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REVIEW 4 major objections 5 minor 57 references

The effects of expansion and turbulence on the interplanetary evolution of a magnetic cloud

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Spherical expansion alone, with no shock or ambient field, drives the radial growth of magnetic clouds.

desk verdict A genuinely new combination—flux rope plus expansion plus turbulence—with a clean epsilon_0 classification, but the quantitative alpha_R/epsilon_0 anti-correlation is partly contaminated by the switch-on transient. read the letter →

arxiv 2505.15527 v1 pith:KELQYETY submitted 2025-05-21 astro-ph.SR physics.space-ph

Mattia Sangalli , Andrea Verdini , Simone Landi , Emanuele Papini This is my paper · ORCID
classification astro-ph.SRphysics.space-ph MSC 85A3076W05
keywords coronalmassejectionsmagneticcloudsfluxropesexpandingboxmodelmagnetohydrodynamicssolarwindexpansionturbulenceradial
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

Magnetic clouds — the twisted magnetic tubes carried outward by coronal mass ejections — grow in radial size as they travel from the Sun to Earth orbit, and the standard explanation is that their magnetic pressure exceeds the ambient wind's pressure. This paper argues that the spherical geometry of the expanding wind is by itself enough to break the cloud's static equilibrium: the anisotropic stretching pushes material outward along the radial direction and pulls it inward transversely, producing a head-tail radial velocity profile and radial size growth even with no shock, no ambient magnetic field, and no drag. The dimensionless ratio $\epsilon_0 = t_A/t_\mathrm{exp}$ — internal Alfvén crossing time over expansion time — organizes how much the cloud grows radially versus transversely, while the plasma $\beta$ (gas pressure over magnetic pressure) sets its overall size. If the argument holds, radial expansion is an internal dynamical response to geometry, and $\epsilon_0$ becomes a useful classifier for different kinds of magnetic-cloud expansion.

What carries the argument

The load-bearing setup is the expanding box model, a semi-Lagrangian numerical treatment that follows a plasma parcel moving radially at constant speed while the transverse domain expands as $a(t)=R(t)/R_0$ and the radial size stays fixed; spherical expansion enters as anisotropic geometric stretching of gradients and as linear friction terms in the ideal MHD equations. The organizing dimensionless parameter is $\epsilon_0 = t_A/t_\mathrm{exp} = (L_\mathrm{FR}/R_0)(U_0/c_A^0)$, the ratio of the flux rope's internal Alfvén crossing time to the propagation/expansion time. Around $\epsilon_0^* = (4/\pi)(B_{\theta,0}/B_{z,0}) = 2/\pi$ for the chosen twist, magnetic-tension communication across the cross-section either keeps the aspect ratio saturating near one ($\epsilon_0 < \epsilon_0^*$) or lets it grow without bound ($\epsilon_0 > \epsilon_0^*$). A second parameter, the plasma $\beta$ $\beta_0 = 2 P_\mathrm{bg}/B_\mathrm{FR}^2$, sets the overall size isotropically.

What would settle it

A multi-distance in-situ catalog of shockless magnetic clouds, binned by estimated $\epsilon_0$, could settle it: the organizing role of $\epsilon_0$ predicts that the radial-size scaling exponent $\alpha_R$ and the local expansion parameter $\zeta$ both decrease as $\epsilon_0$ increases from 0.2 to 3, and that clouds above the critical $\epsilon_0^* = 2/\pi$ keep an increasing aspect ratio rather than saturating near one. If those trends are absent in the data, the claim that $t_A/t_\mathrm{exp}$ controls radial expansion is wrong.

Watch

Extended reading notes

Core claim

The paper argues that the anisotropic stretching of a spherically expanding solar wind is by itself sufficient to break the static equilibrium of a cylindrical flux rope and generate the radial expansion observed in magnetic clouds. In the expanding-frame simulations, the radial direction is pushed outward by magnetic pressure while the transverse direction is pulled inward by magnetic tension; the result is a front-to-back (head-tail) radial velocity profile and a radial size increase, with transverse growth less than the kinematic expectation. The dimensionless ratio $\epsilon_0 = t_A/t_\mathrm{exp}$, with $t_A$ the internal Alfvén crossing time and $t_\mathrm{exp}$ the expansion/propagation time, determines how strongly the structure resists transverse stretching and how much its radial extent grows, while the plasma $\beta$ controls the overall size. Adding turbulent fluctuations perturbs the transverse structure and can transport axial field outward, but the radial velocity profile and radial size increase remain coherent.

Load-bearing premise

The results assume a static, unperturbed flux rope that suddenly starts expanding at 30 solar radii, so whatever internal dynamics the cloud developed earlier, and any interaction with the ambient magnetic field or a sheath, are absent.

Editorial extensions

If this is right

  • Magnetic clouds with small $\epsilon_0$ (slow propagation relative to internal Alfvén speed) should show the strongest radial expansion and an aspect ratio that levels off, while fast clouds should stay closer to the kinematic, mostly transverse expansion.
  • The radial head-tail velocity profile and radial size growth should survive in the presence of turbulence; only the transverse structure is significantly eroded, so single radial cuts through the cloud still look like expanding flux ropes.
  • Estimates of the local expansion parameter $\zeta$ and the global radial-size exponent $\alpha_R$ should both decrease as $\epsilon_0$ increases, and $\alpha_R$ should stay below unity for the parameter range studied.
  • When the internal Alfvén time is much shorter than the expansion time, the decay exponent of the peak magnetic field, $\alpha_B/2$, is a workable proxy for the radial-size exponent $\alpha_R$.

Reading between the lines

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

  • One consequence the authors leave implicit: $\epsilon_0$ could serve as a classification axis for in-situ magnetic-cloud catalogs, separating slowly expanding, well-connected clouds from fast, kinematically dominated ones, and this could be tested with existing multi-event datasets.
  • Because the mechanism is geometric, it should act on any magnetic structure in spherical expansion, not just this particular equilibrium; a direct test would be to repeat the runs with a force-free flux rope and check that the radial head-tail profile still emerges.
  • The abrupt switch-on at 30 solar radii is an idealization that likely overestimates the transient imbalance phase; a run that starts closer to the Sun or ramps the expansion gradually would show whether the 1 AU radial sizes and $\alpha_R$ exponents shift upward toward the observed upper range.
  • The turbulence results suggest a sharpening prediction: for $\epsilon_T = t_\mathrm{NL}/t_\mathrm{exp}$ near unity, turbulent eddies should be able to diffuse the axial field out to distances comparable to the cloud size, while for much smaller $\epsilon_T$ they cannot, and this could be checked by measuring magnetic coherence length versus cloud speed in situ.
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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. This paper uses expanding-box MHD simulations of a 2.5D cylindrical magnetic flux rope carried by a spherically expanding, unmagnetised solar wind to isolate the internal dynamics of a magnetic cloud. Starting from a static, pressure-balanced equilibrium at 30 R_sun, the authors find that the anisotropic spherical expansion alone perturbs the equilibrium, producing a radial head-tail velocity profile and a radial size increase, while magnetic tension resists transverse stretching. The non-dimensional expansion rate epsilon_0 = t_A/t_exp is proposed as the controlling parameter for radial growth and transverse resistance, the ambient plasma beta controls the overall size, and superposed turbulence is shown to disturb the transverse structure while leaving radial expansion approximately coherent. The results are compared with statistical 1 AU observations and with dimensionless estimates of the radial scaling exponent alpha_R and expansion parameter zeta.

Significance. If the central mechanism is correct, the paper provides a clean and useful organizing parameter, epsilon_0, for magnetic-cloud radial expansion and demonstrates numerically that spherical geometry alone can generate the observed radial expansion without sheath, shock, or ambient-field interaction. The study has clear strengths: a systematic parameter scan in epsilon_0 and beta_0, a quantitative force decomposition in Section 3.2, high-resolution turbulence runs, and an unusually candid list of limitations in Section 6.2. The qualitative picture is well supported by the reported fields, velocity maps, and size evolutions. However, the quantitative validation of the epsilon_0-dependence is not yet robust: the alpha_R fits include an initialisation transient for the runs that set the trend, and the zeta anti-correlation contains an explicit 1/epsilon_0 definitional factor. The quantitative claims therefore need a transient-free re-analysis before they can be regarded as established predictions.

major comments (4)
  1. [5.2, Fig. 15] The claimed anti-correlation between alpha_R and epsilon_0 is not yet established, because the fitting window a>2 includes the switch-on transient for exactly the runs that determine the trend. The paper itself states in Section 5.2 that for runs A4-A6 'we still get a transitional phase ... which leads to a systematic underestimation of alpha_R', and because epsilon_0 is varied by changing the propagation speed (Table 1), larger epsilon_0 also means less travel time to 1 AU, so the transient occupies a larger fraction of the sampled evolution. Please re-fit alpha_R using only the quasi-steady phase for each run, report the asymptotic late-time slope separately, and show that the anti-correlation survives this removal of the transient.
  2. [Eq. (25), Section 5.2] The reported zeta values are not independent evidence for the epsilon_0-dependence of the local expansion: Eq. (25) defines zeta with an explicit 1/epsilon_0 prefactor, so even a physical velocity slope Delta u_x/Delta x that is independent of epsilon_0 would produce an anti-correlation between zeta and epsilon_0. The paper acknowledges this in one sentence, but the subsequent conclusion that zeta is 'anti-correlated to epsilon_0 similarly to alpha_R' continues to rely on the definitional trend. Please quantify the separate contributions by reporting, for example, epsilon_0 * zeta = a Delta u_x/Delta x as a function of epsilon_0, and base the physical interpretation on the scaling of the velocity slope itself.
  3. [Sections 2.2 and 6.2] The abrupt switch-on of expansion at R0 = 30 R_sun from an exact static equilibrium is acknowledged in Section 6.2 as 'probably not very realistic' and as overestimating the duration of the dynamically imbalanced phase. This idealisation is load-bearing for all quantitative outputs: it biases the 1 AU radial sizes, the fitted alpha_R values, and the zeta estimates, and it weakens the comparison with observations in Table 2. A transient-free analysis, for example by initialising with a self-similar expansion profile or by explicitly demonstrating that the fitted exponents are stable when the transient interval is excluded, is needed before the reported exponents can be attributed to the long-term expansion mechanism rather than to the initialisation.
  4. [Section 5.1, Table 2] The statement that the comparison with the Salman et al. (2020a) Cat-III averages shows 'quite good agreement' overstates the validation. For all three representative runs the 1 AU values of <B>, <n>, and L_FR lie below the observed means, and <beta> = 0.25-0.30 falls outside the observed 0.1 +/- 0.1 range; only the expansion speed V_exp is consistent with the quoted dispersion. Please either quantify the agreement with uncertainties or explicitly present Table 2 as a consistency check in the lower-end parameter limit, rather than as validation of the central scaling claims.
minor comments (5)
  1. [Section 5.2] There is a typo in 'The values of zetaestimated from runs A2-A6'; it should read 'zeta estimated'. In addition, the reported alpha_R and zeta values are given without uncertainties, which makes the comparison with observed ranges such as alpha_R = 0.81 +/- 0.19 difficult to assess.
  2. [Section 2.1, Eq. (22)] The notation T_x and T_y in Eq. (22) is introduced without a formal definition; please define these as the magnetic tension terms and clarify which components of the tension are retained in the two coordinate projections.
  3. [Table 1] The table headers use superscripts a-d that are not explained in the caption; please add an explicit note that the superscripts refer to the equations listed below the table.
  4. [Appendix B] The dissipative terms are explicitly not derived from the MHD dissipative terms in the expanding frame, but this is stated only in the appendix. Since the turbulent spectral slopes in Section 4.1 may be affected by the dissipation model, this caveat should also appear in the main text where the spectra are interpreted.
  5. [Sections 6.1 and 5.1] Section 6.1 says that the simulations were 'validated' with 'quite good agreement', which is stronger than the nuanced discussion in Section 5.1; please harmonise the wording so the conclusions match the quantitative caveats.

Circularity Check

1 steps flagged · score 4.0 of 10

Partial definitional circularity in the ζ–ε0 anti-correlation; core expanding-box results are independent.

  1. self definitional [Section 5.2, Eq. (25) and following text]
    "ζ= ∆ux ∆x a ε0 ,(25) ... We find ζ=0.85 to 0.49 for runs A2 to A6 (ε0=0.2 to 3.2), anti-correlated to ε0 similarly to αR. ... We note that an intrinsic anti-correlation exists between ζ and ε0 by definition in Eq. (25), but the same reasoning as Sect. 3.4 holds: the radial expansion velocity scales more weakly with ε0 than does the available time."

    The expansion parameter ζ in Eq. (25) is constructed with an explicit multiplicative 1/ε0 factor. At a fixed observation distance a, any velocity-gradient term Δu_x/Δx that is independent of ε0, or grows more slowly than linearly, yields ζ decreasing with ε0; hence the reported anti-correlation of ζ with ε0 in Fig. 16 is partly an identity. The paper acknowledges this, and the residual content is the separate dynamical statement that Δu_x/Δx grows only as ~ε0^{1/2} (Sect. 3.4). Because the central validation narrative also invokes α_R (a direct fit to σ_x(a)) and the geometric ε0* = 2/π estimate, the definitional component is partial rather than total.

full rationale

The core derivation is self-contained: an exact static MHD flux-rope equilibrium (Eqs. 13, 14, A.1–A.5) is placed into the expanding-box MHD equations (Eqs. 5), whose anisotropic stretching terms are the only perturbation. The resulting radial push and transverse pull are diagnosed directly from force balances (Figs. 4, 5), and the dependence on ε0 is checked by varying ε0 across runs A2–A6 (Table 1). These are genuine simulation outputs, not fits to the target quantities. The critical rate ε0* = 2/π follows from the quarter-circle tension-communication estimate (Eq. 23), not from fitting. Self-citations (Papini et al. 2019, 2021 for the code and turbulence setup; Dong et al. 2014 for EBM variants) are methodological and are not load-bearing for the physical conclusions. The one partially circular element is the ζ–ε0 anti-correlation: Eq. (25) contains an explicit 1/ε0 factor, so part of the reported trend is definitional, and the authors explicitly note this. The α_R–ε0 anti-correlation is a genuine fit, though the paper flags that the a>2 window still contains the switch-on transient for runs A4–A6, and Section 6.2 concedes that starting from an unperturbed flux rope at R0 = 30 R☉ overestimates the imbalance phase. Those limitations affect robustness but are not circularity. Overall, partial definitional circularity in one supporting estimate; the main mechanism and parameter study remain independent.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claims rest on the EBM's anisotropic stretching picture (domain assumption), a static idealized flux-rope equilibrium, and several hand-chosen control parameters (epsilon_0, beta_0, twist ratio 1/2, fluctuation amplitude 0.5, dissipation coefficients). No new physical entities are introduced. The quantitative outputs (alpha_R, zeta, alpha_B) depend on the chosen fitting range a>2. These choices, rather than the physics of a particular event, should be kept in mind when reading the comparison with observations.

free parameters (6)
  • Non-dimensional expansion rate epsilon_0 = 0.2, 0.4, 0.8, 1.6, 3.2 (runs A2-A6; AR=1.0)
    Central control parameter, chosen by hand; claimed to organize the radial expansion behavior and the zeta, alpha_R trends.
  • Ambient plasma beta beta_0 = 0.6, 1.0, 2.0, 4.0 (runs B3, A3, C3, D3)
    Second control parameter; range limited by positivity of internal temperature profile.
  • Twist ratio B_theta,0/B_z,0 = 0.5
    Arbitrarily fixed; sets the magnetic pressure to tension ratio and hence the predicted critical epsilon_0* = 2/pi.
  • Initial turbulent amplitude delta_B/B_FR = 0.5 (runs Y3, Y3k, Y3h, Z3)
    Arbitrary choice, called 'strong turbulence'; partly controls the transverse spreading of axial field.
  • Dissipation coefficients mu, eta, kappa = 7.5e-5 to 2.0e-4 (scaled as a^-1 in turbulent runs)
    Ad hoc, not derived from MHD dissipation (Appendix B); used to increase effective resolution.
  • alpha_R fitting window lower bound a_min = 2
    Chosen to exclude the initial transient; acknowledged to bias high-epsilon_0 runs.
assumptions (5)
  • domain assumption Expanding box model (EBM) with anisotropic gradients and frictional terms correctly represents the internal dynamics of a parcel of plasma in a spherically expanding radial flow.
    Used to write Eqs. (5) and the scaling laws (7)-(10), after Grappin et al. (1993).
  • domain assumption The solar wind flow is spherical, uniform and non-magnetised, and the magnetic cloud propagates at constant radial speed U0.
    Section 2.2: 'we assume the plasma flow to be everywhere spherical ... and uniform ... non-magnetised'; limits applicability to shockless magnetic clouds.
  • domain assumption Local cylindrical symmetry: the flux rope curvature radius is much larger than its radial size, so partial_z = 0 and the dynamics is 2.5D.
    Section 2.2 introduces the 2.5D geometry and neglect of axial dynamics.
  • domain assumption The initial configuration is a static, stationary, axially symmetric equilibrium (Eq. 13) with uniform density.
    Section 2.3 sets the initial condition from which expansion starts; the paper notes this may not be realistic at R0=30 R_sun.
  • ad hoc to paper Dissipative terms act on rescaled fields with the same form as non-expanding MHD; this is not formally derived from MHD dissipative terms.
    Appendix B states 'the dissipative ones do not come from a formal derivation starting from MHD dissipative terms'.

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Cite this review

Pith. "Pith review of The effects of expansion and turbulence on the interplanetary evolution of a magnetic cloud." pith.science (2026). https://pith.science/paper/KELQYETY

@misc{pith2026250515527,
  author       = {Pith},
  title        = {Pith review of: The effects of expansion and turbulence on the interplanetary evolution of a magnetic cloud},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KELQYETY}},
  note         = {Machine review of arXiv:2505.15527}
}
read the original abstract

Coronal mass ejections (CMEs) represent the most extreme solar products, showing complex and dynamic structures when detected in situ. They are often preceded by a shock and carry a magnetic cloud organised as a flux rope, surrounded and permeated by turbulent fluctuations, and whose radial size expands during propagation. We investigate the internal dynamics of the 2D section of a cylindrical flux rope propagating at constant velocity in the spherically expanding solar wind, employing the expanding box model, which allows for high spatial resolution. Our setting is simplified, with uniform and non-magnetised solar wind, to which we superpose turbulent fluctuations. We find that the spherically expanding geometry alone perturbs the flux rope equilibrium, producing a radial head-tail velocity profile and a radial size increase. The ratio between the expansion and Alfv\'en timescales, associated respectively to propagation and internal crossing time, controls the resistance to transverse stretching and the increase of the flux rope radial extent; the plasma beta controls the overall size of the structure. Turbulent fluctuations mainly affect the flux rope transverse structure, spreading its axial field at distances comparable to its size; on the contrary, dynamics along the radial direction remains coherent and the increase in radial size is still consistently observed. We validate our results by comparison with statistical observations and dimensionless estimates, such as the expansion parameter and the radial size scaling exponent, suggesting that the ratio between internal and propagation timescales might help in better classifying different kinds of radial expansions for flux ropes.

Figures

Figures reproduced from arXiv: 2505.15527 by the authors.

Figure 1
Figure 1. Geometry and coordinate system for the expanding box model. We define x as the spatial coordinate along the mean flow (local radial coordinate), z as the local direction of the flux rope axis (along which the fields are assumed to be invariant), and y completes the right-handed system. The flux rope has an initial circular section. The position of the box is R(t), which increases with time as the flux rope propagate… view at source ↗
Figure 2
Figure 2. Initial configuration of the main plasma parameters for the ref￾erence run A3: the solid lines show respectively the axial out-of-plane magnetic field Bz (blue), poloidal in-plane magnetic field Bθ (violet), the kinetic pressure P (orange) and the passive scalar s as pinch tracer (grey), all as a function of the local radial coordinate r ′ . Bθ ′ (r ′ )eˆθ ′ and P = P(r ′ ). With such assumptions the condition for a… view at source ↗
Figure 3
Figure 3. Run A3: from top to bottom, evolution of magnetic field |B| (a), velocity ux (b) and uy (c) and density ρ (d). For |B| and ρ the fields’ decay with heliocentric distance has been compensated for better visualisation. The in-plane magnetic field is represented in panels (a-c) as constant-Az black lines, whereas the outermost boundary of the pinch tracer is represented in panel (d) as a white dashed line. All the quan… view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: Run A3: evolution of the main dynamical terms (solid and dashed blue lines), their resultant (black line) and the velocity field (orange dash-dotted line, different scale), along both x (left panels) and y (right panels). The 1D cuts are taken at half domain (i.e. they…
Figure 5
Figure 5. Figure 5: Run A3: evolution of the peaks of the dynamical terms with heliocentric distance, along x (left) and y (right). The peaks are computed inside the region of non-zero pinch tracer, in order to filter out the outward propagating shock front. The top panels show the absolu…
Figure 7
Figure 7. Figure 7: Time evolution of the maximum of ux and minimum of uy (both computed across a 1D cut passing through the axis, as in [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 6
Figure 6. Figure 6: Heliospheric evolution of the flux rope size estimates σx and σy (top panel) and the y-x aspect ratio (bottom panel) for runs A2, A3, A4, A5, A6, that is, increasing ε0. Lighter shades represent increas￾ing parameter values. Run A3 is represented as a dash-dotted line.…
Figure 8
Figure 8. Figure 8: Same as [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 9
Figure 9. Figure 9: Root mean square amplitude of fluctuations for runs Y3h (no ex￾pansion, left panel) and Y3 (ε0 = 0.4, right panel). Magnetic (green) and velocity (red) fluctuations are normalised to the average sound speed (magnetic fluctuations are expressed in Alfvén units before no…
Figure 10
Figure 10. Figure 10: Omnidirectional spectra of velocity and magnetic field (Eq (19)) as a function of the normalised wave-number for run Y3. Dif￾ferent times are shown as indicated in the colour bar. The spectrum corresponding to the flux rope is visible at k/k0 ≲ 6 in the magnetic spect…
Figure 11
Figure 11. Figure 11: Snapshots for successive times of the magnetic field for run Y3. The total magnetic field |B| is represented by the colour-coded map, and the in-plane magnetic field is shown with constant-Az black lines. Only a portion of the domain is shown, see text [PITH_FULL_IMA…
Figure 12
Figure 12. Figure 12: Maps of the in-plane magnetic field, Bpl = q Bx 2 + By 2 (left panels, colour coded) and of the two components of the velocity field, ux and uy (central and right panels, colour coded), at t = 16. The pinch tracer edge is drawn as a solid black line. Top and bottom re…
Figure 14
Figure 14. Figure 14 [PITH_FULL_IMAGE:figures/full_fig_p014_14.png]
Figure 13
Figure 13. Figure 13: Snapshot at t = 16.0 (a = 7.4) of the magnetic field for runs A3 (isolated flux rope), Z3 (with fluctuations smaller inside the flux rope by a factor 5), Y3 (with equal fluctuations amplitude everywhere). The axial field Bz is represented by the colour-coded map, wher…
Figure 15
Figure 15. Figure 15: Heliospheric evolution of the flux rope radial size S [AU] versus distance R[AU] for runs A2-A6. Only the range a > 2 (R > 0.29 AU) is considered, to avoid the first dynamical transient for most runs (even though it is still visible and important in runs A4-A6). The e…
Figure 16
Figure 16. Figure 16: Total magnetic field intensity |B| (top panel) and radial veloc￾ity ux (bottom panel) for runs A2-A6, along a radial cut through the flux rope axis, for the final times (R ≃ 1 AU). In the bottom panel, the peak of ux is drawn with markers (the same as in [PITH_FULL_I…

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