{"id":"bb259ca8-3c13-4151-9a4a-4c4dec49d975","arxiv_id":"2506.11188","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":11,"one_line_summary":"Forecasts show that cross-correlating kSZ temperature-squared maps with galaxy-reconstructed velocity-squared maps can jointly constrain hydrogen and helium reionization, making helium measurable with CMB-HD and MegaMapper.","lead":"Future microwave surveys and galaxy maps could together reveal two separate eras when the universe's hydrogen and helium became ionized. This paper proposes a way to combine CMB small-scale power maps with galaxy velocity measurements to expose the faint helium era, which is tied to the first quasars.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The ~1-sigma He reionization constraints in Fig. 10 rely on the idealized galaxy-velocity reconstruction of Eqs. (39)-(43); realistic scale-dependent transfer functions and noise from Refs. [91,92] are not modeled and can suppress the signal below detectability.","rationale":"The paper is a well-specified forecast; the mathematical construction of the K-eta cross-correlation is coherent and extends Smith & Ferraro. I agree with the reader's CONDITIONAL verdict. The central claim—that CMB-HD x MegaMapper can jointly characterize H and He reionization—is conditional on the reconstructed \\eta field being an essentially unbiased tracer of the true \\eta, aside from a single amplitude b_vg. Section III B lists the known degradation sources (photo-z, RSD, Fingers-of-God, masks) but explicitly leaves modeling to future work. For the CMB-HD x MegaMapper baseline, photo-z is less relevant because MegaMapper is spectroscopic, but the scale-dependent transfer function of the velocity reconstruction remains. Refs. [91,92] quantify similar effects for LSST-like samples; a comparable suppression is expected for MegaMapper. The He reionization forecasts in Fig. 10 sit near the boundary (fractional error ~1), so a modest suppression of C^{K\\eta} or an increase in N_{\\eta\\eta} can erase the detection. The concrete test above would settle this. Therefore the verdict should remain CONDITIONAL: the paper's methodology is sound and publishable, but the headline He claim should be framed as an optimistic upper-bound forecast until realistic velocity-reconstruction noise is incorporated.","tokens_in":43329,"tokens_out":11702,"duration_ms":134386,"concrete_test":"Apply the velocity-reconstruction pipeline of Hadzhiyska et al. (2024, PRD 109, 103534) to a MegaMapper-like spectroscopic mock, produce \\hat\\eta maps, measure the transfer function T_\\eta(k,z) and total noise N_{\\eta\\eta}(k,z), then recompute the CMB-HD x MegaMapper Fisher matrix by replacing P^\\perp_{\\eta\\eta} in Eqs. (42)-(43) with T_\\eta^2 P^\\perp_{\\eta\\eta} + N_{\\eta\\eta}. If the resulting fractional errors on y_re^He and Delta_y^He exceed unity at L_max=200, the headline claim is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing assumption is that the galaxy-reconstructed squared-velocity field \\hat\\eta entering C^{K\\eta}_L in Eq. (43) is, up to a single amplitude b_vg, the true \\eta field, with the only noise being the shot-noise-dominated term of Eqs. (39)-(40). The authors list the known violations—photo-z errors, RSD, fingers-of-God, survey masks, and scale-dependent velocity reconstruction bias—but defer a quantitative analysis to future work (Sec. III B and Sec. V). For the headline CMB-HD x MegaMapper baseline, photo-z is less relevant since MegaMapper is spectroscopic, yet the scale-dependent transfer function and nonlinear velocity noise remain. Refs. [91,92] find that these effects suppress reconstructed velocity power substantially even for spectroscopic-like samples; a single marginalization over b_vg cannot absorb a scale-dependent bias. Because the He reionization forecasts in Fig. 10 have fractional errors close to unity at L_max ~ 200, even a factor-of-two degradation in C^{K\\eta} (or an increase in N_{\\eta\\eta}) pushes y_re^He and Delta_y^He above 1-sigma, collapsing the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper extends the kSZ trispectrum estimator of Smith & Ferraro (2017) to model the joint contribution of hydrogen and helium reionization to the small-scale CMB temperature field, and introduces a new cross-correlation between the kSZ-squared field K(ˆn) and a galaxy-reconstructed, redshift-binned radial-velocity-squared field eta_alpha(ˆn) (Eqs. 30, 42, 43). The ionized-electron power spectrum is derived from an HOD-based bubble model following Refs. [13, 43, 47], with explicit dependence on the assumed small-scale electron profile. Fisher-matrix forecasts (Eq. 49) are presented for two baselines, CMB-S4 x LSST and CMB-HD x MegaMapper, jointly marginalizing over ten reionization parameters plus a velocity-to-galaxy bias ratio b_vg. The authors find that the KK auto-correlation alone constrains only H reionization (y_re^H within 1 sigma), while adding the K eta cross-correlation yields sub-1 sigma errors on all H reionization parameters and roughly 1 sigma errors on the He redshift-evolution parameters y_re^He and Delta_y^He for CMB-HD x MegaMapper (Figs. 9-10). The He signal is shown to be strongly suppressed relative to H in the redshift-integrated KK statistic, which motivates the tomographic cross-correlation. The paper's closing claims are explicitly conditional on an idealized velocity-reconstruction model and on the neglect of several non-Gaussian foreground terms, as discussed in the major comments.","tokens_in":43650,"tokens_out":24101,"duration_ms":260374,"significance":"The proposed K-eta cross-correlation is a genuinely new observable, and the joint H+He treatment with explicit H x He mixed terms is more complete than earlier forecasts. If the He constraints hold up, the kSZ trispectrum becomes a quantitative joint probe of both reionization epochs, and the LSST-versus-MegaMapper comparison gives a concrete, actionable argument for a Stage-5 spectroscopic survey. Strengths worth naming explicitly: all signal and noise expressions are given in closed form (Eqs. 31-32, 39-43, 48), making the forecasts reproducible from the text alone; the P^ion_ee derivation reduces to the established expressions of Refs. [13, 43, 47] in the appropriate limits; the manuscript is transparent about its omitted effects (photo-z errors, scale-dependent velocity-reconstruction bias, tSZ/lensing/CIB non-Gaussian terms) and cites Refs. [91, 92] for the magnitude of the photo-z degradation; and the electron-profile dependence of the forecasts is explored rather than ignored. The tension between these explicit limitation statements and the strength of the abstract's and Sec. IV C's claims is the main reason the revision is major rather than minor.","major_comments":[{"comment":"The headline He reionization claim (Fig. 10: y_re^He and Delta_y^He measurable at roughly 1 sigma) rests on the idealized model of the galaxy-reconstructed eta field in Eqs. (35)-(43). The signal template in Eq. (43) uses the true power spectrum P_etaeta, which is only recovered if the estimator weights satisfy P_{eta-hat,eta} = P_etaeta exactly (Eq. 36), and the only velocity noise is the shot-noise term of Eq. (39) with b_v = 1 at all redshifts. The manuscript itself lists the violations (photo-z errors, redshift-space distortions and fingers-of-God, survey masks, satellite velocity bias, smoothing) and states in Sec. V that 'we do not include the effects of photo-z errors,' citing Refs. [91, 92] for a factor of about 2 SNR reduction at low redshift for LSST-like samples. Because the projected He fractional errors in Fig. 10 sit close to unity at the plateau beyond L_max ~ 100-200, a factor-of-2 suppression of C^{K eta} or inflation of N^{eta eta} pushes y_re^He and Delta_y^He above unit fractional error, erasing the central claim for He; a single marginalization over b_vg cannot absorb the scale-dependent transfer functions found in Refs. [91, 92]. I regard this as the decisive sensitivity of the paper's main claim, and I request a quantitative stress test that propagates a fiducial scale-dependent reconstruction transfer function and noise model (or, minimally, a factor-of-2 degradation applied to C^{K eta} and N^{eta eta}) and that reports whether the He parameters remain below unit fractional error.","section":"III B, Eqs. (35)-(43); Sec. V"},{"comment":"The KK noise model N^{KK}_L (Eq. 32) and the covariance (Eq. 48) assume a Gaussian small-scale temperature field. The tSZ Poisson contribution ('roughly modeled as a constant offset for large L'), the lensing-induced trispectrum ('comparable to the reconstruction noise N^{KK}_L'), and non-Gaussian CIB/tSZ cross terms are explicitly left out, and the authors state in Sec. IV A that they 'do not account for nuisance parameters to marginalize over this shot-noise effect.' These terms enter the covariance of both the KK and K eta spectra and hence influence the He and H parameter errors directly. This omission matters at the claimed precision: the paper's own electron-profile variation study in Sec. IV C shows changes in forecasted fractional errors up to factors of about 2 between the NFW/AGN and W_e x NFW electron profiles, and the late-time electron distribution is not itself marginalized. I request that at least one representative nuisance marginalization be added (for example, a free amplitude for the late-time kSZ/tSZ offset and a free late-time electron-profile amplitude), or that the authors demonstrate quantitatively that these terms do not shift the Fig. 10 error bars in the relevant direction.","section":"IV A; Sec. V"},{"comment":"The amplitude of the He-dependent signal that drives the Fig. 10 constraints is set by the fiducial patchy-He parameters Rbar_He = 15 Mpc, sigma_lnR^He = ln 2, and b_He = 6.0, which the authors adopt 'due to weaker current constraints and a shortage in simulations of He reionization' (Sec. II C 2). In a Fisher forecast the parameter errors scale approximately inversely with the modeled signal amplitude, so the headline He result is conditional on the He bubble model in a way that the H result, anchored by more abundant observational and simulation input, is not. Because the He errors are marginal even at the fiducial point, I recommend a short robustness scan over the He bubble parameters (for example Rbar_He = 5 and 30 Mpc, and b_He = 4 and 10) to confirm that the measurability claim is not an artifact of the fiducial choice, or an explicit statement that the He constraints are model-conditional.","section":"II C 2; Fig. 10"}],"minor_comments":[{"comment":"The line-style mapping stated in Sec. IV C (solid = y_re, dashed = Delta_y, dot-dashed = Rbar, dotted = sigma_lnR) does not match the order in which the legend entries appear in the figure files (y_re, Delta_y, sigma_lnR, Rbar); please make the style-to-parameter mapping unambiguous and consistent between the text, the captions, and the legends.","section":"Figs. 9-10"},{"comment":"The statement that in the absence of He terms and bubble parameters the forecasts 'appropriately condense to the forecasts presented in Ref. [26]' is asserted without a numerical check, despite Sec. III A reporting substantial model differences from Ref. [25] (for example, a stronger late-time contribution to C^{KK}_L); a short table comparing marginalized errors with Ref. [26] would substantiate this claim.","section":"IV C"},{"comment":"The bibliography contains duplicates: Refs. [15] and [17] are the same La Plante et al. paper, Refs. [16] and [18] are the same paper, Refs. [49] and [106] are the same Shaw, Rudd, and Nagai paper, and Refs. [45] and [80] are the same Planck result; please consolidate the duplicate entries.","section":"References"},{"comment":"There are several typos, including 'due to is low relative abundance' in Sec. I, 'Ref, [25]' in Sec. III A, 'th CMB S4 x LSST' in the Fig. 10 caption, and 'the estimation SNR' in Sec. IV C; a careful proofread is needed.","section":"Throughout"},{"comment":"The sentence 'we assume sigma^H_lnR = sigma^He_lnR = ln 2' mixes the already-fixed H value with the new He assumption; it should read 'we assume sigma^He_lnR = ln 2 (the same value as sigma^H_lnR)' for clarity.","section":"II C 2"},{"comment":"The statement that P^perp_etaeta 'results in a z-independent quantity' is asserted without a derivation; since this property underlies the use of Eq. (42) in the forecasts, a one-line confirmation of the cancellation (for example in Appendix B) would be helpful.","section":"III A, after Eq. (31)"}],"recommendation":"major_revision","confidential_remarks":"This is a solid forecasting study squarely within the journal's scope, and the K-eta cross-correlation framework is likely to be widely cited. My main concern is the presentation discipline: the abstract and Sec. IV C state the He result in relatively strong terms ('will allow for measurement'), while the paper's own Sec. V enumerates omissions that could plausibly flip the roughly 1 sigma He constraints. If the requested robustness tests are added, I would support publication; if the authors prefer not to add them, the He claim should be explicitly qualified as conditional on the idealized velocity-reconstruction and foreground models. No concerns about citation practice beyond the duplicate-reference cleanup listed in the minor comments."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know two things about this paper: the K-eta cross-correlation is a genuine new statistic that meaningfully extends the Smith-Ferraro trispectrum, and the headline claim—that CMB-HD x MegaMapper can measure He reionization parameters at ~1 sigma—rests on velocity-reconstruction assumptions the authors themselves flag as idealized.\n\nWhat is actually new: they build a joint H/He reionization model in the HOD/bubble framework, derive the ionized-electron power spectrum including He and H terms, and then propose cross-correlating the kSZ-squared field with a galaxy-reconstructed squared radial-velocity field. That redshift-binned cross-correlation is the main addition. The Fisher machinery is standard but complete: all signal and noise expressions are given, and the forecasts include marginalization over bubble parameters and b_vg. They are also honest about what they left out—photo-z errors, RSD, fingers-of-God, masks, and non-Gaussian foregrounds are all named but not modeled.\n\nThe soft spots are real, and the stress-test note holds up. The load-bearing assumption is that the reconstructed eta field equals the true eta up to a single bias b_vg, with shot-noise-only errors. Refs [91,92]—which they cite—find factor-of-2 SNR degradation and scale-dependent biases even for spectroscopic samples. A single b_vg marginalization cannot absorb that. Because the He parameter errors in Fig. 10 are near unity at Lmax~200, a factor-of-2 degradation likely pushes y_re^He and Delta_y^He above 1-sigma. The H reionization constraints are more robust; the He result is the fragile one. They also ignore tSZ and lensing trispectrum contamination without marginalizing, though they cite bias-hardening work that suggests these can be removed.\n\nNone of this makes the paper bad. It is a clean forecast with a new statistic and honest caveats. The issue is calibration: the abstract and conclusions present the He reach as a forecast when it is really an optimistic upper-bound forecast. If the authors add a simple velocity-reconstruction degradation model (even just the factor-of-2 from the cited papers) or explicitly recast the He constraints as conditional on idealized reconstruction, the paper would be solid. The math is coherent, the citation pattern is fair, and the derivation is reproducible from the text.\n\nBottom line: this deserves a serious referee. I would send it to review and ask the authors to quantify the impact of the listed systematics or soften the headline claims. It is the kind of paper that will be cited as the first K-eta forecast, and the statistic itself is worth having on the record.","headline":"The K-eta cross-correlation is a genuine new statistic, but the headline He reionization constraints are conditional on idealized velocity reconstruction that could easily erase them.","tokens_in":44250,"tokens_out":2708,"would_cite":true,"duration_ms":32350,"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":"Helium reionization becomes measurable via kSZ-galaxy cross-correlation.","keywords":["kinetic Sunyaev-Zel'dovich effect","patchy reionization","hydrogen reionization","helium reionization","CMB trispectrum","velocity reconstruction","galaxy surveys","Fisher forecast"],"falsifier":"A concrete test would be to run the same Fisher pipeline with a velocity-reconstruction noise model taken from realistic light-cone galaxy mocks that include photo-z scatter, redshift-space distortions, fingers-of-God, and survey masks instead of the shot-noise formula in Eq. (39); if the reconstructed-$\\eta$ SNR falls by the factor of about 2 reported for LSST-like photo-z samples, the CMB-HD x MegaMapper He-reionization constraints in Fig. 10 would degrade below 1-$\\sigma$ detectability. A separate check would be to replace the analytical bubble model with a simulation-based reionization map and recompute the kSZ trispectrum and cross-correlation amplitudes, which would test whether the assumed bubble radii and ionized-electron power spectrum are the main drivers of the forecasted sensitivity.","tokens_in":43135,"feed_emoji":"🔭","tokens_out":6633,"duration_ms":71662,"temperature":0.7,"pith_summary":"This paper argues that the kinetic Sunyaev-Zel'dovich (kSZ) effect, a small-scale CMB distortion from scattering off free electrons, can be turned into a joint probe of both hydrogen (H) and helium (He) reionization. The key move is to add a redshift-resolved cross-correlation: the kSZ temperature-squared maps used in earlier trispectrum work are correlated with the squared radial-velocity field reconstructed from galaxy surveys at redshifts below about 5. Using forecasts tied to CMB-S4-like and CMB-HD-like surveys crossed with LSST-like and MegaMapper-like galaxy data, the paper finds that the CMB-HD x MegaMapper combination can measure the midpoint and duration of He reionization at about 1-sigma while determining all H reionization parameters below 1-sigma. This matters because He reionization is tied to quasars and active galactic nuclei, so measuring both epochs together would let observations separate the roles of stars and quasars in ionizing the intergalactic medium.","feed_headline":"kSZ-galaxy cross-correlation can date helium reionization","feed_subtitle":"Adding z-binned galaxy velocity data to CMB kSZ maps yields ~1-sigma constraints on He reionization for CMB-HD x MegaMapper.","key_machinery":"The central object is the four-point (trispectrum) kSZ statistic built from filtered temperature-squared maps. The CMB map is split into high-$\\ell$ bands; each band is squared to make a field $K_i(\\hat{n})$ measuring local small-scale kSZ power. Large-scale variations of $K_i$ are sourced by the squared radial peculiar velocity field $\\eta(\\hat{n},z) = v_r^2 / \\langle v_r^2 \\rangle$, whose coherence length sets the angular-scale dependence of the statistic. The paper's new ingredient is a cross-correlation between these $K_i$ fields and redshift-binned $\\eta_\\alpha$ fields reconstructed from galaxy surveys through the linear continuity equation, with a minimum-variance estimator whose noise is set by shot noise in the galaxy density. This cross-correlation adds tomographic information at $z \\lesssim 5$, where He reionization is taking place, and it is what lifts the He signal out of the redshift-integrated background.","core_discovery":"The paper's central claim is that the redshift-integrated kSZ trispectrum, already sensitive to patchy H reionization, can be extended to He reionization by cross-correlating the kSZ-weighted temperature-squared field $K(\\hat{n})$ with a galaxy-reconstructed squared radial-velocity field $\\eta(\\hat{n}, z)$ binned in redshift. The authors model both ionization epochs with a halo-model and bubble prescription, derive the ionized-electron power spectrum including H, He, and mixed terms, and then perform an information-matrix forecast. Their headline quantitative result is that adding the $z$-binned $\\eta$-field data allows measurement of the He reionization parameters $y_{\\rm re}^{\\rm He}$ and $\\Delta_y^{\\rm He}$ near 1-$\\sigma$ for a CMB-HD x MegaMapper baseline, while the same baseline yields sub-1-$\\sigma$ errors on all H reionization parameters. Without the galaxy cross-correlation, the auto-correlation trispectrum leaves He parameters essentially unconstrained. The paper therefore proposes that the kSZ effect, previously regarded as a hydrogen-reionization timing statistic, can become a quantitative probe of both epochs if the assumed galaxy velocity reconstruction is achieved.","pith_inferences":["Beyond the paper's forecasts, the same $K \\times \\eta$ framework could be extended to a bispectrum-level statistic correlating the $K$ fields with galaxy density itself, which would be more sensitive to small-scale patchiness and quasar clustering during He reionization.","If velocity reconstruction degrades by the factor of about 2 that the cited photometric-redshift studies find for LSST-like samples, the He parameter errors would roughly double, making the headline He detection marginal rather than secure.","A successful joint measurement would allow kSZ-based constraints on quasar-driven helium reionization to be combined with fast-radio-burst dispersion measures and He II Lyman-$\\alpha$ forest observations, providing independent cross-checks on the timing and morphology of the epoch.","The reliance on linear continuity and an assumed velocity-reconstruction bias $b_v = 1$ suggests that realistic survey masks, fingers-of-God, and residual redshift-space distortions will need to be folded into the Fisher forecasts; the relative advantage of a spectroscopic follow-up like MegaMapper over a photometric sample may therefore be understated in the paper."],"forward_implications":["If He reionization parameters can be measured, the epoch of the second ionization of helium becomes a direct observable tied to quasar and AGN activity rather than only an inference from Lyman-$\\alpha$ forest or intergalactic-medium temperature measurements.","Jointly fitting H and He parameters prevents neglected-He biases; the paper finds that using $\\ell$-binned $K$ fields keeps H-He covariance minimal, so omitting He would not strongly bias H constraints when that binning is used.","The forecast detection SNR for CMB-HD x MegaMapper reaches roughly 100 at $L_{\\rm max} \\sim 50$ when combining the auto- and cross-correlation signals, so the fields do not need to be reconstructed to very small angular scales for a detection.","If only the redshift-evolution parameters $y_{\\rm re}$ and $\\Delta_y$ are targeted, without marginalizing over bubble-size parameters, the CMB-HD x MegaMapper baseline can place roughly $3\\sigma$ constraints on all four midpoint and duration parameters for both epochs at $L_{\\rm max} \\sim 200$.","The constraints depend on the assumed small-scale electron profile; switching to a $W_e(k) \\times$ NFW profile changes H parameter errors by up to about a factor of 2 and He parameter errors by up to about a factor of 1.5."],"supporting_citations":[{"why":"Supplies the original kSZ trispectrum statistic and the temperature-squared map construction that this paper extends to two ionization epochs.","marker":"[25]"},{"why":"Establishes the $\\ell$-binning and forecast methodology for characterizing reionization with the kSZ trispectrum, which this paper adapts and extends.","marker":"[26]"},{"why":"Provides the joint H/He reionization modeling and earlier cross-correlation forecasts that motivate the fiducial parameter choices and baseline comparisons used here.","marker":"[13]"},{"why":"Gives the bubble and halo-occupation prescription for ionization-fraction fluctuations that underlies the ionized-electron power spectrum derivation.","marker":"[47]"},{"why":"Provides the reionization model and fiducial bubble-radius parameters, including the tanh ionization-fraction parametrization, used in the forecasts.","marker":"[43]"},{"why":"Provides velocity-reconstruction noise forecasts for photometric-redshift samples, cited for the factor-of-about-2 SNR degradation that this paper does not include.","marker":"[91]"},{"why":"Gives realistic light-cone velocity-reconstruction tests for LSST-like samples, cited for photo-z and redshift-space-distortion degradation effects.","marker":"[92]"},{"why":"Demonstrates application of the kSZ trispectrum to real CMB data and discusses bias-hardening, cited as the basis for neglecting the lensing trispectrum bias in the forecasts.","marker":"[30]"}],"fun_headline_variants":["kSZ-galaxy cross-correlation measures helium reionization","Galaxy velocities + kSZ trispectrum constrain He reionization","Joint kSZ and galaxy data yield 1-sigma He reionization constraints","Patchy helium reionization probed by kSZ-galaxy cross-power","kSZ trispectrum plus galaxy velocities dates He reionization"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The forecast assumes that galaxy surveys can reconstruct the squared radial-velocity field $\\eta$ with essentially ideal errors: linear continuity between galaxy density and velocity, velocity-reconstruction bias $b_v = 1$, shot-noise-only errors, and no degradation from photo-z errors, redshift-space distortions, or masks; if real reconstruction is noticeably worse, the helium reionization constraints, already near 1-$\\sigma$, would weaken.","fun_headline_variants_meta":{"raw":{"variants":["kSZ-galaxy cross-correlation measures helium reionization","Galaxy velocities + kSZ trispectrum constrain He reionization","Joint kSZ and galaxy data yield 1-sigma He reionization constraints","Patchy helium reionization probed by kSZ-galaxy cross-power","kSZ trispectrum plus galaxy velocities dates He reionization"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000455,"raw_usage":{"total_tokens":2360,"prompt_tokens":1096,"completion_tokens":1264,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":712,"completion_tokens_details":{"reasoning_tokens":1168}},"tokens_in":712,"tokens_out":1264,"duration_ms":13285,"temperature":1.0,"reasoning_tokens":1168,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T04:13:30.049181+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A concrete test would be to run the same Fisher pipeline with a velocity-reconstruction noise model taken from realistic light-cone galaxy mocks that include photo-z scatter, redshift-space distortions, fingers-of-God, and survey masks instead of the shot-noise formula in Eq. (39); if the reconstructed-$\\eta$ SNR falls by the factor of about 2 reported for LSST-like photo-z samples, the CMB-HD x MegaMapper He-reionization constraints in Fig. 10 would degrade below 1-$\\sigma$ detectability. A separate check would be to replace the analytical bubble model with a simulation-based reionization map and recompute the kSZ trispectrum and cross-correlation amplitudes, which would test whether the assumed bubble radii and ionized-electron power spectrum are the main drivers of the forecasted sensitivity.","supporting_citations":[{"cited_title":"The Maximum B-mode Polarization of the Cosmic Microwave Background from Inhomogeneous Reionization","cited_arxiv_id":"astro-ph/0607652","evidence_quote":"Gives the bubble and halo-occupation prescription for ionization-fraction fluctuations that underlies the ionized-electron power spectrum derivation."}],"review_version":1}