Novelty assessment and a falsifiable research program

Independent audit addition, 6 September 2026. The original model work is preserved. This document distinguishes evidence from proposed work and complements 05-audit/literature-audit.md and 05-audit/derivations.md.

Is anything novel demonstrated here?

No new astrophysical discovery is demonstrated by the repository as it stands. The physical mechanism, principal observational handles, and moment-based mitigation already appear in the cited literature. The model comparison is useful as a synthesis exercise and as a record of how criticism changes an answer. It is not three independent observations of the sky: the models draw on overlapping literature, and later stages explicitly share text.

There is a credible opportunity for a new method or validation result: demonstrate, on data excluded from training, whether distance-resolved geometry adds predictive information beyond a well-calibrated empirical spin-moment prior. The essays motivate this question but do not answer it. Even a carefully measured failure of external priors could be scientifically valuable by quantifying where tomography ceases to help.

The targeted search documented in the literature audit is not exhaustive. “I did not find this exact protocol” would not justify calling it the first of its kind.

The central experiment

Question: At fixed microwave likelihood, moment basis, parameter budget, and ancillary-data availability, does the correct association of distance-layer geometry with dust emission improve held-out polarization prediction beyond empirically learned spectral complexity?

The null is that tomography provides no additional predictive value after controlling for dust brightness, noise, angular structure and empirical complexity. The alternative is that the correct layer associations improve prediction, especially where polarized cancellation and SED spread make scalar extrapolation fragile. This is a conditional prediction claim, not an assumption that a higher cloud count always means higher contamination.

Fit an identical bandpass-integrated foreground model in every comparison:

For ideal monochromatic bands $L_b=\ln(\nu_b/\nu_0)$ and $G_b=\partial_T\ln[B_{\nu_b}(T)/B_{\nu_0}(T)]$ at the pivot. The reference-frequency subtraction in the temperature derivative matters. In an actual instrument derive these basis vectors by differentiating its integrated response, including units and color calibration. Keep unnormalized complex moments where the reference polarization is small; dividing by nearly canceled $M_0$ creates unstable ratios.

Compare these models on identical pixels and held-out bands:

1. Single-MBB baseline: enough to quantify why flexibility is needed, but too weak to establish the value of tomography on its own.
2. Empirical-prior baseline: the same retained moments as the proposal, with priors learned from separate sky regions and allowed to depend on brightness, noise, latitude and measured angular morphology.
3. Tomography-conditioned prior: the identical likelihood and moment basis, but the prior mean/covariance comes from posterior draws of distance layers, angles, emissivity conversion and physical SEDs, calibrated only on training regions.
4. Matched sham prior: preserve marginal prior widths, layer counts and distributions, but disrupt the association of angle/SED/column information within predeclared environmental strata. This tests whether the correct association matters, rather than merely adding an informative width or a latitude proxy.
5. Oracle diagnostic in simulations: the true generating layer information supplies an upper benchmark. It is not an achievable observational method and should never be mixed into the reported data comparison.

Use the same effective parameter budget and compare an equal-information sham as well as a fully empirical model. A gain relative only to an intentionally underfit MBB is insufficient. Report whether prior tightening or the correct spatial association supplies the gain.

Data and independence requirements

There is now a concrete probabilistic starting point for the HI-distance association: McCallum et al.'s Milky Way Atlas (2026) jointly infers local HI density and velocities using HI4PI and extinction. It should be compared with simpler matching in the experiment, while propagating its errors and shared extinction inputs. Its existence advances implementation readiness; it does not establish that the resulting magnetic-layer associations predict microwave polarization correctly.

A band is truly held out only if it was excluded from the fit and from the ancillary product, calibration and model-selection path that predicts it, or if those shared inputs are explicitly represented in the joint covariance. Spatial folds should be contiguous regions with buffers wider than relevant smoothing/correlation lengths. Random neighboring pixel splits exaggerate independent sample size.

Select target/control regions using independent ancillary information before examining validation residuals. Restrict the pilot to common data support; propagate uncertainty or mark insufficient coverage elsewhere. A missing risk prediction must not be displayed as a safe region.

Metrics, null tests and decision rules

The primary endpoint is the difference in held-out log predictive density for joint Q/U, accumulated over predeclared independent regions with the appropriate covariance. This scores both prediction and uncertainty. Pair it with whitened residual norms, posterior predictive checks, interval coverage and signed cross-products $\operatorname{Im}(P_bP_a^*)$. The cross-product avoids treating a low-signal angle ratio as a reliable direct measurement. Angular RMS alone is insufficient near cancellation.

A continuous risk product should predict a specified quantity: for example, probability that a held-out spectral-null residual exceeds a predeclared noise-normalized threshold. Assess calibration curves and discrimination on excluded regions. Compare against brightness-only, cloud-count-only, HI-coherence-only, and empirical-moment baselines. Publish uncertainty and coverage maps alongside the risk estimate.

Run the following nulls and stress tests:

• Identical SEDs with different angles; common angles with different SEDs; 90° cancellation and a zero crossing; symmetric multilayers with canceled rotation. These distinguish curvature, rotation and singular coordinates.
• Randomized ancillary associations within matched brightness/noise/latitude strata; matched sky rotations or region permutations must preserve relevant selection and spatial statistics.
• Frequency-dependent polarization-angle offsets, gains, bandpasses, I-to-P leakage, beam mismatch and correlated noise, injected separately and jointly. Evaluate marginalization over them rather than assuming a clean instrument.
• Wrong grain family, missing faint/far layer, merged or split clouds, incorrect HI-distance association, optical-to-emission conversion scatter, and within-layer turbulence absent from the inference family.
• Signal injection with CMB and synchrotron, including foreground/CMB chance correlation. Demonstrate that a strong dust prior does not remove the injected CMB.
• Alternative map releases and splits as instrument-sensitivity tests, with their statistical dependence acknowledged.

Choose the model, masks, folds, statistic and multiplicity adjustment before unblinding test data. A proposed success criterion is a positive held-out score improvement whose region-level uncertainty interval excludes zero, accompanied by calibrated coverage and survival of the sham-prior test. This is a proposed design decision, not an achieved significance. A failure to outperform the empirical baseline is a reportable result if statistical power and data support are sufficient.

The later cosmological gate

Only after predictive validation should the project claim a benefit to primordial-B inference. Use sky simulations with power-spectrum structure, the experiment's mask/filter transfer, beam and bandpass response, noise, systematics, lensing treatment, and the actual r likelihood. Compare mean r bias, variance, mean squared error, confidence/credible-interval coverage and residual BB spectra under the same settings. Low r-bias in the correct-model case alone does not validate the prior.

A possible predeclared engineering goal is $|\mathrm{bias}(\hat r)|<0.2\sigma_r$ together with lower mean squared error than the empirical-moment baseline and nominal interval coverage across held-out foreground families. The 0.2 factor is a proposed criterion to negotiate for the target experiment, not a literature requirement. Determine simulation count from the precision needed on bias and coverage; report Monte Carlo uncertainty rather than asserting nominal coverage from a handful of realizations.

The interactive two-layer and periodic-map laboratories supplied with this audit are educational/diagnostic preparations for these checks. Their arbitrary morphology and absent instrument likelihood cannot produce a credible numerical $\Delta r$ forecast.

Deliverables that could constitute a paper

The first achievable research product is a reproducible pilot predictive-validation study: released data-selection masks, provenance of every training/validation input, empirical and tomography-conditioned priors, blind predictions, sham-prior comparisons and full uncertainty calibration. Its central figure should show predictive gain versus independently estimated coherence/SED spread, with uncertainty and data support, not just an attractive 3D reconstruction.

A second product is a simulation benchmark for transferable priors in which inference and truth use intentionally different foreground families, matched computational/parameter budgets, and realistic missing ancillary information. The key result would be a measured region of validity or a demonstrated failure boundary. Generic simulation and compression already have close precedents, so the contribution must be the controlled comparison and documented performance.

A third, more data-intensive product is a cloud-to-cloud transfer test: infer a distribution of optical-to-microwave conversion and polarized SEDs in training clouds, then predict independent cloud Stokes spectra without fitting their target bands. This directly tests whether grain information adds knowledge beyond an empirical environmental prior.

None of these outcomes has yet been measured by this repository. The justified upgrade is from broad essays to a falsifiable, reproducible program with correct algebra and explicit prior art. A genuine discovery would be the independently confirmed result of that program, whether an improvement, a new physical constraint, or a well-established limit on what tomography can predict.