Preserved original model output. Check claims against the independent audit →

1. Factual / physics errors

• The statement that “as soon as several volume elements with different $\{\beta_d,T_d,p_0,\gamma,\psi\}$ occupy the same beam, neither $p$ nor $\psi$ nor the effective $\beta_d$ is frequency-independent” is false. Angle decorrelation requires a correlation between SED differences and polarization orientation. Different angles with identical SEDs give a frequency-independent net angle; different SEDs with identical angles do not rotate the polarization. The controlling expression is

and rotation occurs only when both $P_i(\nu)/P_j(\nu)$ varies with frequency and $\psi_i\ne\psi_j$.

• The polarization-angle conventions are not consistently defined for use with Planck/CMB maps. The draft declares an IAU convention and writes $U=+pI\sin2\psi$, but Planck polarization products and the usual CMB harmonic convention require an explicit $U$-sign conversion when quoting IAU angles. More importantly, it alternates between $\psi$ as the electric-vector angle and $\psi$ as the H I-inferred magnetic-field angle. Thermal-emission polarization is rotated by $90^\circ$ from $\mathbf B_{\rm POS}$; assigning an H I angle directly to the displayed $Q,U$ equations changes the signs of both Stokes parameters. The map convention and the $90^\circ$ rotation must be specified before discussing $B$, $TB$, or $EB$.

• “The plane-of-sky field $\mathbf B_{\rm POS}$ sets $\psi$ and, through $\gamma$, the local polarization fraction” is wrong. A projected orientation contains no measurement of the inclination $\gamma$. The later admission that $\gamma$ is poorly measured contradicts the earlier claim that the projected field makes the polarized sky “a derived quantity.”

• The displayed moment expansion is internally inconsistent. If

the first temperature derivative is proportional to $\Theta(\nu,\bar T)$, not $\Theta(\nu,\bar T)-\Theta(\nu_0,\bar T)$. The latter applies when the fundamental SED contains $B_\nu(T)/B_{\nu_0}(T)$ and $A$ is a reference-frequency intensity. The draft mixes these two amplitude conventions.

• The formula relating Gaussian $\beta_d$ scatter to $\mathcal R_\ell$ is presented as generally applicable. The exponential—or its displayed Taylor expansion—requires assumptions about the independence and statistics of the amplitude and $\beta$ fields. At fixed $\ell$, multiplication by a spatial $\beta$ field couples harmonic modes; $\Delta\beta_{\rm rms}$ alone does not determine $\mathcal R_\ell$.

• “Standard ILC nulls a single dust SED” misstates ILC. Ordinary ILC enforces unit response to the CMB and minimizes variance; it does not normally impose a dust-null constraint. Spatially varying dust mixing increases residuals and can induce ILC bias, but the relevant failure is not the nulling of one assumed dust SED. Constrained or moment-deprojected ILCs add explicit foreground constraints.

• The RAT alignment formula is unusable as printed. It omits the radiation anisotropy $\gamma_{\rm rad}$, leaves the hatted/normalized quantities undefined, and suppresses the IR-damping factor. It also reuses $\gamma$ elsewhere for magnetic inclination, inviting a physically serious ambiguity. The actual approximation contains normalized $n_{\rm H}$, $T_{\rm gas}$, $\bar\lambda$, $\gamma_{\rm rad}U$, and $1+F_{\rm IR}$ factors; it is not a direct function of a 3D extinction map alone. See the derivation in Hoang et al..

• The claim that a several-kelvin cloud-temperature difference plus $\alpha\gtrsim60^\circ$ can generically produce tens of degrees of 150–353 GHz rotation omits a third necessary condition: comparable polarized amplitudes, usually near cancellation. A dominant cloud produces little rotation regardless of the second cloud’s angle. Temperature-only extrapolation noise using Planck-compatible distributions has also been found to be more than an order of magnitude below then-current errors, so the draft must distinguish possible extreme two-cloud configurations from expected sky statistics (Poh & Dodelson).

• McBride, Bull & Hensley are used selectively. Their important result is that broad LOS distributions of $T_d$ and $\beta_d$ generally bias the physical interpretation of fitted dust parameters but usually do not significantly bias recovered CMB $Q,U$ unless SED and angle variations occur together. Their intermediate example gave only about $0.12\sigma$ CMB-amplitude bias; the large bias was an illustrative turbulent-angle model (McBride et al.). The draft’s placement of this citation under a generic “single MBB fails” argument obscures that distinction.

• Pelgrims et al.’s inferred $\sim15\%$ cloud-to-cloud variation in the 353/217 polarized-intensity ratio is correctly quoted, but the next sentence—“That 15% is a $\sim10\%$ variation in the polarized SED shape”—has no defined conversion or properly identified citation. The study detected a statistical excess of angle changes in a selected sample; it did not recover individual-cloud $T_d$, $\beta_d$, grain sizes, or 150 GHz residuals (Pelgrims et al.).

• The draft treats smaller grains at fixed radiation field as a superposition of MBBs. Stochastically heated grains are not described by equilibrium MBBs. Meanwhile, for large grains in the long-wavelength Rayleigh regime, $\beta_d$ is controlled strongly by material dielectric response, disorder, inclusions, and structure—not by $n(a)$ alone.

• The expression for $\tau_i$ from $\delta A_{V,i}$ is underdefined. Depending on whether $K_V$ is in magnitudes per H, optical depth per H, or opacity per mass, it requires a factor of 1.086 and an explicit dust-to-gas convention. This is not merely notation because the proposed layer amplitudes depend on it.

2. Missing physics

• The central physical quantity is the joint, polarized emissivity-weighted distribution

especially covariances such as $\mathrm{Cov}(\beta,\mathrm e^{2i\psi})$ and $\mathrm{Cov}(T,\mathrm e^{2i\psi})$. Three separate products—a distance-extinction cube, an average grain model, and an H I orientation cube—do not supply this joint distribution. The draft never defines how their cells are probabilistically associated.

• Polarized residual moments must be spin-2, generally complex quantities. Scalar intensity moments in $\beta$ and $T$ cannot represent residual frequency-dependent polarization angles. Each spin moment has real and imaginary components, and the first-order complex moment already describes frequency rotation. This formalism is directly relevant but absent from H2 (Vacher et al.).

• The draft never states what is actually observed per layer. Gaia provides extinction to stars, H I provides brightness and morphology in velocity channels, and Planck provides integrated $Q,U$. None measures layer-resolved $T_d$, $\beta_d^P$, $\kappa_\nu$, $\gamma$, or polarized amplitude. Those are precisely the quantities the forward model later treats as fixed or tightly predicted.

• Starlight polarization is cumulative. A star “whose Gaia distance falls in the layer” does not directly give that layer’s angle. Differential tomography requires foreground/background stellar pairs or a joint inversion of stellar $q,u$, with intrinsic stellar polarization, distance uncertainty, selection effects, and angular sparsity propagated.

• A scalar radiation-field strength $U$ is insufficient for RAT alignment. Alignment depends on the radiation spectrum and anisotropy, grain helicity and magnetic susceptibility, damping, and the competition between B-RAT and potentially k-RAT regimes. Extinction-derived density plus an assumed cloud thickness cannot supply these quantities.

• Grain size is not enough to map extinction to polarized microwave emissivity. The missing degrees of freedom include composition, shapes, porosity, aggregation, dielectric functions, iron-inclusion abundance, and their environmental variation. The existence of a viable single-composition astrodust model that explains nearly frequency-independent FIR polarization demonstrates that $n(a)$ does not uniquely predict $\beta_d^P-\beta_d^I$ or $p(\nu)$ (Hensley & Draine).

• H I traces only part of the dusty ISM. H I optical-depth corrections, CO-dark molecular gas, ionized-gas dust, IVC dust-to-gas variation, and non-filamentary neutral material can all break the assumed H I–dust layer correspondence.

• The nonlocal nature of $E/B$ is largely absent. Pixel masking and spatially varying weights create $E$-to-$B$ mixing; angle and amplitude errors contribute differently to $BB$; and reproducing an H I–Planck map correlation does not establish control of the degree-scale dust $B$ modes used for $r$.

• The empirical status is not calibrated sharply enough. Planck’s large-region analysis found no evidence for dust decorrelation, and the BICEP/Keck H I analysis found no evidence for decorrelation in its deep field (Planck XI, BICEP/Keck XVI). SPIDER found spatial SED variation and local MBB tension but no significant full-region LOS-decorrelation detection (SPIDER). These results do not negate the Pelgrims detection, but they require the proposal to state where the effect is measured, where it is merely allowed, and where it is absent.

• Bandpass integration, thermodynamic-unit conversion, beam mismatch, transfer functions, calibration covariance, and reference-frequency colour corrections are missing from the forward likelihood. A monochromatic $Q_\nu,U_\nu$ model is inadequate for an $r\sim10^{-3}$ residual claim.

3. Overclaims

• “Turn an underconstrained 2D extrapolation into a layered … forward model” overstates the information gain. The LOS is discretized, but almost every layer’s polarized SED and amplitude remains latent. Discretization does not make the inverse problem identifiable.

• “A 3D extinction map provides the same information in true distance” as an H I cloud count is too strong. The 516 Edenhofer radial bins are grid sampling, not 516 independent measurements along every LOS, and the released posterior has strongly correlated spatial uncertainties. Low-extinction high-latitude directions are not automatically the best-resolved layer decompositions merely because much of their dust is local (Edenhofer et al.).

• “Unimodal” extinction versus distance does not imply small $\omega_2^\beta$ or temperature moments. A single cloud may contain illumination gradients, composition variation, unresolved substructure, and beam-scale mixing. Conversely, multiple distance peaks with identical polarized SEDs need not produce decorrelation.

• “A 3D dust map that also traces density and crudely $U$ therefore predicts a 3D alignment map” is unsupported. The proposed density comes from extinction divided by a “fiducial thickness,” while $U$ comes from a $T_d$ prior; neither is a layer-resolved measurement, and using $T_d$ to infer $U$ while claiming to predict $T_d$ is circular.

• “With [$\mathbf B_{\rm POS}$], the polarized sky becomes a derived quantity” is false. It supplies, at best, an orientation proxy. Polarized amplitude still requires emissivity, alignment efficiency, inclination, field tangling, and layer association.

• The global $r>0.75$ correlation of H I-derived and Planck $Q,U$ maps is promoted into layer-level predictive power. That result applies to velocity-integrated, large-scale maps; Clark & Hensley explicitly describe a position–position–velocity proxy, not a distance-resolved magnetic-field measurement (Clark & Hensley). In the BICEP field the reported $B$-mode template correlation is scale-dependent and only about 10–65%, not a 75% per-layer reconstruction.

• The model does not “automatically” generate $\mathcal R_\ell<1$: it gives unity if layer SEDs are the same or if the relevant morphologies remain proportional. Nor does it automatically generate $EE/BB\simeq2$; that requires the correct joint statistics of density morphology and field orientation, not merely a list of angles.

• Calling H0 “already an improvement” is unjustified. Masking or deweighting may reduce foreground bias, but it also increases sample variance, changes mode coupling, and can create $E/B$ leakage. Improvement must be demonstrated in mean-squared error or $r$-coverage, not asserted from successful flagging.

• “A physical forward model is falsifiable, which a phenomenological MBB is not” is incorrect. An MBB is directly falsifiable with held-out frequencies, residual spectra, and posterior-predictive tests. A high-dimensional physical model can be harder to falsify if flexible amplitudes and moments absorb discrepancies.

• The closing claim that the ingredients “can already … predict the frequency dependence of $\mathcal R_\ell$ and $\psi(\nu)$” exceeds the evidence. Existing work shows statistical association and flagging power; the draft presents no real-sky, out-of-sample layer model that predicts those observables quantitatively.

4. Weak links in the pipeline

5. Referee demands

1. Write a consistent band-integrated generative model for $Q+iU$, with one declared Planck/IAU/CMB convention, the emission–field $90^\circ$ rotation, thermodynamic-unit conversion, beams, and the full intensity-orientation normalization.

2. Replace the scalar residual moments in H2 with the spin-moment formalism, or prove that the proposed fixed layer angles make all remaining complex moments negligible. Angle–SED covariance must remain explicit.

3. Provide an identifiability calculation for $N_{\rm lay}=1,2,3,\ldots$: mixing-matrix rank, condition numbers, Fisher/posterior correlations with CMB $Q,U$, and the effect of nearly aligned layers and nearly identical SEDs. State which layer quantities are data, which are priors, and which are fitted.

4. Construct the layer association in one probabilistic likelihood rather than by ex-post matching. The likelihood must include extinction posterior samples, H I velocity/distance ambiguity, H I optical depth, starlight cumulative $q,u$, missing gas phases, and false cloud splits/mergers.

5. Demonstrate genuine held-out prediction. Fit only ancillary data plus 353 GHz, freeze the model, and predict 217/220 and then 95/150 GHz $Q,U$, $\Delta\psi$, $EE$, $BB$, and all cross-frequency $\mathcal R_\ell$. Perform this separately on Pelgrims target/control samples and on the BICEP/Keck and SPIDER fields.

6. Run blinded end-to-end $r$ simulations in which the reconstruction receives mock Gaia stars, H I spectra, and starlight-polarization catalogues—not the true 3D cube. Include MHD substructure, multiple grain compositions, out-of-model dust, synchrotron, lensing, realistic bandpasses, beams, calibration/leakage systematics, and survey masks.

7. Compare against appropriate baselines: one-MBB fits, independent $Q/U$ SEDs, scalar and spin moments, standard and constrained ILC, and phenomenological decorrelation likelihoods. Report $\Delta r$, $\sigma_r$, residual $D_\ell^{BB}$, coverage, sky fraction, and failure rate—not only goodness of fit.

8. Quantify requirements on the ancillary maps: allowable errors in layer column, layer angle, velocity–distance association, $T_i$, $\beta_i$, and $p_{0,i}$ for residual dust to remain below a stated $r$ threshold. Without this error budget, “help” cannot be converted into foreground-control performance.

9. Add ablation tests showing the incremental value of 3D extinction, H I orientation, starlight tomography, and grain priors separately. This is necessary because a strong 353 GHz calibration may dominate the result and conceal that the purported physical inputs add little predictive information.

10. Correct the moment and RAT equations, define all normalization factors, replace “related analyses” and “Huffenberger / Cukierman” with precise citations, and discuss the counter-results that find small temperature-induced extrapolation noise or no measurable decorrelation in particular CMB fields.

6. Severity list

• blocker The proposed inputs do not identify layer-resolved polarized amplitudes or SEDs; the core inverse problem remains underdetermined.

• blocker No end-to-end demonstration connects the ancillary products to controlled $BB$ residuals or unbiased $r$.

• blocker The H I-velocity-to-extinction-distance association—the step that couples each angle to each SED—is assumed rather than inferred or validated.

• major The draft claims that multiple layers automatically cause frequency-dependent $p$, $\psi$, and $\beta$; the necessary SED–angle covariance is omitted.

• major The polarization-angle, $U$-sign, and magnetic-field-versus-electric-vector conventions are insufficiently consistent for an $E/B$ analysis.

• major The temperature moment equation mixes incompatible amplitude normalizations.

• major H2 uses scalar moments where complex spin-2 moments are required for frequency-dependent angle residuals.

• major The projected field is incorrectly treated as constraining inclination and layer polarization amplitude.

• major Grain size and RAT theory are overclaimed as predictors of $\beta_d^P$, $T_d$, opacity, and $p_0$ without layer-specific composition, optical constants, radiation anisotropy, or gas conditions.

• major The ILC mechanism is misdescribed.

• major Extreme two-cloud rotations are presented without the comparable-amplitude/cancellation condition or a realistic occurrence rate.

• major Statistical H I/Planck correlations and the Pelgrims selected-sample detection are extrapolated into quantitative 95–150 GHz cleaning power that those studies did not demonstrate.

• major The proposal does not propagate ancillary-map posterior uncertainties or account for circular calibration and validation on Planck 353 GHz.

• minor The raw $p=\sqrt{Q^2+U^2}/I$ definition is used around observational claims without noting noise and intensity-zero-level bias.

• minor The $\tau_i$ conversion omits essential unit and opacity conventions.

• minor Several references are vague, misordered, or used beyond their demonstrated scope.