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Critique of the draft on 3D dust maps, grain sizes, and projected B-fields for CMB B-mode dedusting

The draft is a well-structured literature survey with several calculations that check out (the two-layer angle table, the $1-R^2$ residual arithmetic, and the small-angle $E\to B$ conversion). It is not a serious dedusting proposal. The leap from existing extinction cubes, mean grain models, and sparse starlight tomography to per-cent-level control of polarized dust at $r\sim10^{-3}$ is not supported by the data products it cites, and several of the load-bearing transfer functions are mis-specified.

1. Factual / physics errors

The single-region Stokes model is the thin-limit cartoon, not the radiative-transfer expression the rest of the paper needs. The draft writes

Polarization is perpendicular to $\mathbf{B}_\perp$, and $p\propto\cos^2\gamma$ is the standard leading factor if $\gamma$ is the angle between $\mathbf{B}$ and the plane of the sky. Two problems follow. First, total intensity itself depends on inclination: the unpolarized remainder grows as the field tips toward the line of sight, so the observed fraction is of the form $p=p_{\max}\cos^2\gamma/(1-\alpha p_{\max}\sin^2\gamma)$ (Fiege & Pudritz; Planck Int. XX / 2018 XII), not $p_0 F\cos^2\gamma$. That matters once Faraday RMs or Local Bubble geometries are invoked to supply $\gamma_i$, because $I$ and $P$ then do not share a common geometric factor. Second, $F$ is being asked to absorb imperfect RAT alignment, unresolved MHD tangling, and beam depolarization at once. Those are different operators on the Stokes vector and do not factor out of a frequency-dependent layer sum.

The $1-R^2$ residual is the wrong operational residual for modern component separation. The draft states that after “scaling a 353 GHz template to 150 GHz with the best single scalar” the leftover is $1-R^2\approx 2(1-R)$ of the 150 GHz dust power, and that a 30% amplitude layer with $\Delta\beta=0.3$ is “invisible to Planck” at $217\times353$ yet leaves $\sim0.7\%$ of 150 GHz dust, hence $\delta r\sim10^{-3}$. The two-layer algebra is correct for that toy estimator (I reproduced $\psi_{\rm eff}(353)=11.6^\circ$, $\psi_{\rm eff}(150)=9.2^\circ$, and $1-R^2\simeq0.7\%$). What is not correct is identifying that leftover with the residual of Commander, FGBuster, a BK-style multi-frequency likelihood, or a constrained ILC. Those methods already float $\beta_d$ (and often $T_d$) per pixel or per region, and they use more than two bands. The relevant residual is the component of the superposition that is orthogonal to the fitted parametric family, not the residual of a single scale factor. Quoting $1-R^2$ as the B-mode contamination therefore overstates the unmodelled power by mixing a 2014-style template extrapolation with 2018–2022 pipelines.

The coherent-rotation $E\to B$ formula is applied as if $\delta\psi$ were a sky-constant miscalibration. $\delta C_\ell^{BB}\approx 4\,\delta\psi^2 C_\ell^{EE}$ is the small-angle result for a global rotation (or a pixel-constant rotation inside a patch). Frequency-dependent angle from line-of-sight superposition is a spatially varying spin-2 field whose $E/B$ mixing has a kernel set by the coherence of the misalignment, not by $8\,\delta\psi^2$ times the local dust $BB$. Order of magnitude is fine; using “rotations of $1^\circ,2^\circ,3^\circ$ leave $0.2\%,1\%,2\%$ of dust $BB$” as a pixel-wise tax on $r$ is not.

“$\beta$ is a property of the material’s dielectric function” is overstated even in the Rayleigh limit. For $a\ll\lambda$, mass opacity is size-independent for a homogeneous grain, so a single dielectric function does set $\beta$. Millimetre $\beta$ in the ISM is also set by (i) two-level-system / disordered-charge physics (Meny et al. 2007, which the draft cites and then drops from the forward model), (ii) porosity and ice mantles, (iii) mixing of materials along the line of sight, and (iv) which part of a composite size distribution is warm enough to emit. The draft’s later claim that a 3D $R(V)$ map plus an alignment function converts $(\beta^I_i,T^I_i)$ into $(\beta^P_i,T^P_i)$ with a prior of width $0.1$ treats $\beta$ as if it were a grain-lab number. It is not.

Faraday rotation measures do not constrain dust-layer inclination $\gamma_i$. The draft lists Hutschenreuter et al. (2022) RM reconstructions as supplying “the line-of-sight component and hence the inclination $\gamma_i$ that sets $\cos^2\gamma_i$.” RM is $\propto\int n_e B_\parallel\,dl$. Dust emission is $\propto\int n_d B_\nu(T)\,dl$. The ionized and dusty volumes are not the same, the filling factors differ, and a single RM through a high-latitude sightline does not invert to per-cloud $\gamma_i$ for the Local Bubble wall versus an IVC. This is not a noisy version of the right observable; it is the wrong observable.

Galactic-field models are the wrong $\mathbf{B}$ for high-latitude dust. Unger & Farrar (2024)-style coherent disk/halo models describe the large-scale field that organizes cosmic rays and Faraday depth. High-latitude polarized dust at $\ell\sim80$ is dominated by the local, turbulent, bubble-wall field (the same Local Bubble literature the draft cites). Using a Galactic-field model for “more distant layers” does not give the POS angle of a 200 pc sheet.

Planck Int. L is summarized more sharply than the paper supports. “$R^{BB}_\ell(217\times353)\approx0.95$ at $\ell\approx50$–$160$ in low-column regions” is in the right ballpark for PIP-L’s most extreme patches, but PIP-L’s result was a statistical combination of regions with a column-density trend, later shown by Sheehy & Slosar (2018) and Planck 2018 XI to be consistent with noise and systematics. Planck 2018 XI’s actual statement is that if the large-region limit applies to small patches, “decorrelation might not be a problem for CMB experiments aiming at $r\simeq0.01$.” The draft’s “pointedly excludes the next generation” is editorial; the Planck paper did not quantify $r\sim10^{-3}$.

Minor factual nits. (i) “Dedusting is the PASIPHAE collaboration’s term” is territorial; the word is used in the CMB-foreground literature independently of PASIPHAE. (ii) Whittet & van Breda (1978) is $R_V\approx5.6\,\lambda_{\max}/\mu{\rm m}$, not $5.5$. (iii) LiteBIRD’s classic 15-band set is $40$–$402\,{\rm GHz}$; post-reformation documents quote $\sim34$–$448\,{\rm GHz}$ and a total $\delta r<0.002$ rather than $10^{-3}$. (iv) Vacher et al. (2022) used LiteBIRD frequencies from 100 to 402 GHz, not the full 15-band set, when they obtained $\sigma_r=8.8\times10^{-4}$. (v) The Clark & Hensley (2019) $r>0.75$ is a map-level $Q,U$ correlation with Planck; the power-spectrum correlation ratio is scale-dependent and already lower in $BB$ than in $EE$. None of these nits carry the argument, but they accumulate in a paper that is selling per-cent-level residuals.

The two-layer table, the Gaussian-scatter formula $R=\exp[-\frac12\sigma_\beta^2\ln^2(\nu_1/\nu_2)]$, the two-uncorrelated-layer formula, Planck 2018 XI/XII numbers ($\beta_d^P=1.53\pm0.02$, $T_d=19.6\,{\rm K}$, $p_{\max}\approx22\%$, $R_{P/p}\approx5.4\,{\rm MJy\,sr}^{-1}$), Planck Int. XXII ($\beta^P=1.59\pm0.02$, $\beta^I=1.51\pm0.01$, $21\pm6\%$ drop in $p$ from 353 to 70 GHz), BK18, Tristram et al. (2022), Vacher et al. (2022) $\sigma_r=8.8\times10^{-4}$, McBride, Bull & Hensley (2023) $>10\sigma$ bias, Edenhofer et al. (2024) (54 million stars, $1.25\,{\rm kpc}$, $14'$, 516 bins), Zelko et al. (2022) (500 million voxels, factor-of-two $\tau_{353}/E(B-V)$), Zhang & Green (2025), Pelgrims et al. (2021, 2024), and BICEP/Keck XVI are cited in line with the papers.

2. Missing physics

A Galactic-dust / CMB-foreground specialist would expect the following and did not get them.

Line-of-sight superposition is not the only source of $R_\ell<1$. Decorrelation in $C_\ell$ is produced by any spatial variation of the SED inside the mask, including pixel-to-pixel $\beta,T$ variation with a single layer per pixel. That piece is already the target of Commander $\beta,T$ maps, moment expansions (Chluba, Hill & Abitbol 2017; Vacher et al. 2022, 2023), and BK’s $\Delta_d$. Three-dimensional extinction cubes address a subset: discrete clouds along a sightline with misaligned $\psi_i$. The draft’s opening arithmetic (30% layer, $\Delta\beta=0.3$, $\delta r\sim10^{-3}$) is presented as if it were the generic foreground error. Planck 2018 XI found no evidence for decorrelation on large sky fractions; BICEP/Keck XVI found none in the BK field; Pelgrims et al. (2021) had to select multi-cloud, $\gtrsim60^\circ$-misaligned sightlines to see a 217–353 angle shift. The typical high-latitude sightline, especially at $|b|\gtrsim60^\circ$ where the Local Bubble wall dominates (Skalidis & Pelgrims 2019; Pelgrims et al. 2020; O’Neill et al. 2024), is closer to one effective layer. That is the opposite of the scare example, and it is not used to reweight the $\delta r$ budget.

CIB in the intensity used to fit 3D $T,\beta$. Zelko et al. assign $T$ and $\beta$ per Bayestar voxel by matching five Planck/IRAS bands. At high latitude those bands are a large CIB fraction, even on large scales; on $10'$–$30'$ scales the CIB can dominate 353–857 GHz. The draft mentions CIB in the limitations list and then still treats “$T^I_i,\beta^I_i$ from the 3D emission fit” as the polarized-SED shape. Without a CIB-separated intensity model (HI-correlated dust, GNILC, or similar), high-latitude voxel temperatures are not dust temperatures.

The 500-million-voxel fit is grossly underconstrained. Five FIR maps at $5'$–$10'$ give a few million independent beams, not $5\times10^8$ independent $(T,\beta)$ pairs. Zelko et al. must regularize heavily in distance and angle. Per-layer SEDs are interpolated, not measured. The draft never says this.

Polarized AME and dust–synchrotron correlation. Planck Int. XXII and 2018 XI both discuss a low-frequency rise in the dust-correlated polarization SED and a measurable dust–synchrotron correlation. The draft’s forward model is CMB + synchrotron + layered dust, with polarized AME declared “outside the dust model but inside the same bands” in one sentence. For LiteBIRD’s 40–90 GHz channels that is inside the likelihood, not a footnote. A 3D dust model does not automatically protect $r$ from a spinning-dust or correlated-synchrotron residual.

HI is not dust. Gaussian components in HI4PI (Panopoulou & Lenz 2020) are velocity peaks, not emitting slabs with a single $T,\beta,\psi$. At high latitude the distance–velocity relation is weak; IVCs can sit at very different distances from LVCs with similar $v_{\rm LSR}$. Molecular and ionized gas are missed. BICEP/Keck XVI explicitly found no IVC contribution in the BK field and no filament/non-filament decorrelation — a field-specific null that the strategy section does not metabolize.

Optical dichroism versus submillimetre emission is not a scalar $R_{P/p}$. Starlight $q,u$ are cumulative dichroic extinction to the star; 353 GHz $Q,U$ are emission-weighted. $R_{P/p}$ cancels $\cos^2\gamma$ and $F$ only for a single cloud of fixed temperature and a grain population that is the same at $\lambda_{\max}$ and at $850\,\mu{\rm m}$. The draft itself says millimetre polarized emission is dominated by $a\gtrsim0.1\,\mu{\rm m}$ while $R(V)$ and $\lambda_{\max}$ mix $0.01$–$0.3\,\mu{\rm m}$. Layer-dependent $B_\nu(T)$ then makes $R_{P/p}$ layer-dependent. Planck 2018 XII’s near-constancy of $R_{P/p}$ is an integrated diffuse-ISM fact, not a per-cloud calibration.

Intra-layer MHD structure. Halal, Clark & Tahani (2024) is cited for LOS splitting; the same physics produces field tangling inside a 14′ voxel. A single $\psi_i$ per “layer” leaves a statistical $E/B$ and a high-$\ell$ decorrelation that no 3D extinction cube currently resolves. DustFilaments / MHD skies exist specifically because this term is not a discrete cloud sum.

Reionization versus recombination, full sky versus deep field. The $\delta r\sim10^{-3}$ scaling is a recombination-bump, clean-patch argument ($r_d\sim0.1$ at 150 GHz, $\ell\sim80$). LiteBIRD’s reionization bump ($\ell<20$) is full-sky, large-scale, synchrotron-bright, and includes intermediate latitudes where Edenhofer’s $1.25\,{\rm kpc}$ cube does not reach the disk. The draft notes the 1.25 kpc ceiling once and then proposes a LiteBIRD pixel fit with $N\le3$ as if the same 3D products applied.

Instrumental angle, bandpass mismatch, and cosmic birefringence are named in §5 and then not propagated into the error budget of §4. A predicted frequency-dependent dust angle is degenerate with a miscalibrated polarization angle and with isotropic birefringence. A wrong 3D prior on $\delta\psi(\nu)$ biases both $r$ and $\beta_{\rm biref}$.

What “grain size distribution” actually is. The question asks for the size distribution. What exists is: an average MRN/WD01/astrodust distribution on high-latitude sightlines, an empirical alignment function (Hensley & Draine 2023), and a 3D $R(V)$ map. There is no per-voxel $n(a)$, no per-voxel radiation field $U$, and no per-voxel gas density. Alignment thresholds in RAT theory depend on all three (Hoang & Lazarian 2016). The draft’s bullet “which layers polarize” assumes those quantities.

3. Overclaims

“Everything that produces frequency-dependent angles and SED curvature is now generated by the model rather than parametrized.” False. Intra-layer $T/\beta$ variance, TLS temperature dependence of $\beta$, magnetic-dipole emission, alignment variations, CIB in the intensity fit, missing dust beyond 1.25 kpc, and sub-beam tangling are not generated. They are either ignored or dumped into $\alpha_i$, $\delta\psi_i$, and a global $\Delta\beta^P$.

“The polarization problem then reduces to solving for $2N$ real amplitudes per pixel plus the CMB, a linear problem that current band counts can handle for $N\le3$ if the SED shapes are fixed.” If the angles are known, there are $N$ amplitudes, not $2N$. If the angles are free, $2N$ amplitudes of layers with $\Delta\beta\sim0.3$ and $\Delta T\sim4\,{\rm K}$ are nearly degenerate: the design matrix is ill-conditioned by the smallness of the SED difference, which is exactly why McBride, Bull & Hensley (2023) and Vacher et al. (2022) found extra parametric freedom to be degenerate with $r$. Band count does not fix a condition number set by $\Delta\beta\ln(\nu_1/\nu_2)$. The later remark that “conditioning comes less from the small SED differences than from the different $Q/U$ ratios of misaligned layers” is the same fact restated: you cannot separate the layers at one frequency, so the leverage remains the frequency-dependent weight, i.e. the small SED difference.

“A prior of width 0.1 on $\beta^P-\beta^I$ is far more constraining than what polarization data alone provide per pixel.” Planck Int. XXII already measured a mean offset $\approx0.08$. Planck 2018 XI’s $\beta^P=1.53$ versus typical $\beta^I=1.51$ is smaller. Hensley & Draine (2023) astrodust versus Guillet et al. (2018) THEMIS versus Draine & Fraisse (2009) silicate-only do not agree on the sign and frequency dependence of $p(\nu)$. A Gaussian of width 0.1 around an unsettled mean is the same prior already used in parametric pipelines; it is not new information from a size distribution.

“Starlight $q_i,u_i$ times $R_{P/p}$ gives that layer’s 353 GHz $Q_i,U_i$ directly; $\cos^2\gamma_i$ and $F_i$ cancel.” This is the Tassis & Pavlidou (2015) conversion, valid for one optically thin cloud with a universal $R_{P/p}$. It is not demonstrated per layer, not demonstrated at PASIPHAE’s high-latitude polarizations of a few tenths of a percent, and not compatible with a factor-of-two variation in $\tau_{353}/E(B-V)$ (Zelko et al. 2022) unless that variation is absorbed into a layer-dependent $R_{P/p}$ — which then reopens the amplitude $\alpha_i$ the draft wants to prior at “a few tens of per cent.”

The $\delta r\sim10^{-3}$ tax is used as a universal conversion. “Any un-modelled effect that leaves one per cent of dust $BB$ in the cleaned map produces $\delta r\sim10^{-3}$.” That holds only if the residual sits at $\ell\approx80$ in a patch with $r_d\sim0.1$ and is not marginalized. Planck XXX’s cleanest $N_{\rm side}=8$ pixels have $r_d$ consistent with $\sim0.03$ or lower; the BK field is $\sim0.02$–$0.2$ depending on the estimator. One per cent of $r_d=0.03$ is $3\times10^{-4}$. Conversely, on LiteBIRD’s 70% sky the same 1% residual is catastrophic. The table in §1 therefore cannot underwrite both SO/S4 deep fields and LiteBIRD reionization.

The “sanity check of the payoff” is an optimistic tail presented as a forecast. “If the 3D map shows one layer carrying 90% of the polarized column and the tomography shows the remainder misaligned by less than $20^\circ$, $|\delta\psi_{\rm eff}|\lesssim0.5^\circ$ … residual below $10^{-4}$ in $r$.” The arithmetic of that configuration is right. The 3D map does not show polarized column; it shows extinction. The tomography does not exist over the CMB patches. And the complementary configuration (the first row of the table) is sold in §2 as already $\delta r\sim10^{-3}$. A method whose residual spans $10^{-4}$ to $10^{-3}$ depending on quantities it cannot yet measure is not a control of the residual.

“With LiteBIRD and CMB-S4 data: joint fits with the structural priors, in which the data themselves refine $\alpha_i$, $\delta\psi_i$ and $\Delta\beta^P$.” This reintroduces the extra freedom §2.4 said was degenerate with $r$. External information only helps if the priors are tighter than the degeneracy. “Tens of per cent” on $\alpha_i$ and tomography-error priors on $\delta\psi_i$ at degree scale are not shown to be that tight.

“None of these gaps prevents the staged use described in section 4.” Risk maps and field selection from cloud counts (Pelgrims et al. 2021) are available today and are the one part of the program that does not overclaim. Calling the full per-layer forward model a “prior” for LiteBIRD/S4 without an end-to-end bias study is the overclaim.

4. Weak links in the pipeline

4.1 3D emission maps $\nrightarrow$ layer polarized SEDs

The chain is: Gaia extinctions $\to$ distance bins $w_i=A_{V,i}/A_V$ $\to$ Zelko-style $T_i,\beta^I_i$ from Planck/IRAS $\to$ polarized MBB per layer.

Breaks:

• Extinction is not emission. Zelko et al. find $\tau_{353}/E(B-V)$ varies by a factor of two. That is a 100% amplitude error, not a 10% $\alpha_i$ prior.
• Intensity-weighted $(T,\beta)$ is not the large-grain, aligned-grain $(T^P,\beta^P)$. Small/stochastically heated grains contribute to IRAS 100 $\mu{\rm m}$ and Planck 857 GHz and almost nothing to 150 GHz polarization.
• Distance resolution of parsecs at $14'$ does not make a voxel a single physical cloud. At 200 pc, $14'$ is $\sim0.8\,{\rm pc}$; at 1 kpc it is $\sim4\,{\rm pc}$. High-latitude sightlines often have one dominant wall plus a faint distant tail that 1.25 kpc may or may not capture.
• CIB, zodiacal light, and Planck zero levels sit in the same five bands used to infer $T_i$.
• “Decorrelation risk maps” from the number of extinction layers are useful for masking. They do not give the polarized weights. A dense, poorly aligned layer can dominate $A_V$ and not $\mathcal{P}$; that is supposed to come from grain physics, which is the next broken link.

4.2 Grain size distribution $\nrightarrow$ $\beta^P-\beta^I$, $p_i$, or $R_{P/p}(R_V)$

The chain is: 3D $R(V)$ (Zhang & Green 2025) $\to$ aligned-grain size via $\lambda_{\max}$ $\to$ RAT threshold $a_{\rm align}(U,n)$ $\to$ which layers polarize and the I-to-P SED offset.

Breaks:

• $R(V)$ is a one-parameter optical/NIR extinction-curve slope. Millimetre polarized emission is weighted to the largest aligned grains. The draft admits this in §5 and ignores it in §3.2’s five “helps.”
• $U_i$ and $n_i$ are not mapped. Volume density requires a path length through the cloud; a 3D extinction cube gives column per voxel, not $n_{\rm H}$ unless the sheet is resolved and the filling factor is unity. The Local Bubble wall may be a thin sheet; IVCs are not.
• Hensley & Draine (2023) argue for frequency-independent FIR $p$ (astrodust); Draine & Fraisse (2009) silicate-only has $p$ rising from $\sim3\%$ at $100\,\mu{\rm m}$ to $\sim15\%$ at 1 mm; Planck Int. XXII has $p$ falling $21\pm6\%$ from 353 to 70 GHz. The draft correctly calls this “not settled” and then uses it as a transfer function anyway.
• Laboratory millimetre opacities of realistic analogues are not in the model (the draft says so). Without them, $\beta(T)$ is a fudge factor, which is what modified-blackbody component separation already is.

4.3 Sky-projected B $\nrightarrow$ per-layer $\mathcal{P}_i(\nu_0)$

The chain is: starlight tomography (PASIPHAE / BISP-1 / TRIShUL) or HI fibres or Local Bubble models $\to$ $\chi_i$ $\to$ misalignment maps and starlight$\times R_{P/p}$ amplitudes.

Breaks:

• Published degree-scale tomography is 4 deg² (Pelgrims et al. 2024), at $(l,b)\approx(103.3^\circ,22.3^\circ)$, not a CMB deep field. PASIPHAE is in progress; high-latitude stellar polarizations are a few tenths of a percent; Uppal et al. (2025) need cloud polarizations $\gtrsim0.1\%$ and a few hundred stars. That is not a 14′ Stokes cube.
• Starlight behind the last usable star does not constrain more distant dust. At the Galactic poles the stellar density and the polarization S/N both collapse.
• HI-fibre angles (Clark & Hensley 2019) are a remarkable morphological prior at large scales, not a per-velocity-component $\psi_i$ at $\ell=80$ with the accuracy implied by an $8\,\delta\psi_i^2$ residual. BICEP/Keck XVI’s 10–65% correlation of the HI morphology template with the maps (dust+CMB+noise) is the relevant number for cleaning, not the abstract’s $r>0.75$.
• Velocity $\neq$ distance. McCallum et al. (2026) tying HI4PI to Edenhofer is a reconstruction, not a measurement, and is ambiguous at high latitude by construction.
• A single $\psi_i$ per layer ignores the tangling that sets $p$ and $E/B$ inside the layer (Planck 2018 XII’s $p$–$\mathcal{S}$ anticorrelation).

4.4 Combining the three does not make a well-posed CMB likelihood

The forward model

has, on paper, external $N,w_i,T^I_i,\beta^I_i,\psi_i,\mathcal{P}_i(\nu_0)$. In 2026 the only all-sky, CMB-resolution pieces are: a 1.25 kpc extinction cube, Planck 353 GHz (emission-weighted mean $\psi$), HI PPV morphology, and a mean grain model. The quantities that actually break the $r$–moment degeneracy — per-layer polarized amplitudes and angles at $\lesssim30'$ over the survey footprint — are the ones listed as “4 deg² published, PASIPHAE in progress” and “patchy, degree-scale.”

Predicted spin-moment templates ($\mathcal{W}_1^\beta=\sum_i\mathcal{P}_i(\beta_i-\bar\beta)$, etc.) inherit the phase of $\mathcal{P}_i$. Deprojecting a wrong-phase moment in a constrained ILC (Remazeilles, Rotti & Chluba 2021) removes the wrong mode and can increase the $r$ bias. The draft never discusses a mistemplated deprojection.

A BK-style cross-spectral prior $C_\ell^{ab}=\sum_{ij}\hat g_i(a)\hat g_j(b)\,C_\ell^{ij}$ replacing $\Delta_d$ is the most plausible near-term use. It is also a hard prior on a quantity the layer maps do not currently predict at the few-per-cent level. An incorrect $\Delta_d(\ell)$ shape is a coherent bias on $r$, which is worse than BK18’s empirical $\Delta_d$ with a few-per-cent envelope.

5. Referee demands

Before this is a dedusting proposal rather than a review of PASIPHAE-adjacent literature, require:

1. End-to-end $r$ bias, not a two-layer table. Inject a 3D polarized sky (DustFilaments, MHD, or a layered cube with the Edenhofer $w_i$ and a realistic $\psi_i$ error model). Run the proposed layered fit / moment-template ILC / BK likelihood at LiteBIRD, SO, and S4 noise. Report $\langle\hat r\rangle-r_{\rm in}$ and $\sigma(r)$ versus (i) a single MBB, (ii) free $\beta,T$ moments, (iii) the 3D prior with the actual 2026 data quality (not the table’s “status in 2026” column). If the 3D prior is tighter than free moments but biased, that is a fail.

2. A null test on the BICEP/Keck field. BK18 is consistent with $\Delta_d=1$; BK XVI finds no filament/non-filament or IVC decorrelation. The pipeline applied to that field must recover $\Delta_d\approx1$ and not inject a $\delta r\sim10^{-3}$ correction. Pelgrims-style target/control splits should be repeated inside the BK mask.

3. Error propagation from each ingredient, separately. Monte Carlo: $\sigma(\psi_i)$, $\sigma(w_i)$, $\sigma(\beta^I_i)$, scatter in $R_{P/p}$, CIB in $T_i$. Plot residual $BB$ at 150 GHz and $\delta r$ against each. In particular, show the $\delta\psi_i$ that PASIPHAE actually delivers at high latitude (few $\times0.1\%$ polarizations, degree-scale pixels) and the corresponding $8\,\langle\delta\psi^2\rangle$ leakage. Do not quote the 90%/20° optimistic case as the payoff.

4. Condition numbers. For $N=2,3$ layers with $\Delta\beta\in[0,0.3]$, $\Delta T\in[0,4]\,{\rm K}$, $\Delta\psi\in[0^\circ,90^\circ]$, publish the condition number of the linear amplitude system at LiteBIRD and SO band sets. If it is $\gtrsim10^2$ for realistic $\Delta\beta$, the “linear problem current bands can handle” sentence comes out.

5. CIB-cleaned 3D $T,\beta$. Repeat Zelko et al. after subtracting a CIB model, or fit only the HI-correlated intensity. Show that high-$|b|$ voxels still have a constrained $T_i$. If they do not, drop “layer SEDs from intensity” from the polarization pipeline.

6. Per-layer $R_{P/p}$, not the Planck XII mean. Using the 4 deg² Pelgrims et al. (2024) tomography plus Planck 353 GHz, measure $P_i/p_i$ per cloud. If the scatter is larger than the “tens of per cent” $\alpha_i$ prior, the starlight$\to$353 GHz transfer is not a calibration.

7. Split the science case. Separate forecasts for (a) SO/S4 recombination bump on a high-latitude deep field, where a Local Bubble wall plus HI fibres might actually be enough, and (b) LiteBIRD reionization on $f_{\rm sky}\sim0.7$, where 1.25 kpc, degree-scale tomography, and synchrotron/AME dominate. Do not use $r_d\sim0.1$ at $\ell=80$ as the conversion for both.

8. Foregrounds that are not layered dust. Polarized AME (even as an upper limit), spatially varying $\beta_s$, and the Planck 2018 XI dust–synchrotron correlation must sit in the same likelihood. A 3D dust model that ignores them can still bias $r$ at $10^{-3}$.

9. Mistemplated moment deprojection. Show what happens when the predicted $\mathcal{W}_1$ map has a 20° phase error or a missing cloud. Constrained ILC is not conservative with respect to template error.

10. Do not replace $\Delta_d$ with a hard $C_\ell^{ij}$ prior until the predicted 217×353 $R_\ell$ matches Planck 2018 XI (large sky) and Pelgrims et al. 2021 (selected sightlines) and BK16 (deep field) simultaneously. Those three data sets currently tell different stories; a single 3D model has to fit all three or the prior is selecting the answer.

11. State the residual floor from intra-layer turbulence with an MHD or DustFilaments simulation degraded to Edenhofer + degree-scale $\psi$. That floor is the number to compare with $\delta r\sim5\times10^{-4}$, not the two-cloud table.

12. Birefringence. Any claimed frequency-dependent dust angle must be shown not to bias isotropic cosmic birefringence at the $0.05^\circ$–$0.3^\circ$ level currently under discussion, or the dust model is a cosmological systematic of a different kind.

6. Severity list

• blocker — Treating $1-R^2$ from a two-frequency scalar template as the residual of parametric / ILC component separation, then converting 0.7% of 150 GHz dust into a generic $\delta r\sim10^{-3}$.
• blocker — Forward model that claims per-layer $(\beta^P,T^P,\mathcal{P}_i,\psi_i)$ are supplied externally, while the only all-sky polarized constraint is the 353 GHz emission-weighted mean and 4 deg² of tomography.
• blocker — “Everything that produces frequency-dependent angles and SED curvature is now generated by the model rather than parametrized.”
• blocker — No end-to-end $r$-bias demonstration; the proposal is a ingredients list.
• major — Intensity 3D $T,\beta$ (Zelko) cannot be used as polarized layer SEDs at high latitude without CIB control and without a demonstrated extinction$\to$emission conversion better than the observed factor-of-two scatter.
• major — $R_{P/p}$ and $\cos^2\gamma,F$ cancellation presented as a per-layer amplitude calibration; they are an integrated diffuse-ISM correlation.
• major — Grain-size / $R(V)$ / RAT chain used to pick which layers polarize and to set $\beta^P-\beta^I$ to $\pm0.1$, despite the draft’s own admission that millimetre grains, alignment physics, and competing dust models are unsettled.
• major — Faraday RMs and Galactic-field models listed as sources of per-layer $\gamma_i$ and distant-layer $\chi_i$.
• major — Ill-conditioned $N\le3$ linear fit sold as well-posed because LiteBIRD has 15 bands; degeneracy is set by $\Delta\beta$, not by band count (the draft’s own §2.4).
• major — Re-introducing $\alpha_i,\delta\psi_i,\Delta\beta^P$ as free parameters “refined by the data” after arguing that extra freedom is degenerate with $r$.
• major — Conflating LOS decorrelation on Pelgrims-selected sightlines with the sky that SO/S4/BK actually observe, where BK XVI found no decorrelation and the Local Bubble wall is one dominant layer.
• major — Single $\delta r\sim10^{-3}\leftrightarrow 1\%$ dust-$BB$ conversion applied to both clean-patch recombination science and full-sky reionization science.
• major — Predicted spin-moment templates / hard $C_\ell^{ij}$ priors without a mistemplate study; a wrong phase is a coherent $r$ bias.
• major — Polarized AME and dust–synchrotron correlation omitted from the working model.
• minor — $P=p_0 F\cos^2\gamma\,I$ omits the inclination dependence of $I$.
• minor — Coherent-rotation $E\to B$ formula used for a spatially varying LOS effect.
• minor — “Dedusting is PASIPHAE’s term”; $R_V=5.5\lambda_{\max}$ vs 5.6; LiteBIRD 40–402 vs 34–448 and $\delta r<10^{-3}$ vs $<0.002$; PIP-L $R\approx0.95$ as a single number.
• minor — Clark & Hensley $r>0.75$ quoted without the scale dependence of the $BB$ correlation ratio.
• minor — Intra-layer tangling acknowledged in §5 and absent from the residual floor in §4.3.

The usable core of the draft is narrower than the title: 3D extinction and HI cloud counts are already a field-selection and masking tool (Pelgrims et al. 2021), and PASIPHAE-like tomography is the right external observable for the spin-2 part of LOS decorrelation, which no extra MBB parameter can represent. Grain size distributions and 3D emission $T,\beta$ cubes, at current fidelity, do not close the polarized SED. Until the blocker items are replaced by a pipeline with a measured $r$ bias, this is a research program, not a dedusting method.