Discriminating Weak Lensing from Intrinsic Spin Correlations Using the Curl‐Gradient Decomposition
Bibliographic record
Abstract
The distortion field defined by the ellipticities of galaxy shapes projected on the sky can be uniquely decomposed into a gradient and a curl component. If the observed ellipticities are induced by weak gravitational lensing, then the distortion field is curl free. Here we show that, in contrast, the distortion field resulting from intrinsic spin alignments is not curl free. This provides a powerful discriminant between lensing and intrinsic contributions to observed ellipticity correlations. We also show how these contributions can be disentangled statistically from the ellipticity correlations or computed locally from circular integrals of the ellipticity field. This allows for an unambiguous detection of intrinsic galaxy alignments in the data. When the distortions are dominated by lensing, as occurs at high redshifts, the decomposition provides a valuable tool for understanding properties of the noise and systematic errors. These techniques can be applied equally well to the polarization of the microwave background, where it can be used to separate curl-free scalar perturbations from those produced by gravity waves or defects.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".