconstruction quality and a false-alarm probability of reconstruction (FAPR) to assess whether reconstructed waveforms could arise from noise. The headline claims are that IMSST achieves maximum reconstruction distances of about 37 kpc for aLIGO and 317 kpc for ET at a match threshold of 0.75, and that IMSST outperforms STFT, whose ET limit is reported as 186 kpc. The paper also reports FAPR values for a library of 2096 CCSN waveforms at 10 kpc and 100 kpc, with and without amplitude normalization.","tokens_in":16022,"tokens_out":5219,"duration_ms":46398,"significance":"If the central quantitative claims were supported, the paper would provide evidence that a higher-resolution time-frequency representation can improve waveform extraction from noisy CCSN data. The paper has notable strengths: it uses a broad catalog of magnetorotational and neutrino-driven CCSN waveforms, applies whitening and bandpass preprocessing, defines a concrete match-score criterion, and estimates FAPR from independent noise-only realizations. However, the central comparison between IMSST and STFT is undermined by the paper's own reconstruction equation: the full-frequency integral of the IMSST representation is exactly the STFT reconstruction, so the reported 317 kpc versus 186 kpc difference requires an unstated coefficient-selection rule that never appears in the manuscript. The FAPR values are also internally inconsistent across sections, and the dataset accounting is arithmetically wrong. These are load-bearing defects that make the numerical results unverifiable and the central claim unsupported as written.","major_comments":[{"comment":"The IMSST reconstruction formula in Eq. (14) integrates Ts[N] over all frequencies. Substituting Eq. (12) into Eq. (14) gives (2πg(0))^{-1} ∫∫ G(τ,ω) δ(η-ω_R^[N](τ,ω)) dω dη = (2πg(0))^{-1} ∫ G(τ,ω) dω, which is exactly the STFT reconstruction in Eq. (3) for the same window. Therefore, for identical input data and window, the full-band IMSST and STFT reconstructions are numerically identical, and the 317 kpc versus 186 kpc difference reported in Section 3.4 and Fig. 5 cannot arise from the stated method. The paper does not specify any post-processing selection rule, such as ridge extraction, frequency-band restriction, masking, or thresholding before inversion. Without such a rule the comparison is undefined, and with an unstated rule the result is not reproducible.","section":"Section 2.2, Eqs. (12)-(14)"},{"comment":"The FAPR values for the ET, 100 kpc, unnormalized simulation are inconsistent across the manuscript. Section 3.3 gives 1.3e-1 for IMSST; Section 3.4 text gives 2.1e-2 for IMSST and 1.4e-2 for STFT; the Fig. 6 caption and Section 4 state 1.3e-1 and 5.6e-2 for IMSST and STFT, respectively. Since FAPR is a central quantitative result of the paper, the text must report one auditable set of values; the current disagreement prevents verification of the false-alarm claims.","section":"Sections 3.3 and 3.4 versus Fig. 6 caption and Section 4"},{"comment":"The dataset accounting is inconsistent: 2096 waveforms injected twice gives 4192 simulated datasets, not 4170 as stated. The same 4170 count is then used for the pure-noise datasets and for the ET runs. This arithmetic discrepancy, together with the FAPR inconsistencies above, prevents an auditor from reconstructing the numerical analysis from the text.","section":"Section 3.3, dataset accounting"}],"minor_comments":[{"comment":"The phase model s(t) = A(t)e^{i(φ(t)+φ'(t)(u-t)+0.5φ''(u-t)^2)} uses an undefined variable u and appears to be missing a closing parenthesis around the quadratic term; please clarify the notation and correct the expression.","section":"Eq. (9)"},{"comment":"The expression for G(τ,ω) appears to contain a typographical issue in the exponent, with braces missing around the denominator; the derivation from Eq. (9) should be shown explicitly.","section":"Eq. (11)"},{"comment":"The notation for the reassigned frequency is inconsistent: Eq. (12) uses ω_R^[N] while the surrounding text uses ω̂_R^[N]; please use a single symbol throughout.","section":"Section 2.2"},{"comment":"The figure captions refer to 'FAR' while the text defines and uses 'FAPR'; please standardize the terminology.","section":"Figures 4 and 6 captions"},{"comment":"The Data Availability statement lists only the waveform sources; providing the analysis code and the specific IMSST parameter choices (window width, iteration number, bandpass design) would be necessary for reproducibility, especially given the missing reconstruction-selection rule.","section":"Data Availability"}],"recommendation":"reject","confidential_remarks":"The Eq. (14) issue is not a minor omission: it invalidates the central IMSST-versus-STFT comparison as presented, because the full-band inversions are mathematically identical. The FAPR inconsistencies and the 4170/4192 accounting error reinforce the conclusion that the numerical results lack an auditable trail. This is a load-bearing defect that would require the authors to specify and justify a coefficient-selection rule and re-run the analysis, after which the claims could in principle be reassessed in a new submission."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper's central claim – that IMSST outperforms STFT in reconstructing CCSN waveforms (317 kpc vs 186 kpc for ET) – is not supported by the method as written. The stress-test note is correct: substituting Eq. (12) into Eq. (14) gives exactly the STFT reconstruction formula, because the reassignment delta integrates to unity. So, as stated, the two methods produce identical waveforms. The only way to get different distances is an unstated post-processing step (e.g., selecting coefficients on a ridge or in a frequency band). That step is not described anywhere, so the comparison is not reproducible.\n\nWhat is genuinely new here is the application of IMSST to a broad catalog of simulated CCSN waveforms, with a careful FAPR calculation and a match-score threshold. The paper is also honest that its results do not significantly improve over the authors' earlier EEMD study. The figures are informative, and the use of public waveform catalogs is proper.\n\nThe soft spots are load-bearing. Beyond the Eq. (14) issue, the FAPR values are internally inconsistent: Section 3.4 reports IMSST at 100 kpc as 2.1e-2, while Fig. 6's caption and the Discussion say 1.3e-1. The normalized STFT value also disagrees (1.4e-2 vs 5.6e-2 vs 9.7e-4). The dataset count is off: 2096 waveforms injected twice should give 4192 datasets, not 4170. No code or parameter values (window width, iteration number, frequency limits) are provided, so even the non-IMSST parts are hard to audit.\n\nThis paper is not ready for peer review in its current form. A referee would spend most of the report on the undefined method and the numerical contradictions, and the central result would not survive. If the authors clearly specify the actual coefficient-selection rule and fix the number inconsistencies, the application might be worth revisiting. As it stands, I would not cite it or bring it to a reading group.","headline":"The IMSST-vs-STFT comparison is undefined: Eq. (14) makes the two reconstructions identical, so the headline distances are unsupported.","tokens_in":16520,"tokens_out":3283,"would_cite":false,"duration_ms":29291,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that the improved multisynchrosqueezing transform (IMSST) reconstructs simulated core-collapse supernova gravitational-wave waveforms at a match threshold of 0.75 out to about 317 kpc with the Einstein Telescope and 37…","keywords":["core-collapse supernovae","gravitational wave data analysis","time-frequency analysis","improved multisynchrosqueezing transform","waveform reconstruction","Einstein Telescope","advanced LIGO","match score"],"falsifier":"Recompute the ET match-score curves exactly as described in the method section: if the reconstructed waveform is the full-frequency integral of the IMSST plane from Eq. (14), the curves must coincide with STFT's, because that integral equals $(2\\pi g(0))^{-1}\\int G(\\tau,\\omega)\\,d\\omega$. Any difference between IMSST and STFT therefore depends on a coefficient-selection rule that the paper does not specify; stating that rule and showing that it changes the match scores would settle the claim.","tokens_in":15465,"feed_emoji":"🔭","tokens_out":14444,"duration_ms":120147,"temperature":0.7,"pith_summary":"Core-collapse supernova gravitational waves are too stochastic for matched-filter searches, so this paper asks whether a high-resolution time-frequency transform can pull their waveforms out of noisy detector data directly. Its central claim is that the improved multisynchrosqueezing transform (IMSST) can: in simulated advanced LIGO and Einstein Telescope data, the method recovers injected supernova waveforms with match score at least 0.75 out to about 37 kpc and 317 kpc, respectively, and under the Einstein Telescope simulation it reaches 317 kpc versus 186 kpc for the standard short-time Fourier transform. The paper also reports false-alarm probabilities of reconstruction as low as $6.2 \\times 10^{-3}$ for amplitude-normalized aLIGO data and $1.5 \\times 10^{-2}$ for normalized ET data at that threshold. If those numbers hold, a sharper time-frequency picture would be a practical waveform-extraction tool for supernova searches, not just a visualization aid.","feed_headline":"Time-frequency method recovers supernova waves out to 317 kpc","feed_subtitle":"At match score 0.75, the new time-frequency method reaches 317 kpc with Einstein Telescope, versus 186 kpc for STFT.","key_machinery":"The central object is the IMSST time-frequency representation $T_s^{[N]}(\\tau,\\eta)$, built from the STFT $G(\\tau,\\omega)$ by the iterative synchrosqueezing map $\\hat{\\omega}_R^{[N]}(\\tau,\\omega)=\\mathrm{Round}(\\mathrm{Round}(2\\hat{\\omega}^{[N]}(\\tau,\\omega))/2)$, which reassigns each coefficient to a sharply located frequency. The reconstruction identity is Eq. (14), $s(\\tau)=(2\\pi g(0))^{-1}\\int T_s^{[N]}(\\tau,\\omega)\\,d\\omega$, which carries the argument by turning the time-frequency plane back into a waveform. The quality metric is the match score $\\eta$ of Eq. (16), with threshold 0.75, and the false-alarm probability of reconstruction comes from the noise-only match-score distribution. The sharper time-frequency concentration is what the paper credits for the improved match scores.","core_discovery":"The paper's discovery claim is that IMSST—a time-frequency tool that sharpens the short-time Fourier transform by iteratively reassigning spectral energy onto instantaneous-frequency curves with a rounding operation—can reconstruct simulated CCSN gravitational-wave waveforms from single-detector data. Using a library of magnetorotational and neutrino-driven waveforms spanning $9$–$60\\,M_\\odot$, injected into aLIGO and ET noise and then whitened and bandpass-filtered, the authors measure agreement through the match score and take 0.75 as the success threshold. They find maximum reconstructable distances of about 37 kpc for aLIGO and 317 kpc for ET with IMSST, versus 186 kpc for STFT under the ET simulation. They report false-alarm probabilities at threshold: $2.1\\times10^{-2}$ and $6.2\\times10^{-3}$ for aLIGO at 10 kpc, and $1.3\\times10^{-1}$ and $1.5\\times10^{-2}$ for ET at 100 kpc, before and after amplitude normalization to $5\\times10^{-21}$. The authors conclude that IMSST reconstructs CCSN waveforms more effectively than STFT, that reconstruction quality is driven by signal amplitude rather than explosion mechanism, and that the false-alarm/reconstruction-rate trade-off must be balanced in practice.","pith_inferences":["Because Eq. (14) integrates the whole time-frequency plane and reduces to the STFT reconstruction, the reported IMSST-vs-STFT gap requires an unstated coefficient-selection step (for example, keeping only ridge or band coefficients); making that selection rule explicit would let other groups reproduce the 317 kpc reach.","A natural control experiment would apply the same selection rule to plain STFT coefficients, separating any gain from the sharper representation from gain due to discarding noise-dominated coefficients.","The FAPR framework could be turned into a detection statistic by scanning thresholds and sky positions, giving a per-trial false-alarm rate rather than fixed-location values.","Extending the single-detector reconstruction to a detector network with coincidence checks would likely lower FAPR and give a more realistic estimate of the distances at which CCSN waveforms could actually be recovered."],"forward_implications":["At the 0.75 match threshold, IMSST would give ET a CCSN waveform-reconstruction reach of about 317 kpc, roughly 1.7 times the 186 kpc reach claimed for the same STFT-based reconstruction.","The reported false-alarm probabilities (as low as $6.2\\times10^{-3}$ for normalized aLIGO data and $1.5\\times10^{-2}$ for normalized ET data) imply that, under the paper's noise model, threshold-passing reconstructions are unlikely to be pure-noise artifacts.","Because match scores track signal amplitude rather than the magnetorotational or neutrino-driven mechanism, the method would recover waveforms without distinguishing the explosion mechanism, and match score alone cannot classify CCSN types.","Amplitude normalization to $5\\times10^{-21}$ lowers FAPR and raises the reconstruction event rate for both detectors, indicating that recoverability is governed mainly by detected strain rather than waveform morphology."],"supporting_citations":[{"why":"It defines the IMSST, the time-frequency transform whose coefficients the paper inverts to reconstruct waveforms.","marker":"Yu (2020)"},{"why":"It defines the MSST iteration and the 2-D instantaneous-frequency estimate that IMSST improves on.","marker":"Yu et al. (2018)"},{"why":"It defines the short-time Fourier transform baseline against which IMSST is compared.","marker":"Gabor (1946)"},{"why":"It supplies the magnetorotational CCSN waveforms in the simulation library.","marker":"Dimmelmeier et al. (2008)"},{"why":"It supplies the magnetorotational waveform M2 used as a case study.","marker":"Richers et al. (2017)"},{"why":"It supplies the neutrino-driven waveform N1 used as a case study.","marker":"Powell & Müller (2020)"},{"why":"It supplies the neutrino-driven waveform N2 used as a case study.","marker":"Yakunin et al. (2017b)"},{"why":"It sets the match-score threshold of 0.75 and provides the earlier EEMD reconstruction context.","marker":"Yuan et al. (2024)"}],"fun_headline_variants":["Time-frequency method reaches 317 kpc for supernova gravitational waves","Improved time-frequency method recovers supernova waves at 317 kpc vs STFT's 186","Supernova wave reconstruction: refined method hits 317 kpc","Outperforming STFT: time-frequency method recovers supernova waves to 317 kpc"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the IMSST reconstruction used to produce the match scores is not the full-frequency integral of Eq. (14)—which is mathematically the same as the STFT reconstruction—but includes an additional, unstated step of choosing which time-frequency coefficients to keep; without that selection rule the reported 317 kpc versus 186 kpc comparison is not defined and not reproducible.","fun_headline_variants_meta":{"raw":{"variants":["Time-frequency method reaches 317 kpc for supernova gravitational waves","Improved time-frequency method recovers supernova waves at 317 kpc vs STFT's 186","Supernova wave reconstruction: refined method hits 317 kpc","Outperforming STFT: time-frequency method recovers supernova waves to 317 kpc"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001197,"raw_usage":{"total_tokens":5062,"prompt_tokens":1196,"completion_tokens":3866,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":812,"completion_tokens_details":{"reasoning_tokens":3779}},"tokens_in":812,"tokens_out":3866,"duration_ms":24570,"temperature":1.0,"reasoning_tokens":3779,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T20:09:19.305547+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the ET match-score curves exactly as described in the method section: if the reconstructed waveform is the full-frequency integral of the IMSST plane from Eq. (14), the curves must coincide with STFT's, because that integral equals $(2\\pi g(0))^{-1}\\int G(\\tau,\\omega)\\,d\\omega$. Any difference between IMSST and STFT therefore depends on a coefficient-selection rule that the paper does not specify; stating that rule and showing that it changes the match scores would settle the claim.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It defines the short-time Fourier transform baseline against which IMSST is compared."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It sets the match-score threshold of 0.75 and provides the earlier EEMD reconstruction context."}],"review_version":1}