{"id":"794c250b-7e17-4983-9806-502030235938","arxiv_id":"2505.09674","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"An eigen-decomposition-based hybrid basis and summary statistic for 21cm line-intensity mapping captures light-cone evolution effects and yields about 30 percent tighter Fisher-forecast parameter constraints than the power spectrum.","lead":"The paper introduces a new statistical tool for analyzing 21cm observations of the Epoch of Reionization that accounts for the universe's evolution along the line of sight. The new method tightens forecast constraints on astrophysical parameters by about 30 percent compared to the traditional power spectrum.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 30% improvement is a matched-filter result: the hybrid basis is built from fiducial 21cmFAST lightcones (Secs. II.B, III.C) and only eigenvector robustness, not Fisher-gain robustness, is tested; if basis mismatch shrinks the gain, the headline claim weakens.","rationale":"I read the paper as a methodological proposal whose central quantitative claim is the approximately 30% improvement in Fisher-forecast parameter constraints. For that claim to hold in any realistic application, the hybrid basis must remain nearly optimal when it is estimated from imperfect data or from a slightly wrong model. The reader's weakest-assumption statement identifies exactly this: the covariance eigenvectors are computed from only 10 fiducial-parameter realizations and the forecast uses the true fiducial basis, so the improvement is a matched-filter result. I agree with that assessment. The paper is transparent about model dependence in Section V.A and shows qualitative eigenvector stability for one parameter, but it never tests whether the headline Fisher gain survives basis mismatch. This is the most load-bearing concern because it directly controls the practical significance of the central claim; the monopole question is also worth clarifying, but the foreground-avoidance mask probably zeroes the k=0 and k_perp=0 modes, making it less decisive than the matched-filter issue. The mathematical construction is otherwise sound: in the coeval limit the basis reduces to Fourier modes, the hybrid orthogonality is enforced by Gram-Schmidt, and the Fisher treatment is conservative with respect to the omitted covariance term. A single rerun of the forecast with a mismatched basis would settle whether the 30% improvement is robust. Since the reader already recommends conditional acceptance with requests to quantify model dependence, my read does not change the verdict.","tokens_in":34047,"tokens_out":8191,"duration_ms":99744,"concrete_test":"Recompute the Section IV Fisher forecast using a hybrid basis constructed from non-fiducial lightcones, e.g., 21cmFAST simulations with f_esc,10 increased by 10%, and separately from signal-plus-thermal-noise lightcones after the foreground-avoidance mask, while evaluating M and P on the same fiducial and perturbed boxes as in the paper. Compare marginalized 1-sigma errors to the fiducial-basis result. If the average improvement over the two Fourier methods falls from about 30% to below about 10%, the headline claim is matched-filter dependent; if it stays near 30%, the basis-mismatch concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that M(k_perp,i) yields roughly 30% tighter parameter constraints than the 2D power spectrum (Sec. IV). This is demonstrated with a Fisher forecast in which the hybrid basis is fixed to the fiducial 21cmFAST model: Sec. II.B constructs the line-of-sight covariance from 10 fiducial-parameter lightcone realizations, Sec. II.D retains the first 20 converged eigenvectors, and Sec. III.C states that the covariance matrices for the basis use fiducial astrophysical parameters. The derivatives dM/dtheta are then evaluated by projecting fiducial and perturbed lightcones onto this same fiducial basis. That is the definition of a matched filter: it measures performance when the compression basis is known perfectly. In practice the basis must be estimated from noisy, foreground-windowed, possibly RFI-gapped data, or from an approximate model. The paper's robustness test (Sec. V.A, Fig. 8) shows only that the first four eigenvectors are qualitatively similar for a 10% change in one parameter; it does not quantify how the 30% Fisher improvement degrades under basis mismatch. If the gain is concentrated in the eigenvector part, a modest mismatch could substantially reduce it. The proposed iterative strategy (power spectrum first, then basis) is plausible but unvalidated. This is not an internal inconsistency, but it makes the headline improvement an upper bound rather than a demonstrated robust gain.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces a new summary statistic M(k_perp,i) for cosmological fields that are non-stationary along the line of sight. The statistic is based on an eigen-decomposition of the line-of-sight covariance matrix, with the basis taken from 21cmFAST lightcone simulations and completed by Fourier modes in a hybrid construction. The authors compare Fisher-matrix forecasts for seven EoR astrophysical parameters using this statistic against two power-spectrum-based approaches in a HERA-like setting, including thermal noise and a foreground wedge. They report that the new statistic produces approximately 30% tighter constraints than the Fourier approaches, and they discuss the model-dependence of the basis and a possible iterative strategy for practical application.","tokens_in":34301,"tokens_out":4695,"duration_ms":53211,"significance":"If the reported information gain is robust, the paper would provide a useful new data-compression tool for line-intensity mapping surveys that observe large redshift spans, where power-spectrum analyses are known to be suboptimal. The mathematical construction is clear, and the demonstration that the eigenbasis reduces to the Fourier basis in the coeval limit is a helpful validation. The paper is also honest about the model-dependence of the method and proposes a plausible power-spectrum-first workflow for estimating the basis. However, the headline gain is computed in a matched-filter setting, and the robustness test shown does not directly address how the gain degrades under basis mismatch. The credibility of the central claim therefore requires additional quantitative evidence rather than a change in the theoretical framework.","major_comments":[{"comment":"The 30% improvement quoted in Section IV is a matched-filter result. The line-of-sight covariance matrix used to build the basis is computed from fiducial-parameter 21cmFAST lightcones (Section II.B), and the Fisher derivatives dM/dtheta are evaluated by projecting fiducial and perturbed lightcones onto this same fiducial basis (Section III.C). This measures how well a basis tuned to the true model performs, not how well a basis estimated from data or from a slightly misspecified model performs. The robustness test in Section V.A (Figure 8) only shows that the first four eigenvectors are qualitatively similar under a 10% change in f_esc,10; it does not quantify how the Fisher gain changes under basis mismatch. I recommend adding a test in which the Fisher matrix for M is recomputed using a basis constructed from perturbed parameters, from a different realization subset, or from noise-degraded data, and reporting the gain relative to the power spectrum as a function of the model offset.","section":"Secs. II.B, II.D, III.C, IV"},{"comment":"The comparison between M(k_perp,i) and P(k_perp,k_parallel) may be unfair because M includes modes that the power spectrum comparison excludes. In the coeval limit, Section II.C states that M is identical to the 2D power spectrum with the index i corresponding to a specific k_z mode; consequently, the i=1 eigenvector corresponds to the k_z=0 constant/global mode, which standard power-spectrum analyses remove. The paper does not specify whether the 'Full Lightcone 2D Power Spectrum' excludes k_parallel=0, nor how the Gram-Schmidt construction affects the low-index modes. If a substantial part of the gain comes from the first one or two eigenmodes, the improvement could reflect the re-inclusion of the monopole or large-scale mean rather than lightcone-induced correlations. Please quantify the Fisher information contributed by each eigenmode and rerun the comparison with i=1 (and, if relevant, i=2) removed, or include k_parallel=0 in the power-spectrum comparison in a controlled way.","section":"Secs. II.C, II.D, IV"},{"comment":"The claim that the first 20 eigenvectors have converged is not supported by a quantitative diagnostic. The covariance matrix is computed from 10 realizations of a 250x250x1690 Mpc box, which gives many lines of sight, but no eigenspectrum gap, no split-sample comparison, and no realization-to-realization scatter of the eigenvectors is shown. Because the Fisher gain depends on the fidelity of these modes, I ask for a convergence test, such as a scree plot with error bars from jackknifed realizations or a split-sample comparison of the resulting Fisher matrix. Without such a diagnostic, the retained-mode choice remains an ad hoc element of the central forecast.","section":"Sec. II.D"}],"minor_comments":[{"comment":"The Introduction ends with 'We summarize our conclusions in Section IV', but the conclusions are presented in Section VI; please correct the cross-reference.","section":"Sec. I"},{"comment":"There are several typos: 'the the Hydrogen Epoch of Reionization Array', 'the the Low-Frequency Array', and repeated words around Eq. (12) ('and andu'); please proofread.","section":"Sec. I"},{"comment":"In the paragraph describing the powerbox test, 'computationally less expansive' should be 'computationally less expensive'.","section":"Sec. II.B"},{"comment":"The sentence beginning 'with Npixels or Nobserved frequencies along the' is incomplete and should be finished or rewritten.","section":"Sec. II.C"},{"comment":"The caption appears inconsistent with the text: it says M2 uses 'unperturbed Fourier modes', while the text says M2 corresponds to the case where modulated amplitude vectors are perturbed; please clarify which basis is modified in each panel.","section":"Fig. 4"},{"comment":"In Eq. (13), the quantities B and t are used but not explicitly defined in the text; please define the bandwidth and integration time before use.","section":"Sec. III.B.2"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and the basic construction is sound, but the central quantitative claim is currently a matched-filter upper bound. I would be willing to accept after the authors add a basis-mismatch robustness test and address the fairness of the comparison with the power spectrum. The paper should not be rejected, as the proposed statistic is a reasonable and potentially useful contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a genuine methodological contribution. Blamart and Liu diagonalize the line-of-sight covariance from 21cmFAST lightcones, keep the 20 converged eigenvectors, Gram-Schmidt them against Fourier modes, and define a new quadratic summary statistic M(k_perp,i). The estimator is designed to capture exactly the Fourier-mode correlations that the light-cone effect creates and that the power spectrum ignores. The mathematical construction is clean, and the coeval-limit check — where the eigenbasis reduces to the Fourier basis — is a good validation. The hybrid basis (converged eigenvectors plus Fourier modes) is also a sensible practical compromise between completeness and numerical convergence.\n\nThe forecast pipeline is more realistic than most: HERA baselines, foreground-wedge avoidance, thermal noise from 21cmSENSE, and a comparison against both full-box and sliced power spectra. The authors are also transparent in Section V.A that the basis is model-dependent, and they sketch a sensible iterative strategy for real data.\n\nThe soft spot is the headline claim itself. The 30% improvement is a matched-filter result: the basis is built from fiducial-parameter simulations, and the Fisher derivatives are obtained by projecting perturbed lightcones onto that same fiducial basis. Their robustness test (Figure 8) shows only that the first few eigenvectors are qualitatively similar under a 10% change in f_esc,10. It does not quantify how the 30% Fisher gain degrades under basis mismatch. Since the gain comes from reduced off-diagonal Fisher elements, and the eigenvector part is exactly where mismatch would bite, the claim should be read as an upper bound until that test is done.\n\nThere is also a possible unfair comparison: M(k_perp,i) appears to retain the global-mean (monopole-like) mode — the first eigenvector resembles the global 21cm signal as a function of redshift — whereas the power spectrum typically excludes the monopole. If so, part of the gain is just the global signal, which is physically interesting but not a like-for-like comparison with P(k). Minor points: the Fisher matrix uses only mean derivatives, not variance derivatives (acknowledged in a footnote), and no code is released for the basis construction.\n\nWho is this for: 21cm EoR analysts and anyone building summary statistics for line-intensity mapping. It deserves a serious referee. I would send it out, asking for three things: clarify the monopole treatment, run an explicit basis-mismatch test (build the basis at slightly wrong parameters and recompute the Fisher gain), and release the code. Conditional acceptance after that.","headline":"A clean new eigenbasis summary statistic for light-cone 21cm data; the 30% Fisher gain is real but currently a matched-filter upper bound, not a demonstrated robust improvement.","tokens_in":34872,"tokens_out":2705,"would_cite":false,"duration_ms":31000,"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 claims that a new hybrid eigenbasis summary statistic beats the power spectrum for 21 cm light cones, yielding about 30 percent tighter constraints on seven reionization parameters in an interferometer forecast.","keywords":["21 cm cosmology","light cone effect","non-stationary fields","power spectrum","line intensity mapping","Epoch of Reionization","eigenbasis","Fisher forecast"],"falsifier":"Repeat the Fisher comparison with the hybrid basis recomputed from light-cone realizations whose astrophysical parameters are shifted by more than ten percent from the fiducial values, or from a single noise-dominated realization; if the roughly 30 percent tightening over the Fourier power spectrum shrinks below the sampling uncertainty or reverses, the reported advantage is a matched-filter artifact rather than a robust property.","tokens_in":33778,"feed_emoji":"📡","tokens_out":10267,"duration_ms":92703,"temperature":0.7,"pith_summary":"This paper argues that the power spectrum stops being the right summary statistic once a survey's line of sight spans a large chunk of cosmic history, because the light cone breaks translational invariance and creates correlations between Fourier modes. It introduces a new statistic, $M(k_\\perp,i)$, built from an eigen-decomposition of the line-of-sight covariance, completed with Fourier modes to keep the basis numerically stable. In a Fisher forecast for a 320-antenna interferometer observing the 21 cm signal from the Epoch of Reionization, the statistic tightens constraints on seven astrophysical parameters by roughly 30 percent compared with two standard Fourier power-spectrum analyses. If the claim holds, future reionization surveys could extract noticeably more information from the same data at essentially no extra computational cost.","feed_headline":"New statistic beats power spectrum by ~30% in 21 cm forecasts","feed_subtitle":"It recovers mode correlations Fourier power spectra discard, tightening reionization parameter forecasts.","key_machinery":"The object that carries the argument is the line-of-sight covariance matrix, estimated by averaging products of brightness-temperature fluctuations over many lines of sight in a long light-cone volume. Diagonalizing it yields eigenvectors that look like Fourier modes whose amplitudes are modulated with redshift; the first of these resembles the sky-averaged 21 cm signal, and the plotted modes all cross zero near the absorption-to-emission transition. Because only the highest-eigenvalue eigenvectors converge with a finite number of sight lines, the paper uses a hybrid basis: the first 20 eigenvectors plus Fourier modes made exactly orthogonal through Gram-Schmidt. The summary statistic $M(k_\\perp,i)$ is then the binned squared expansion coefficient of the field on this hybrid basis, playing the role that $P(k_\\perp,k_\\parallel)$ plays in the stationary case.","core_discovery":"The central claim is that for a 21 cm light cone spanning redshifts 5 to 10, the Fourier basis no longer diagonalizes the line-of-sight covariance, and the lost information lives in correlations between different line-of-sight Fourier modes. The paper constructs the basis that does diagonalize that covariance, keeps the first 20 converged eigenvectors, orthogonalizes the remaining Fourier modes against them with Gram-Schmidt, and defines the quadratic statistic $M(k_\\perp,i) \\equiv (1/N_{\\rm LS}V)\\sum_{k_\\perp}|\\alpha_i(k_\\perp)|^2$. Forecasts with a 320-antenna interferometer, foreground avoidance, and thermal noise show roughly 30 percent tighter constraints on seven EoR astrophysical parameters than either the full light-cone two-dimensional power spectrum or a sliced light-cone power spectrum, with the gain coming mainly from reduced parameter degeneracies. In the coeval limit without a light cone, the eigen-decomposition returns the ordinary Fourier basis, so the new statistic contains the power spectrum as a special case.","pith_inferences":["If the basis must be estimated from real, noise-dominated data rather than from clean fiducial simulations, the reported 30 percent gain is likely to shrink; the paper's matched-filter forecast uses the true fiducial basis.","The same eigen-decomposition logic should transfer to other line-intensity mapping lines, such as CO or [CII], and to Cosmic Dawn or Dark Ages surveys, where the light-cone effect is even more pronounced relative to the comoving volume.","Because the first eigenvector resembles the redshift-dependent sky-averaged 21 cm signal, one could try to model the modulating envelope analytically from the global brightness-temperature history, removing the need for simulation-based basis estimation.","A natural stress test is to replace the Fisher mean-only forecast with a full likelihood or simulation-based inference that includes the variance term, which the paper itself notes can only add information; the comparison between $M(k_\\perp,i)$ and the power spectrum could shift."],"forward_implications":["For a 21 cm light cone spanning $z=5$ to $z=10$, the new summary statistic $M(k_\\perp,i)$ yields parameter constraints roughly 30 percent tighter than the full light-cone two-dimensional power spectrum and the slicing approach.","The improvement comes primarily from reduced degeneracies between the seven astrophysical parameters, visible as smaller off-diagonal Fisher matrix elements, rather than from larger diagonal sensitivities.","In the absence of the light cone, using coeval boxes, the eigen-decomposition recovers the ordinary Fourier basis, so $M(k_\\perp,i)$ reduces to the two-dimensional power spectrum $P(k_\\perp,k_\\parallel)$.","The hybrid construction, keeping the first 20 eigenvectors and completing with Gram-Schmidt-orthogonalized Fourier modes, avoids the slow convergence of high-order eigenvectors while staying near-optimal.","Because the basis is insensitive to at least a 10 percent change in $f_{\\rm esc,10}$, a two-step analysis can use power-spectrum-derived parameter estimates to build the basis and then apply $M(k_\\perp,i)$ for improved constraints."],"supporting_citations":[{"why":"Supplies the light-cone simulations of the 21 cm signal used to estimate the line-of-sight covariance.","marker":"[73]"},{"why":"Supplies the galaxy parametrization and fiducial values for the seven EoR astrophysical parameters.","marker":"[74]"},{"why":"Produces coeval Gaussian fields used to verify that the eigenbasis reduces to the Fourier basis without the light cone.","marker":"[77]"},{"why":"Sets the delay-spectrum mapping between frequency and $k_\\parallel$ used for the instrumental filter.","marker":"[78]"},{"why":"Defines the Epoch of Reionization window used to excise foreground-contaminated modes.","marker":"[79]"},{"why":"Frames why light-cone-induced Fourier-mode correlations are lost in power-spectrum compression.","marker":"[60]"},{"why":"Provides the thermal-noise power-spectrum calculation used to generate noise realizations.","marker":"[95]"},{"why":"Supplies the updated sensitivity calculator used for the uv-eta noise cells.","marker":"[105]"},{"why":"Sets the cosmological parameters used in the simulations.","marker":"[76]"}],"fun_headline_variants":["Eigen-basis beats power spectrum by 30% in 21 cm forecasts","New statistic captures light-cone effects, tightens 21 cm params","Beyond power spectrum: eigen-basis improves 21 cm constraints","Mode correlations give 30% tighter reionization forecasts","Non-Fourier basis recovers lost info in 21 cm light cones"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the line-of-sight covariance matrix estimated from ten fiducial simulation realizations produces eigenvectors that are converged and stable enough that the hybrid basis built from the first twenty of them stays near-optimal for slightly different models and for real data.","fun_headline_variants_meta":{"raw":{"variants":["Eigen-basis beats power spectrum by 30% in 21 cm forecasts","New statistic captures light-cone effects, tightens 21 cm params","Beyond power spectrum: eigen-basis improves 21 cm constraints","Mode correlations give 30% tighter reionization forecasts","Non-Fourier basis recovers lost info in 21 cm light cones"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000777,"raw_usage":{"total_tokens":3443,"prompt_tokens":957,"completion_tokens":2486,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":573,"completion_tokens_details":{"reasoning_tokens":2392}},"tokens_in":573,"tokens_out":2486,"duration_ms":15668,"temperature":1.0,"reasoning_tokens":2392,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:27:02.506573+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the Fisher comparison with the hybrid basis recomputed from light-cone realizations whose astrophysical parameters are shifted by more than ten percent from the fiducial values, or from a single noise-dominated realization; if the roughly 30 percent tightening over the Fourier power spectrum shrinks below the sampling uncertainty or reverses, the reported advantage is a matched-filter artifact rather than a robust property.","supporting_citations":[{"cited_title":"Prelogovi´ c and A","cited_arxiv_id":null,"evidence_quote":"Supplies the light-cone simulations of the 21 cm signal used to estimate the line-of-sight covariance."},{"cited_title":"Murray, B","cited_arxiv_id":null,"evidence_quote":"Produces coeval Gaussian fields used to verify that the eigenbasis reduces to the Fourier basis without the light cone."},{"cited_title":"Collaboration, N","cited_arxiv_id":null,"evidence_quote":"Sets the delay-spectrum mapping between frequency and $k_\\parallel$ used for the instrumental filter."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the Epoch of Reionization window used to excise foreground-contaminated modes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Sets the cosmological parameters used in the simulations."}],"review_version":1}