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REVIEW 4 major objections 5 minor 137 references

Non-linear infusion of intrinsic alignment and source clustering: impact on non-Gaussian cosmic shear statistics

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper argues that the density-weighted $\delta$-NLA model, not the standard NLA, is the strongest intrinsic-alignment contaminant of non-Gaussian cosmic shear statistics, and that underdense probes are the best place to tell IA models…

desk verdict A useful, overdue simulation grid for IA in beyond-2pt lensing, but the headline delta-NLA factor sits on the least-calibrated part of the pipeline. read the letter →

arxiv 2509.25166 v1 pith:UOPYM4UD submitted 2025-09-29 astro-ph.CO

J. Harnois-Déraps , N. Šarčević , L. Medina Varela , J. Armijo , C. T. Davies , N. van Alfen , J. Blazek , L. Castiblanco
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A. Halder K. Heitmann P. Larsen L. Linke J. Liu C. MacMahon-Gellér L. Porth S. Rangel C. Uhlemann the LSST Dark Energy Science Collaboration
This is my paper · ORCID
classification astro-ph.CO
keywords intrinsicalignmentscosmicshearnon-Gaussianstatisticsweaklensingsimulationssourceclusteringtidalfieldsaperturemassvoidprofiles
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Cosmic shear measurements must separate the weak-lensing signal from the intrinsic alignments (IA) of galaxy shapes, and standard analytic models only cover two-point statistics. This paper builds six IA models directly into simulated lensing catalogues by coupling galaxy shapes to projected tidal fields computed from mass shells, then measures how each model distorts non-Gaussian statistics such as the lensing PDF, peak and minima counts, third-order aperture mass, integrated three-point functions, and void profiles. The central result is that the density-weighted $\delta$-NLA model contaminates most probes far more than the standard NLA, in places more than twice as strongly, and that probes of underdense regions -- minima counts, void profiles, and the lensing PDF -- carry the largest model-discriminating power. The paper also isolates the source-clustering term and finds it reaches tens of percent in low-redshift tomographic bins. If correct, these results imply that beyond-two-point cosmic shear analyses that assume only the NLA model will underestimate the IA systematic, and that model mis-specification can shift inferred $S_8$ low.

What carries the argument

The load-bearing object is the projected tidal-field pipeline. For each curved-sky mass shell the density map $\delta(\theta,\phi)$ is converted, via spin-2 harmonic transforms, into the trace-free projected tidal tensors $s_{11}$, $s_{22}$, $s_{12}$ (Eq. 25), smoothed with a Gaussian beam of width $\sigma_G$. These tidal tensors are then coupled to intrinsic ellipticities either linearly, $\epsilon^{\rm NLA}_1=C_1(s_{11}-s_{22})$ and $\epsilon^{\rm NLA}_2=C_1 s_{12}$, or quadratically, through products of tidal components such as $s_{11}^2-s_{22}^2$ and $s_{12}(s_{11}+s_{22})$, with the coupling amplitudes set by the IA parameters $A_{\rm IA}$ and $C_2$. Galaxy positions are placed randomly, Poisson-sampled with a linear bias $b_{\rm TA}$, or drawn from halo occupation distributions, and the resulting intrinsic ellipticities are combined with the reduced lensing shear through Eq. (26) to produce the final catalogues. This machinery matters because it lets six physically distinct IA models share the same lensing light cone, so the non-Gaussian statistics are all measured on matched noise-free maps and the differences are attributable to the IA and source-clustering prescriptions alone.

What would settle it

Recompute the TT and $\delta$-TT infusion using the full three-dimensional tidal field, or much thinner shells, from the same N-body simulation and check whether the two-point shear predictions agree with theory without the ad hoc rescaling factors of 1/2.5 and 1/20; if the mismatch persists, the projected-field assumption is the cause, and the ranking of IA models on non-Gaussian probes should be recomputed.

Watch

Extended reading notes

Core claim

The paper claims that the dominant secondary signal in non-Gaussian cosmic shear statistics is not the simple non-linear linear-alignment (NLA) model but its density-weighted extension, the $\delta$-NLA model: when galaxies trace the matter field with a linear bias, the ellipticity-tidal coupling produces IA contaminations that are at times more than twice as strong as in NLA, especially in tomographic combinations that include low-redshift galaxies. It further claims that the differences between IA models are largest in underdense regions, making minima counts, void profiles, and the lensing PDF the best probes for rejecting an incorrect IA model, and that source clustering contributes roughly ten percent to third-order aperture mass statistics in the lowest redshift bin and can exceed 20 percent for $M_{\rm ap}^3$ and integrated three-point functions when low-redshift data are included. The pipeline generates all six models -- NLA, $\delta$-NLA, TT, $\delta$-TT, and HOD-based NLA/TT combinations -- from one simulated IA-infused catalogue, so the models can be rescaled and reweighted quickly. The paper also shows that if the true IA resembled its $\delta$-TT or HOD-TT implementations, analysing two-point shear with standard NLA or TATT would bias $S_8$ low by more than 0.05.

Load-bearing premise

The paper's results for the quadratic tidal-coupling models rest on the assumption that two-dimensional projected tidal fields from the simulation's mass shells behave like the full three-dimensional tidal field when squared; if that projection step fails, those impacts are simulation artefacts rather than intrinsic-alignment predictions.

Editorial extensions

If this is right

  • Beyond-two-point analyses that model only the NLA will understate the IA contamination; with the $\delta$-NLA model the impact can be more than twice as large on several probes.
  • Underdense-region statistics -- minima counts, void profiles, and the negative tail of the lensing PDF -- are the most informative for distinguishing IA models and for flagging mis-specified IA physics.
  • Source clustering is not negligible for higher-order statistics: it reaches about 10 percent in $M_{\rm ap}^3$ and can exceed 20 percent in $M_{\rm ap}^3$ and integrated three-point functions when the lowest redshift bin is included.
  • IA model mis-specification can masquerade as cosmology: analysing $\delta$-TT or HOD-TT mock data with NLA/TATT two-point models shifts the inferred $S_8$ low by more than 0.05.
  • One simulated IA-infused catalogue can be rescaled across the IA parameter space, so IA systematics can be forward-modelled without rerunning the N-body simulation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the TT-family results rely on projected tidal fields, and the paper itself notes that non-linear operations on the three-dimensional tidal field do not commute with projection, the reported ranking -- with $\delta$-NLA dominant -- may change if the infusion is repeated on thinner shells or with full 3D tidal fields; that test would separate simulation artefacts from IA predictions.
  • The empirical redshift-dependent rescaling factors (dividing TT ellipticities by 2.5 at $z<0.5$, and $\delta$-TT by a further 20) are likely cosmology-dependent, so the relative ordering of models could shift in different cosmologies; re-running the pipeline on mocks with varied $\Omega_m$ and $\sigma_8$ would quantify this.
  • The fact that underdense probes distinguish IA models so cleanly suggests a compressed statistic -- for example the ratio of void-interior to void-ridge lensing signal -- could be engineered as a single IA-model-discrimination number for survey analyses.
  • The MCMC pattern (cosmology recovered for NLA, $\delta$-NLA and HOD-NLA but not $\delta$-TT or HOD-TT) implies that goodness-of-fit, not just parameter shifts, should be used to flag IA mis-modelling in real cosmic shear data.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper presents a pipeline for infusing intrinsic alignment (IA) models into simulated cosmic shear catalogues, based on projected tidal fields extracted from mass shells in the SkySim5000/Outer Rim simulation. Six models are constructed by crossing two tidal couplings (linear NLA and quadratic TT) with three galaxy sampling schemes (random, linearly biased, and HOD-based), and the resulting catalogues are validated against analytic two-point theory and MCMC inference. The paper then measures the impact of IA and source clustering on a suite of non-Gaussian statistics: third-order aperture mass, lensing PDF, peaks, minima, integrated three-point functions, and void profiles. The headline finding is that the δ-NLA model has the largest impact on most probes, at times more than twice the NLA impact, and that underdense-region probes such as minima, void profiles, and the lensing PDF are best suited for distinguishing IA models.

Significance. If the catalogue infusion is trustworthy, this is a valuable resource: it is one of the first systematic comparisons of multiple IA models on non-Gaussian weak lensing statistics, and it explicitly separates source-clustering contributions. The two-point validation for NLA and δ-NLA is clean for the GG and GI terms, and the code being made public after acceptance increases the utility of the work. The study also correctly highlights that underdense probes are potentially powerful discriminators between IA models, which is a useful guide for survey analyses. However, the central quantitative claim depends on the δ-NLA catalogues, whose low-redshift II term is not calibrated and is known to overshoot the analytic prediction by tens to hundreds of percent. The TT-family results are obtained only after ad hoc empirical rescalings by factors of 2.5 and 20, and the HOD-TT inference is catastrophic. These caveats substantially weaken the reassuring narrative of a validated six-model pipeline and need to be addressed before the headline conclusions can be taken at face value.

major comments (4)
  1. [Sec. 5.1, Figs. 4-5 and Sec. 7] The headline claim that δ-NLA has by far the largest impact, at times more than twice the NLA strength, rests on δ-NLA catalogues whose low-redshift II term is not calibrated and is explicitly acknowledged to overshoot the one-loop analytic prediction by tens to hundreds of percent at small angles (Sec. 7). Since the non-Gaussian impacts in Figs. 15-16 are largest for tomographic combinations including the lowest-redshift bin, where this excess lives, the headline result is not cleanly separated from the known simulation/theory mismatch. Please either demonstrate that the excess is physical (e.g., by varying σ_G, using thinner shells, or including an explicit calibration analogous to the TT models) or substantially soften the claim.
  2. [Sec. 5.1, TT and δ-TT calibration] The TT model requires an empirical redshift-dependent rescaling by 1/2.5 at z<0.5, and the δ-TT model additionally requires a global rescaling by 1/20. These calibration factors are not accompanied by any uncertainty estimate or sensitivity analysis, yet the calibrated catalogues are then used to produce the non-Gaussian predictions in Sec. 6. The TT-family higher-order impacts therefore inherit amplitudes that are fixed by hand. The paper should either propagate the calibration uncertainty into the quoted impacts or explicitly label the TT-family non-Gaussian results as qualitative and implementation-dependent.
  3. [Sec. 5.2, Fig. 14] The HOD-TT MCMC analysis is catastrophic, with posteriors pushed against the prior edges, and the summary paragraph of Sec. 5.2 contains an internal contradiction: HOD-TT is listed both among the models for which cosmology is correctly inferred and among the models for which it is not. This inconsistency needs to be fixed, and the validation claim that all six models are reliable must be restricted to NLA, δ-NLA, and HOD-NLA; the quadratic-coupling HOD results should be presented as exploratory given their failure in the two-point inference.
  4. [Eq. (25) and Sec. 5.1] The core assumption that projected, shell-based tidal fields stand in for the full three-dimensional tidal field when computing quadratic couplings is acknowledged by the authors themselves as the likely cause of the TT failure ('non-linear operations on the 3D tidal field, including the TT model, do not commute with projection'). Because this assumption is not tested against a true 3D tidal-field infusion on even one mass shell, the TT and δ-TT higher-order impacts are not established as intrinsic-alignment predictions. A direct comparison between projected and 3D tidal infusion for one shell would resolve whether these results are physical or projection artefacts.
minor comments (5)
  1. [Sec. 2.1] The text says the smoothed redshift distributions are 'shown by the solid lines in Fig. 17', but the relevant figure appears to be Fig. 1; please correct the cross-reference.
  2. [Eq. (21) vs. Eq. (B6)] The two expressions for the TT ellipticity component ϵ_2 disagree in sign: Eq. (21) gives ϵ_2^TT = C_2 s_12 (s_11+s_22), while Eq. (B6) gives ϵ_2^TT = -C_2 s_12 (s_11+s_22). Please reconcile the definitions.
  3. [Sec. 4.2 and Sec. 4.3] The linear-bias sampling is said to use a 1.0 h^-1 Mpc smoothed density field, while Sec. 4.3 and Sec. 5.1 quote tidal-field smoothing scales σ_G of 0.1 and 0.5 h^-1 Mpc; please clarify which smoothing applies to the galaxy-position sampling and which to the tidal-field construction.
  4. [Sec. 5.1] The δ-NLA II excess is described as expected because the one-loop theory is valid only up to k~0.2 Mpc, but the same model is then used without qualification for the headline non-Gaussian results; an explicit statement of the trusted scale range for δ-NLA predictions would avoid over-interpretation.
  5. [Sec. 6] The caption to Fig. 16 states that error bars for the lensing PDF and minima are computed from the TT model, while the text describes jackknife errors for these probes; please ensure the caption and text are consistent.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the headline δ-NLA impact is a direct, disclosed model consequence rather than a fitted or citation-derived prediction, and the TT/δ-TT amplitude calibrations are openly stated rather than relabeled as independent predictions.

full rationale

The paper's central claims are forward-model consequences rather than quantities derived from the same quantities being predicted. The NLA validation compares simulation measurements against an external analytic model computed with CosmoSIS and Halofit, so the two-point agreement is independent of the paper's own outputs. The δ-NLA model is explicitly defined by Eq. (15), ϵδ−NLA = ϵNLA × (1 + δbTA), and the paper does not fit any parameter to the non-Gaussian data vectors; the reported 'largest impact' follows from the model definition and the simulation's nonlinear II behavior, which is acknowledged as an excess relative to one-loop theory rather than presented as an independent validation. The TT and δ-TT models undergo explicit empirical rescaling ('we achieve this calibration by rescaling ϵIA,TT(z<0.5)→ϵIA,TT/2.5' and 'a global ϵIA,δTT→ϵIA,δTT/20.0 rescaling'), and the paper states that these are calibration conditions compensating for the lack of the third tidal dimension, with the caveat that 'non-linear operations on the 3D tidal field, including the TT model, do not commute with projection.' Those rescaled models are then used to compute higher-order statistic impacts, but the paper does not call those impacts independent first-principles predictions; it clearly labels the procedure as model infusion and calibration, not as a test of the model. Self-citations such as Harnois-Déraps et al. (2021a) for projected tidal fields are re-validated internally via the NLA two-point comparison, and Blazek et al. (2019), which includes a coauthor, is used as a comparison theory rather than as a uniqueness theorem forbidding alternatives. No step was found in which a fitted parameter is renamed as a prediction, an ansatz is smuggled in via citation, or a known result is merely relabeled. The TT/δ-TT amplitude dependence is a disclosed modeling limitation and a robustness concern, not a circular derivation.

Assumptions & free parameters 6 free parameters · 7 assumptions · 1 invented entities

The six IA models are anchored by two coupling prescriptions, NLA linear and TT quadratic, whose amplitudes A_IA, b_TA, C_2 and smoothing scale sigma_G are set by hand. The TT-family models additionally require empirical amplitude corrections of 2.5 and 20 fitted to two-point theory, and the delta-TT model is invented in this paper with no independent test. These choices, rather than external data, set the scale of the headline non-Gaussian impacts.

free parameters (6)
  • A_IA = 1.0 (fiducial)
    Overall intrinsic alignment amplitude chosen by hand; all non-Gaussian comparisons use A_IA=1.0, so the relative impacts are at this chosen amplitude.
  • b_TA = 1.0, also 2.0
    Linear galaxy bias for the delta-NLA and delta-TT models; chosen as fiducial values, not fitted to data.
  • C_2 = 1.0 (fiducial)
    Quadratic tidal-torque amplitude; set to 1.0 in the fiducial TT model.
  • sigma_G = 0.1 and 0.5 h^-1 Mpc
    Tidal field smoothing scale; results depend on it, and the authors prefer different values for NLA (0.1) versus TT (0.5), so this is a hand-tuned parameter.
  • TT low-redshift calibration factor = 2.5
    Empirical division applied to epsilon_IA,TT for z<0.5 to make the low-redshift two-point signal match theory.
  • delta-TT global calibration factor = 20.0
    Global division applied to epsilon_IA,deltaTT after the low-redshift factor, compensating for overly strong torquing in the simulated projected fields.
assumptions (7)
  • domain assumption Intrinsic ellipticity is linearly proportional to the tidal field, with NLA normalization C1 from Brown et al. (2002).
    Eqs. (11)-(12) define the NLA model; this is the physical premise being simulated, not established by this paper.
  • domain assumption The TT model is a quadratic coupling between galaxy shape and tidal field, with line-of-sight components suppressed.
    Eq. (19) and Appendix B, taken from Blazek et al. (2019); radial tidal components are assumed to be irrelevant in projection.
  • domain assumption Projected two-dimensional tidal fields from mass shells capture the three-dimensional tidal field relevant for intrinsic alignments.
    Sec. 4.3, Eq. (25); the paper states that non-linear operations such as the TT model do not commute with projection, so this assumption is load-bearing and only approximately true.
  • standard math Born approximation ray tracing, Limber approximation, and Halofit matter power spectra are adequate for lensing kernels and theory validation.
    Secs. 2.1 and 4.1; these are standard tools in cosmic shear work.
  • domain assumption Galaxies trace matter either randomly, linearly with bias b_TA, or through the SkySim5000 HOD prescription.
    Sec. 4.2; the HOD prescription is taken from Korytov et al. (2019), and the three tracer models define the bias scenario.
  • domain assumption The LSST Year-1 redshift distribution and sigma_epsilon=0.27 shape noise model the source sample.
    Secs. 2.1 and 4.4; all catalogue properties and noise-free conclusions depend on these choices.
  • domain assumption Kaiser-Squires inversion with B modes set to zero reconstructs convergence from galaxy ellipticities.
    Secs. 2.2 and 4.1; standard in the field but introduces smoothing and edge effects.
invented entities (1)
  • Extended-TT (delta-TT) model
    purpose: A new intrinsic alignment model combining quadratic tidal torque coupling with galaxies that linearly trace the matter field.
    Sec. 3.4; the paper states no theoretical framework exists and the model currently exists solely in simulations. There is no external prediction to falsify it.

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Cite this review

Pith. "Pith review of Non-linear infusion of intrinsic alignment and source clustering: impact on non-Gaussian cosmic shear statistics." pith.science (2026). https://pith.science/paper/UOPYM4UD

@misc{pith2026250925166,
  author       = {Pith},
  title        = {Pith review of: Non-linear infusion of intrinsic alignment and source clustering: impact on non-Gaussian cosmic shear statistics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UOPYM4UD}},
  note         = {Machine review of arXiv:2509.25166}
}
abstract

Intrinsic alignments (IA) of galaxies is one of the key secondary signals to cosmic shear measurements, and must be modeled to interpret weak lensing data and infer the correct cosmology. There are large uncertainties in the physical description of IA, and analytical calculations are often out of reach for weak lensing statistics beyond two-point functions. We present here a set of six flexible IA models infused directly into weak lensing simulations, constructed from the mass shells, the projected tidal fields and, optionally, dark matter halo catalogues. We start with the non-linear linear alignment (NLA) and progressively sophisticate the galaxy bias and the tidal coupling models, including the commonly-used extended NLA (also known as the e-NLA or $\delta$-NLA) and the tidal torque (TT) models. We validate our methods with MCMC analyses from two-point shear statistics, then compute the impact on non-Gaussian cosmic shear probes from these catalogues as well as from reconstructed convergence maps. We find that the $\delta$-NLA model has by far the largest impact on most probes, at times more than twice the strength of the NLA. We also observe large differences between the IA models in under-dense regions, which makes minima, void profiles and lensing PDF the best probes for model rejection. Furthermore, our bias models allow us to separately study the source-clustering term for each of these probes, finding good agreement with the existing literature, and extending the results to these new probes. The third-order aperture mass statistics ($M^3_{ap}$) and the integrated three-point functions are particularly sensitive to this when including low-redshift data, often exceeding a 20% impact on the data vector. Our IA models are straightforward to implement and rescale from a single simulated IA-infused galaxy catalogue, allowing for fast model exploration.

Figures

Figures reproduced from arXiv: 2509.25166 by the authors.

Figure 1
Figure 1. Tomographic redshift distributions in our simulations, either taken from the Year-1 specifications for LSST (solid, Eq. 4) or from a matched selection applied to an HOD galaxy catalogue (dashed, see Sec. 5.1). 2.1 γ-2PCF Shear two-point correlation functions (γ-2PCF hereafter) can be pre￾dicted from semi-analytical theory with percent-level precision and are therefore an ideal quantity to validate weak lensing simul… view at source ↗
Figure 2
Figure 2. Density field (left) and the associated projected tidal field tensors s11, s22 and s12 (right), for z = 0.18. These cosmic tides are computed from Eq. (25), and used in Eq. (11) and Eq. (21) to infuse IA with a linear or quadratic coupling, respectively. dashed lines closely matching the target n(z). Compared to the ana￾lytical SRD-Y1, the mean redshifts of the five tomographic bins are shifted by [-0.027, -0.018, 0… view at source ↗
Figure 3
Figure 3. Residual between the shear correlation functions with and without IA for ξ+ (left) and ξ− (right), assuming the NLA model with AIA = 1.0 both in the simulation and theory. Measurements shown in orange and green correspond to smoothing scales of 0.1 and 0.5 h −1Mpc in the tidal field. There is no shape noise in the simulations, but it is included in the analytical covariance matrix, from which the error bars are obta… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Same as [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Shear 2PCF ξ+ in the extended-NLA model for the two lowest redshift bins, showing the good agreement between simulations (symbols) and theory (lines) for the GG (black) and GI (blue) terms, while large devia￾tions are observed in the II term (green). Similar results ar…
Figure 7
Figure 7. Figure 7: Same as [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: Same as [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: Cosmological inference from γ-2PCF measured in the NLA￾infused simulations, where either all three TATT parameters are varied (yel￾low) or only AIA is varied (blue) in the model. The cross-hairs represent the truth as fixed in the Outer Rim N-body simulations (Heitmann…
Figure 11
Figure 11. Figure 11: shows exactly this, failing to correctly infer most parame￾ters. In this particular case, S 8 is off by 2σ, AIA and C2 are biased by 4-5σ, while Ωm and bTA are within 1σ. The δ-TT model is even more affected by mis-modelling, with a 3σ shift in both Ωm and S 8, as see…
Figure 12
Figure 12. Figure 12: Cosmological inference from the δ-TT-infused simulations, where all three TATT parameters are varied (yellow) or recovering the case where AIA is fixed (orange), which corresponds to the TT model. 0.30 0.45 m 0.5 1.0 1.5 b T A 0.6 0.0 0.6 C 2 0.6 1.0 1.4 AIA 0.70 0.74…
Figure 13
Figure 13. Figure 13: Cosmological inference from the HOD-NLA-infused simulations, where either all three TATT parameters are varied (yellow), or fixing C2 to 0.0 (purple) . probes). We are careful here not to claim that this is the single cause, but clearly mis-modelling in the IA sector …
Figure 15
Figure 15. Figure 15: Impact of IA and SC on the M3 ap statistics (see Sec. 2.2) for different IA models. The individual panels show the results from four combinations of tomographic bins, as labeled near the upper edge. These measurements are from noise-free kappa maps. The error bars are…
Figure 16
Figure 16. Figure 16: Same as [PITH_FULL_IMAGE:figures/full_fig_p016_16.png]
Figure 17
Figure 17. Figure 17: Same as [PITH_FULL_IMAGE:figures/full_fig_p017_17.png]

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Pith tools

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