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Critique of “Three-dimensional, grain-aware magnetic modeling of polarized dust for CMB $B$-mode cleaning”

The draft’s organizing picture is the standard one: polarized dust is a line-of-sight vector sum; frequency decorrelation of $Q,U$ requires both SED differences and misaligned plane-of-sky fields; 3D structure, grain physics, and $B_{\rm POS}$ are the three ingredients of that sum. That skeleton is not the problem. The problem is that the draft repeatedly treats those ingredients as if they supplied the actual degrees of freedom that bias $r$, cites the wrong papers for the claims that would make that leap, and never shows that the ancillary data exist, at high latitude, at the precision a next-generation $B$-mode analysis would need.

1. Factual / physics errors

Wrong paper, wrong journal, and a claim the cited paper does not make. The closing physical moral is:

“A single MBB does not necessarily become unusable whenever several temperatures exist: finite-band data may be insensitive to the resulting curvature, and simulations find that it can remain approximately unbiased in the absence of polarization-angle mixing. The structural failure occurs when no common real scaling of $Q$ and $U$ exists (Sponseller & Kogut 2023).”

The URL points to MNRAS 519, 4370 (2023). That article is McBride, Bull & Hensley, Characterizing line-of-sight variability of polarized dust emission with future CMB experiments (arXiv:2207.14213). Sponseller & Kogut is a different paper: Mitigating Bias in CMB B-modes from Foreground Cleaning Using a Moment Expansion, ApJ 936, 8 (2022), arXiv:2207.13109.

The scientific mismatch is worse than a swapped author list. McBride et al. find that a per-pixel two-parameter MBB generally returns unbiased CMB Stokes $Q,U$ in that pixel unless both the dust SED and the polarization angle vary along the line of sight. Sponseller & Kogut, using Planck temperature maps to estimate line-of-sight $T_{\rm d}$ variations, find that the bias on $r$ from those variations is significant compared with future experimental targets, and that moments are needed to reduce it. The draft therefore (i) misattributes the two-condition pixel-level result, and (ii) states a conclusion that the paper it named actually argues against, if “unbiased” is read as unbiased $r$. Pixel-level $Q,U$ recovery and power-spectrum $r$ are not interchangeable: spatially varying effective SEDs, extra variance, and $E/B$ leakage can still bias $r$ after per-pixel amplitudes look acceptable. That conflation is a physics error, not a bibliographic nit.

Moment-expansion papers are conflated. The draft writes a map-level complex expansion

with ${\cal M}_\beta\propto\sum_i A_i(\beta_i-\bar\beta)e^{2i\psi_i}$, and cites Mangilli et al. 2021 (arXiv:1912.09567) and Vacher et al. 2022 (arXiv:2111.07742) for both the formalism and the statement that “omitted $\beta_{\rm d}$ and $T_{\rm d}$ moments can bias $r$ at next-generation sensitivities.” Those are three different results:

• Mangilli et al. 2021 expand total-intensity power spectra. They state explicitly that polarized data do not yet have the sensitivity for the same analysis.
• Vacher et al. 2022, A&A 660, A111 (the cited arXiv) expand $BB$ cross-spectra in $\beta$ and $T$ for LiteBIRD-like simulations of spatial SED variation. The moments there are not complex map-level spin-2 objects, and the $r$ bias they report does not require line-of-sight angle mixing.
• The complex, angle-weighted map-level moments are Vacher et al., A&A 669, A5 (2023) / arXiv:2205.01049 (High precision modeling of polarized signals: Moment expansion method generalized to spin-2 fields), which is not cited.

The formula as written is the spin-2 expansion; the $r$-bias simulations cited are the power-spectrum expansion without the $e^{2i\psi}$ structure. “Magnetic tomography constrains their complex phases” is therefore attached to papers that do not have complex phases.

“Vector radiative-transfer model.” The closing sentence claims the three ingredients replace a phenomenological decorrelation parameter with “a physically structured vector radiative-transfer model.” At CMB frequencies and high Galactic latitude the millimetre dust optical depth is $\tau\sim10^{-3}$ or smaller. Polarized emission is an optically thin line-of-sight integral of emissivity with geometric factors, not a vector RT problem (no millimetre dichroic extinction, no multiple scattering). Calling the layer sum “vector RT” inflates a Stokes integral into a method that is not being used and is not needed.

Planck $T_{\rm d}\simeq19.6\,{\rm K}$ is not a polarized measurement. “Planck found that a single MBB with $T_{\rm d}\simeq19.6\,{\rm K}$ and mean polarized spectral index $\beta_{\rm d}^{P}\simeq1.53$ described its broad-region frequency spectra reasonably well” is easy to read as a joint polarized fit. Planck 2018 XI (A&A 641, A11, 2020) fixes $T_{\rm d}=19.6\,{\rm K}$ from intensity and then fits $\beta_{\rm d}^{P}=1.53\pm0.02$. Polarization from 353 GHz down is close enough to Rayleigh–Jeans that $T_{\rm d}$ is not independently measured in $P$. The number is conventional, not a polarized constraint, and using it as a layer temperature prior is exactly the intensity-to-polarization transfer the grain section warns against.

Layer equation double-counts geometry if $p_i$ is an observed fraction. The sum

is consistent only if $p_i$ is an intrinsic (maximum) polarization fraction. If $p_i$ is the layer’s observed $P/I$, $\cos^2\gamma_i$ is already in it. The later data model repeats the problem: $S^P_{bi}(\boldsymbol\theta_i)$ already includes the alignment function $R_m(a)$, while $g_i$ is said to include “inclination, alignment and sub-beam depolarization.” Alignment is then in both factors. This is bookkeeping, but it matters as soon as one tries to put starlight, HI, and microwave $p$ on the same parameters.

Starlight angle vs emission angle in the pipeline. The introduction correctly states that emission $\psi$ is perpendicular to $B_{\rm POS}$ and that starlight polarization is rotated by $\sim90^\circ$. The pipeline then says: assign each layer a projected angle $\psi_i$ from “starlight-polarization tomography, HI morphology and high-frequency polarization.” PASIPHAE/BISP-1 (Pelgrims et al. 2023) infers the plane-of-sky field orientation, not the emission polarization angle. HI filaments are also a $B_{\rm POS}$ tracer. If those angles are copied into $e^{2i\psi_i}$ without the $90^\circ$ rotation, $Q$ and $U$ flip sign. The draft never writes the conversion in the actual model.

“One column of the mixing matrix.” A single MBB per pixel with fitted $(T_{\rm d},\beta_{\rm d})$ is a nonlinear component, not one mixing-matrix column. Linear methods (SMICA, NILC) get a rank-1 dust column only if the SED is spatially uniform. The failure mode under discussion is precisely that dust is not rank-1. Stating the simple model as “one spectral degree of freedom, or one column” mixes parametric and linear language and understates how current pipelines already treat dust.

Poh & Dodelson are not the same paper as Tassis & Pavlidou. Tassis & Pavlidou 2015 state the two-condition mechanism (changing polarized-intensity ratio and misaligned fields). Poh & Dodelson 2017 (PRD 95, 103511) is a Monte Carlo of temperature variations away from the Rayleigh–Jeans limit as the source of that changing ratio, and they quantify an $r\lesssim0.0015$ threshold. Grouping them as jointly “emphasizing this two-condition mechanism” is roughly right on physics and sloppy on what each paper actually computed. Poh & Dodelson’s $r$ number, which is the relevant experimental scale, is not used anywhere in the draft.

2. Missing physics

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

Plane-of-sky / beam mixing is a second, independent decorrelation channel. The draft’s theory section is almost entirely line-of-sight clouds. Power-spectrum $\rho_\ell^{BB}(\nu_1,\nu_2)<1$ is also produced by SED variations across the beam or the analysis region at a single distance. Planck Intermediate Results L already noted that either spatial SED variation or polarization-angle variation can mimic the 217–353 GHz correlation-ratio signal. Ritacco et al. 2023 (A&A 672, A21) detect residual $EE$ after subtracting a mean-SED-scaled 353 GHz template and fit those residuals with first-order MBB moments — a POS/spatial effect, not a tomographic one. 3D extinction maps do not automatically control intra-beam grain or temperature variations. The moment expansion later in the draft is in fact the standard tool for that POS mixing, which is why attaching it only to the layer model is misleading.

The column-density trend in the Planck decorrelation analyses is omitted. Both Planck Int. L and the PR3 re-analysis in Planck 2018 XI found that the apparent 217–353 GHz decorrelation increases toward lower column density (and higher $\ell$). PR3 concluded it was not significant against systematics, but the trend is exactly the regime of $B$-mode patches. The draft’s “not a universal scalar coefficient” is fair; leaving out that the worry is largest where $r$ is measured is not.

The BICEP/Keck field already has a layer-resolved HI test. BICEP/Keck XVI (ApJ 945, 72, 2023) correlates BK and Planck polarization with HI-filament morphology templates, splits velocity components (local Galactic vs Magellanic Stream I), detects filamentary dust polarization down to 95 GHz, measures $\beta=1.54\pm0.13$ for that component, and finds no evidence for LOS frequency decorrelation from IVC inclusion or from filaments vs the rest of the dust in that patch. That is the closest existing implementation of the draft’s strategy on the sky that currently sets the $r$ limit. Omitting it leaves the proposal sounding more novel, and more necessary, than the observational record is.

Silicate vs carbonaceous alignment, not $dn/da$, is the leading grain-physics lever for polarized SEDs. Draine & Fraisse 2009 and Guillet et al. 2018 are cited, correctly, for $P$-vs-$I$ SED differences and degeneracies. What a specialist would then name is: (i) radiative torque alignment with a size cutoff $a_{\rm align}({\cal U},n_{\rm H},B)$; (ii) inefficient alignment of carbonaceous grains vs silicates, which is the usual explanation of $\beta_{\rm d}^{P}\neq\beta_{\rm d}^{I}$ and of $p(\nu)$; (iii) magnetic dipole emission from ferromagnetic inclusions (Draine & Hensley 2013; Hensley & Bull 2018), which can further split the polarized millimetre SED. Planck 2018 XI measured $\beta_{\rm d}^{P}-\beta_{\rm d}^{I}=0.05\pm0.03$. The draft never uses that measurement, never names RATs, and never treats two-material alignment as the default polarized-dust model. Size distribution enters mainly as the alignment cutoff and as $T_{\rm eq}(a)$, which the draft does say, but then the pipeline still lists $dn_m/da$ as a recoverable layer parameter.

Fanciullo et al. 2017 is the wrong environment. That paper concerns molecular clouds and translucent sightlines ($\lambda_{\rm max}$, $P_{353}/p_V$). CMB $B$-mode fields are high-latitude atomic gas. Grain growth, ice mantles, and dense-gas alignment physics do not carry over. Using it to argue that “size changes alone could not explain” millimetre polarized SEDs on $B$-mode sightlines overstates the evidence.

High-latitude 3D geometry is Local Bubble plus a few clouds, and HI velocity is not distance. Most of the polarized dust at $|b|\gtrsim50^\circ$ lives in the Local Bubble wall ($\sim100$–$200\,{\rm pc}$) plus a small number of more distant clouds. Gaia/Bayestar-type maps (the draft cites only Green et al. 2019) historically had poor distance resolution in the nearest hundred parsecs; later GP reconstructions (Leike & Enßlin; Edenhofer et al.) exist and are not mentioned. At high latitude, Galactic rotation does not assign distances to HI channels. HI is a cloud counter and a $B_{\rm POS}$ morphology tracer (Clark, Peek, Pelgrims), not a 3D emission cube. The limitations list says “HI velocity is not always a unique distance indicator”; the strategy section still partitions layers with “HI or molecular velocity components” as if that were tomography where $r$ is measured.

PASIPHAE is a method plus a survey, not an all-sky magnetic cube. Pelgrims et al. 2023 is a Bayesian inversion (BISP-1) demonstrated on mocks and on a limited existing stellar-polarization set. It is not a full-sky, layer-resolved $B_{\rm POS}$ map. High-latitude stellar polarization is sparse and at $p\sim0.1\%$. The draft writes as if the tomography were an available prior.

No quantitative $r$ target. LiteBIRD’s design goal is $\sigma(r)\sim10^{-3}$; CMB-S4 is similar; BICEP/Keck already works at a few $\times10^{-2}$ and includes a dust-decorrelation parameter in the multi-frequency likelihood. Poh & Dodelson estimated LOS extrapolation noise becoming important for $r<0.0015$. Vacher et al. 2022 needed both $\beta$ and $T$ moments to unbias LiteBIRD-like $r$. None of these numbers appear. Without them, “help dedusting” has no metric.

Dust $EB/TB$, $EE/BB$, and frequency-dependent $E\leftrightarrow B$ from angle rotation. The draft lists $EB$ and $TB$ as validation spectra. It does not say that dust already has $EE/BB\sim2$, $\alpha_{EE}\neq\alpha_{BB}$, and a positive $TB$ (Planck 2018 XI), nor that a frequency-dependent polarization angle rotates $E$ into $B$ (Vacher et al. 2023b / 2025). Those are the observables that would actually diagnose the mechanism, not generic “cross-correlations with layer-resolved templates.”

How current pipelines would ingest the priors is unspecified. Commander, SMICA, NILC/cILC, FGBuster, moment-ILC (Remazeilles), and the BICEP/Keck Hamimeche–Lewis multi-component likelihood are never named. “Fitted jointly and hierarchically” is not a method.

Statistical GMF models are not per-sightline templates. Vansyngel et al. 2017 and related layered turbulent GMF models match Planck $EE/BB/TE$ statistically. A “regular-plus-turbulent Galactic magnetic-field model,” listed as a data source, does not predict the cloud-to-cloud $\psi_i$ that cause decorrelation. Turbulence on the cloud scale is the signal; the regular field is not.

3. Overclaims

From data products to a constrained mixing model. The central overclaim is the pipeline itself: partition every line of sight into layers; infer layer-level

assign $\psi_i$ and inclination; then either subtract the posterior mean dust or marginalize it jointly with $r$. No existing data set determines $dn_m/da$, shape, or $R_m(a)$ per high-latitude cloud. Extinction curves at $A_V\sim0.01$–$0.1$ are noisy; polarized extinction to a star is an integral, not a layer SED; millimetre experiments have $\mathcal{O}(10)$ bands, not tens of grain parameters. The draft’s fallback — “a library of physical SEDs… principal components, or… priors on $(T_i,\beta_i)$” — is the only operational proposal, and it is just a physically motivated moment expansion. That is not what the bold sentence “where and how much / how each layer emits / in which Stokes direction” promises.

“Replace an uncontrolled, phenomenological decorrelation parameter.” A phenomenological $\rho_\ell$, $\Delta\beta$, or first-order moment, given a wide prior, is conservative. A tight grain-model or 3D-extinction prior that is wrong is not. The draft itself says “incorrect priors can themselves bias $r$.” The closing paragraph then asserts that the value of the three ingredients is to replace the phenomenological parameter with a physical model “whose degrees of freedom can be constrained, validated and marginalized.” That replacement is an overclaim until someone shows that the physical priors are both informative and calibrated on the residual $r$ they induce when they are misspecified. The draft never does that comparison.

Martínez-Solaeche, Karakci & Delabrouille 2018 are cited as if they showed that 3D information helps cleaning. That paper is a simulated 3D polarized-dust sky (density, $T_{\rm d}$, $\beta_{\rm d}$, small-scale polarization) constrained to match 2D Planck maps, for use as a component-separation testbed. It does not ingest Gaia cubes, grain-size data, or starlight tomography, and it does not demonstrate a reduction in $r$ bias from those products. “Already demonstrate how such information generates more realistic component-separation tests” is true only of simulations, not of dedusting.

PASIPHAE / 3D dust / grain size as if they were on the sky now. Green et al. 2019 is a 2D-integrated reddening cube, not millimetre emissivity. Grain-size distributions in the literature (MRN, WD01, THEMIS, astrodust) are Galactic averages, mostly from extinction and FIR, not layer-resolved, and not specific to the high-latitude atomic ISM. Starlight-polarization tomography at PASIPHAE depth is a future (or at best partial) data set. Writing a “concrete three-component dedusting strategy” in the present tense overstates readiness.

Identifying “low-risk fields dominated by a single nearby structure” is asserted, not shown. This is the most defensible near-term use of 3D maps, and the draft lists it in one bullet. It is not carried through: no criterion (contrast in $A_i$, $\Delta\psi_i$, predicted $\partial\psi/\partial\nu$), no comparison with the BICEP/Keck patch (where BK-XVI found no LOS decorrelation), no statement of how a “low-risk” mask would be propagated into an $r$ likelihood.

4. Weak links in the pipeline

3D “thermal-dust emission” maps do not give millimetre $A_i$ or $s_i(\nu)$. The draft is honest that Gaia products are stellar reddening. The conversion $\kappa_{\rm mm}/\kappa_V$ depends on composition, size, $R_V$, and radiation field — the same grain unknowns the second ingredient was supposed to supply. Using 3D extinction to set layer amplitudes therefore couples the first and second ingredients instead of constraining them separately. CIB fluctuations in faint $I$ maps, also mentioned, mean that even the 2D millimetre intensity prior is not a clean dust column at high latitude. After that conversion, one still has no $Q,U$.

Layer partition is not identified by the microwave data. “The number of statistically independent layers should be selected or regularized; it cannot exceed what the frequency data can support.” With $\sim10$–15 bands, CMB, synchrotron (with curvature), and one dust MBB already use much of that budget. A second cloud with free $(A,T,\beta,p,\psi,\gamma)$ is typically not a microwave-only detection. The 3D/HI/starlight data must do the partitioning. At high latitude they often cannot: reddening is weak, stellar sampling is sparse, and HI velocity is degenerate. The pipeline’s first step fails in the fields that matter, which is why Pelgrims et al. 2021 had to preselect multi-cloud, misaligned sightlines to see a 217–353 GHz angle effect.

Grain-size knowledge does not pin $\beta_i$ or the polarized SED of a layer. The draft’s own Rayleigh-limit paragraph is correct: at $\lambda\gtrsim1\,{\rm mm}$, $C_{\rm abs}\propto a^3$ times a dielectric factor, so $\beta$ is a material/structure index. Size still affects $T_{\rm eq}(a)$ and $R(a)$. That is not enough to generate $S^P_{bi}(\boldsymbol\theta_i)$ per cloud. Optical constants, porosity, iron, and which material is aligned are degenerate (Guillet et al. 2018). A library of Galactic-average SEDs reintroduces a global prior that may be wrong for a given high-latitude cloud (different radiation field, different size cutoff). The microwave data then update $(T_i,\beta_i)$ in the usual way; the grain model has not broken the degeneracy, it has hidden it in the library.

A 2D projected field is the quantity being modelled, not an external constraint. “An ordinary two-dimensional field map gives only the net line-of-sight orientation — the quantity that changes under decorrelation.” High-frequency dust polarization is that net orientation at that frequency. Using 353 GHz $\psi$ as a magnetic prior for cleaning 353 GHz is circular. Starlight and HI can be external, but they weight the column by optical extinction and by atomic gas, not by millimetre polarized emissivity; the draft notes the weighting mismatch in the limitations and then uses those tracers as $\psi_i$ priors anyway. Inclination $\gamma_i$ is not measured by any of the listed tracers (starlight, HI morphology, 353 GHz all see $B_{\rm POS}$). $g_i\propto\cos^2\gamma_i$ therefore remains a free depolarization factor, i.e. a free polarized amplitude, which is what a 353 GHz template already provides.

Moment compression drops the 3D information the first half of the paper was for. If the layer model is immediately replaced by ${\cal M}_0,{\cal M}_\beta,{\cal M}_T$ with priors, the 3D maps and grain models have to specify those priors. The draft says they “determine which moments should be retained and constrain their priors.” No calculation is given of the expected moment amplitudes from a Gaia cube plus a THEMIS/astrodust mix plus a Pelgrims-style $\psi_i$ catalogue. Without that, the moment section is a literature review of Mangilli/Vacher, not a use of the three ingredients.

Hierarchical fitting is unspecified. What are the hyperparameters? A global grain library? A Gaussian process on $\beta(s)$? A cloud catalogue with a Dirichlet prior on $A_i$? How are Gaia distance uncertainties, HI channel correlations, and millimetre bandpasses put in one likelihood? How is the CMB map’s covariance (the object that actually enters the $r$ likelihood) obtained — posterior sampling, or a Fisher forecast? “Dedusting then means either subtracting the posterior mean… or, preferably, marginalizing over dust jointly with $r$” names the right goal and skips the actual statistical architecture.

Instrumental mocks of the same observables. Frequency-dependent $\psi$, $\rho_\ell^{BB}$, and $Q$ vs $U$ spectral indices are also produced by polarization-angle miscalibration, bandpass mismatch, $T\to P$ leakage, and beam mismatch. The draft lists those effects. It does not ask how a 3D physical model would be distinguished from them, or whether feeding Gaia/HI priors into the fit would absorb a calibration error into a fake second cloud.

5. Referee demands

Before this is a serious dedusting proposal, not an essay about ingredients, the following are required.

1. Correct the McBride / Sponseller citation and split the claims. State clearly: (a) pixel-level CMB $Q,U$ from an MBB fit remain approximately unbiased unless SED and angle vary along the LOS (McBride, Bull & Hensley 2023); (b) line-of-sight $T$ mixing can still bias $r$ at PICO/LiteBIRD sensitivity even without angle rotation (Sponseller & Kogut 2022); (c) power-spectrum $\beta,T$ moments can unbias LiteBIRD-like $r$ in the presence of spatial SED variation (Vacher et al. 2022, A&A 660, A111); (d) complex spin-2 moments are a separate map-level tool (Vacher et al. 2023, A&A 669, A5). Do not cite one for another.

2. A quantitative residual-$r$ forecast, on a stated experimental configuration (LiteBIRD, CMB-S4, or a BK-like patch), comparing: single MBB; MBB plus a free decorrelation/$\Delta\beta$ parameter; power-spectrum moments; and the proposed layer model with realistic (not oracle) 3D/grain/$B_{\rm POS}$ priors. Report bias and $\sigma(r)$ when the priors are correct and when they are misspecified (wrong number of clouds, 20% error in $\kappa_{\rm mm}/\kappa_V$, 10° error in $\psi_i$, Galactic-average grain mix on a cloud with a different $a_{\rm align}$).

3. An end-to-end simulation on a polarized 3D MHD dust sky, with Gaia-like stellar sampling, HI velocity cubes (not true distance), sparse starlight polarization, Planck-like 353 GHz, and the experiment’s beams, bandpasses, and $T\to P$ leakage. Show that the pipeline recovers $\psi(\nu)$ and $\rho_\ell^{BB}$, and that it does not fit a second cloud to a bandpass error.

4. High-latitude information budget. For $|b|>50^\circ$, quantify the actual S/N of differential reddening, the number of stars with usable polarization per correlation length, and the distance–velocity degeneracy in HI. If the ancillary data cannot detect a second cloud of the Pelgrims $\sim15\%$ polarized 353/217 contrast, the layer model is not identified where $B$-modes are measured.

5. Confront BK-XVI and Pelgrims 2021 on the same terms. Pelgrims selected misaligned multi-HI sightlines and saw a 217–353 GHz angle effect corresponding to $\sim15\%$ cloud-to-cloud polarized-ratio scatter. BK-XVI, in the patch used for $r$, did not see LOS decorrelation from IVCs or from filaments vs total dust. A proposal that uses 3D dust + HI + $B_{\rm POS}$ must explain when the method is needed, when a single template suffices, and how it would have behaved in the BICEP field.

6. Separate LOS tomography from POS/beam moments. State which of $\rho_\ell^{BB}<1$, $\psi(\nu)$, $\beta_Q\neq\beta_U$, and residual $EE$ after a mean-SED template (Ritacco et al.) is being claimed as the target. 3D maps address LOS structure; they are not a substitute for moments of intra-beam $T,\beta$ variation.

7. Name the alignment physics and the $I$ vs $P$ SED. Put RATs, $a_{\rm align}$, silicate-vs-carbonaceous alignment, and magnetic-dipole emission in the grain section. Use Planck’s $\beta_{\rm d}^{P}-\beta_{\rm d}^{I}=0.05\pm0.03$ as a constraint. Do not advertise $dn_m/da$ as a per-layer fit parameter.

8. Drop “vector radiative transfer.” Write an optically thin Stokes integral. If full polarized RT is ever needed, it is in the optical/NIR for the starlight prior, not in the millimetre emission model.

9. Specify the likelihood interface: which existing component-separation code receives the priors, whether dust is sampled jointly with $r$ or profiled, and how the dust covariance is propagated. A posterior-mean subtraction without that covariance is not acceptable at $\sigma(r)\sim10^{-3}$.

10. A prior-misspecification test that is allowed to lose to phenomenology. If a wide $\Delta\beta$ or first-order moment prior gives a larger but unbiased $\sigma(r)$, and the physical layer prior gives a smaller but biased $r$, the physical model is not an improvement. That comparison is the actual decision the field needs.

11. Environment cut. Restrict grain and 3D claims to the diffuse atomic ISM, or show with data that molecular-cloud results (Fanciullo, BLASTPol) apply at high latitude.

12. Write the $90^\circ$ rotation and the definition of $\gamma$ into the model equation, and do not put alignment in both $S^P_{bi}$ and $g_i$.

6. Severity list

• blocker — No quantitative demonstration that 3D extinction cubes, grain-size knowledge, and projected $B$ fields, as they actually exist at high latitude, constrain the dust degrees of freedom that bias $r$, rather than imprinting misspecified priors. Without an $r$-level forecast and a misspecification test, this is a description of ingredients, not a dedusting method.
• blocker — Layer-level grain parameters $\{dn_m/da,{\rm composition},{\rm shape},R_m(a),\ldots\}$ are not identifiable from any current or near-term data set on $B$-mode sightlines. The operational fallback is a SED library / moment expansion, which does not require the three-ingredient story as written.
• major — Sponseller & Kogut 2023 / MNRAS 519, 4370 is the wrong citation for the two-condition unbiasedness claim; that result is McBride, Bull & Hensley 2023. Sponseller & Kogut 2022 (ApJ) find a significant $r$ bias from LOS temperature mixing. Pixel-level $Q,U$ unbiasedness is not $r$ unbiasedness.
• major — Map-level complex moments, intensity power-spectrum moments (Mangilli 2021), and polarized $BB$ moments for LiteBIRD (Vacher et al. 2022, A&A 660, A111) are treated as one formalism. Magnetic tomography cannot “constrain complex phases” of papers that do not use complex moments.
• major — BICEP/Keck XVI, the existing HI-velocity / filament implementation on the deepest $B$-mode field, is omitted; it found no LOS frequency decorrelation there. Pelgrims 2021 is a selected-sky detection, not a sky-wide requirement.
• major — Plane-of-sky and intra-beam SED variations, which produce $\rho_\ell^{BB}<1$ without tomography, are mentioned in passing and then ignored. Planck Int. L / Planck 2018 XI column-density and $\ell$ trends, and Ritacco et al. 2023 residual maps, are not used.
• major — Closing claim that a “vector radiative-transfer model” replaces phenomenological decorrelation parameters. The emission model is an optically thin sum; phenomenological parameters with wide priors can be safer than tight wrong physical priors (a risk the draft names and then discards).
• major — High-latitude tomography weak links: Gaia reddening $\neq$ millimetre emissivity; HI velocity $\neq$ distance; PASIPHAE is not an all-sky product; 353 GHz $\psi$ is not an external $B$ prior; inclination $\gamma_i$ is unmeasured.
• major — No named component-separation likelihood, no covariance propagation into $r$, no instrumental-vs-sky test for $\psi(\nu)$.
• minor — Planck $T_{\rm d}=19.6\,{\rm K}$ presented as part of the polarized SED fit; it is fixed from intensity.
• minor — $\beta_{\rm d}^{P}-\beta_{\rm d}^{I}$ (Planck 2018 XI) unused; RATs, two-material alignment, and magnetic dipole emission unnamed.
• minor — $p_i\cos^2\gamma_i$ and $S^P_{bi}\times g_i$ double-count alignment/geometry; starlight/HI $\to\psi_{\rm emission}$ $90^\circ$ rotation not written into the pipeline.
• minor — Fanciullo et al. 2017 used outside its molecular-cloud domain; only Green et al. 2019 cited for 3D dust despite later nearby-volume maps.
• minor — Martínez-Solaeche et al. 2018 are a simulation testbed, not evidence that observational 3D maps improve cleaning.
• minor — “One column of the mixing matrix” is the wrong language for a fitted MBB and for the rank-$>1$ failure mode under discussion.
• minor — Poh & Dodelson’s $r\lesssim0.0015$ threshold and LiteBIRD $\sigma(r)\sim10^{-3}$ never appear, so “next-generation sensitivities” is uncalibrated.