{"id":"e98c3d71-d470-4705-9bc9-1b9df59f58a8","arxiv_id":"2507.01798","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"Large-scale patterns in Gaia quasar proper motions differ significantly between redshift bins 1-2 and 2-3, but the author concludes that hidden astrometric systematics are a likely explanation.","lead":"This paper uses machine-learned distance estimates to split 1.5 million distant quasars into three distance bins, then looks for large-scale patterns in how these quasars appear to move across the sky. The patterns differ between bins, but the author states that hidden errors in the Gaia measurements could explain the differences.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The differential VSH signal may be a selection artifact: the ML redshift binning uses astrometric gof_al as a classifier, so the z-bins can differ in Gaia systematic error structure rather than in cosmology; the paper's own filter test shows ~40% coefficient sensitivity.","rationale":"The reader's weakest assumption identifies the same load-bearing point: the analysis assumes that Gaia DR3 systematic errors are uncorrelated with the classifier parameters used to predict redshift, especially astrometric gof_al. The paper verifies only median proper motions versus redshift, not the spatial structure of systematics, and its own filtering test demonstrates strong sensitivity of the fitted VSH coefficients to source selection. An independent verification with Quaia is not a clean control because Quaia is built from Gaia astrometry and the same Gaia proper motions are used. The most direct settlement is to bin by spectroscopic redshifts, which removes the ML classifier coupling entirely. If the signal persists there, the cosmological interpretation is supported; if not, the differential VSH differences are an artifact of the selection function. Since the reader already assigned CONDITIONAL with high confidence and this concern supports that verdict, no adjustment is needed.","tokens_in":29606,"tokens_out":10032,"duration_ms":127064,"concrete_test":"Restrict the analysis to the ~0.28M sources with SDSS DR16Q spectroscopic redshifts, redo the VSH fits with the same cell-averaging and weighting scheme, and compute the z=1-2 versus z=2-3 differences for {mag,2,1,1}, {mag,0,1,0}, and {ele,0,1,0} using spectroscopic redshifts for binning, so that no ML classifier (and hence no astrometric gof_al coupling) enters the bin assignments. If the first-degree differences do not reproduce at S/N >= 3, the signal is attributable to the astrometric-quality selection in the ML redshift predictor. If they do reproduce, the classifier-coupling concern is resolved and the central statistical claim is strengthened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central differential claim rests on comparing VSH fits of proper motions between redshift bins that are defined by an ML predictor whose classifiers include \"astrometric gof al\" (Sec. 5.1). Because gof_al is an astrometric quality statistic, bins selected on zpre can differ in Gaia DR3 systematic error structure even if the cosmological signal is zero. The Fig. 5 check of median proper motion versus redshift is not sufficient: it tests only the first moment, not the spatial pattern of systematics. The paper's own filter test (Sec. 4) finds that cutting G<19.8 and 3-sigma proper motions reduces all prominent VSH coefficients by ~40%, so the fitted coefficients are sensitive to selection cuts of the same kind that vary between bins. The statement in Sec. 4 that bin leakage is \"limited to several percent\" is also inconsistent with Sec. 6.2.2, where only 73.6% of sources stay in the correct bin; the resulting ~26% mixing means the bins are substantially selections on the classifier vector rather than clean redshift slices. Finally, the S/N values are based on formal errors only, while the reduced chi-square near 2 indicates excess variance not captured by those errors, so the quoted significance of 4.3, 3.7, and 3.1 is likely optimistic.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses neural-network-predicted redshifts to divide 1.5 million Gaia DR3 CRF quasars into coarse redshift bins (z=1–2, 2–3, >3), then fits vector spherical harmonic (VSH) models of degree 3 to the proper motion fields of each bin. The central claim is that the proper motion fields of the z=1–2 and z=2–3 bins differ significantly in several first-degree harmonics, notably a rigid spin, a glide along the Galactic axis, and a Galactocentric dipole component. The author interprets this as a possible redshift-dependent kinematic distortion of the universe, while explicitly cautioning that hidden Gaia systematic errors are a more mundane explanation. The analysis is supplemented with internal validation tests, a repetition using Quaia redshifts, and a public release of the synthetic redshift catalog.","tokens_in":29840,"tokens_out":2928,"duration_ms":38387,"significance":"If the differential VSH signal were robust, it would provide a new observational probe of the cosmological principle and of alternative (e.g., Bianchi or Lemaitre-Tolman-Bondi) cosmologies. The paper is valuable for introducing a global VSH methodology to quasar proper-motion cosmology, for making the derived catalog publicly available, and for testing the result with an independent redshift source. The author is also commendably explicit that hidden astrometric systematics may explain the signal. However, the central statistical claim rests on formal errors that the paper's own reduced chi-square values indicate are understated, and the redshift-binning classifiers include an astrometric quality parameter that can plausibly correlate with the spatial structure of Gaia systematics. The significance and robustness of the claimed differential signal are therefore not yet established.","major_comments":[{"comment":"The set of ML classifiers includes astrometric gof_al, which is an astrometric quality statistic. Since the redshift bins are defined by a predictor that depends on gof_al, the z-bins can differ in the spatial pattern of Gaia DR3 systematic errors even if the cosmological proper-motion signal is zero. The verification in Fig. 5 checks only median proper motion components versus redshift, i.e., the first moment of the distribution, not the sky-correlated structure that VSH fits measure. I recommend re-running the differential VSH analysis with z-bins defined by photometric and infrared classifiers only (excluding gof_al and possibly phot_bp_rp_excess_factor), or with the subsample having spectroscopic redshifts, and comparing the coefficients. This is load-bearing for the claim that the first-degree differences are cosmological rather than astrometric selection artifacts.","section":"§5.1, §4"},{"comment":"There is a direct inconsistency in the leakage statement. Section 4 says that leakage of sources between adjacent redshift bins is 'limited to several percent', but Section 6.2.2 reports that only 73.6% of sources remain in the correct bin, with 13.6% leaking to the lower bin and 12.1% to the higher bin. The 26% mixing is not 'several percent', and it matters more than the author suggests. The argument that leakage can only dilute differential signals holds only if leakage is random with respect to astrometric systematics; if the leaked sources are preferentially selected by classifiers that correlate with Gaia error patterns, leakage can create or modify differential VSH coefficients. This needs to be quantified, for example by injecting realistic systematics into the classifier-based binning or by comparing VSH fits on clean spectroscopic-z bins.","section":"§4 versus §6.2.2"},{"comment":"The quoted S/N values for the differences between the z=1–2 and z=2–3 fits (4.3, 3.7, and 3.1) are computed using formal errors only. The paper reports pre-fit reduced chi-square values of 2.11, 1.95, 1.71, and 1.56 for the four samples, indicating excess variance beyond the formal covariances. Applying a conservative inflation of the errors by the square root of the relevant reduced chi-square would bring the claimed significant differences to roughly 3.0, 2.6, and 2.2, i.e., below the S/N>3 threshold. The formal-error-only significance is therefore likely optimistic, and the main differential claim is not established by the current statistics.","section":"§3, Table 2"},{"comment":"The filtering test (G<19.8 mag and 3-sigma proper-motion clipping) reduces all prominent VSH coefficients by about 40%, but the paper does not report whether the differential signal between the z-bins survives this filter. The text states only that the result 'remains somewhat inconclusive'. Because the selection cuts are of the same kind that vary between the ML-defined redshift bins (fainter sources are more numerous at higher z and have different astrometric error properties), a 40% sensitivity of the coefficients to such cuts directly undermines the robustness of the differential claim. The author should present the filtered VSH coefficients and their difference S/N for the 1–2 and 2–3 bins.","section":"§4, filtering test"}],"minor_comments":[{"comment":"The Quaia verification is an independent source of redshifts but uses the same Gaia DR3 proper motions, so it does not test the possibility that the signal is an astrometric artifact. This should be stated more explicitly where the verification is described as 'independent'.","section":"§6.2.1"},{"comment":"The description of phot_bp_rp_excess_factor as a 'parameter of photometric nature' is helpful, but the reader should be reminded that astrometric gof_al is not photometric; its inclusion in the classifier set is the key systematics risk and deserves a dedicated discussion.","section":"§5.1"},{"comment":"The sentence attributing the southern vortex to a possible association with the Small Magellanic Cloud is speculative; the paper does not provide a mechanism or test, so it would be better presented as an unexplained coincidence or removed.","section":"§4"},{"comment":"In the historical discussion, 'SSHs' is used for scalar spherical harmonics; the abbreviation should be defined at first use for clarity.","section":"§6.1.2"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is honest and well-structured, but the central claim currently rests on formal-error-only significance and on a redshift classifier that includes an astrometric quality parameter. Both issues are addressable within the manuscript's scope by re-running the differential analysis with photometric-only classifiers, inflating errors by the excess variance, and correcting the leakage statement. Given the strong caveats in the paper itself, I do not see this as a reject, but the load-bearing statistical and selection-artifact points must be fixed before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a look. The differential VSH analysis of Gaia CRF proper motions split by ML-predicted redshift is genuinely new relative to the local-patch study and whole-sample aberration fits. The paper is careful and unusually honest: the author states up front that hidden Gaia systematics are the more mundane explanation for the signals, and the verification with Quaia redshifts is a real check even though it shares proper motions. The catalog release is a useful community resource.\n\nThe load-bearing claim is that the z=1-2 and z=2-3 bins differ in first-degree VSH coefficients at S/N 4.3, 3.7, 3.1 (spin, polar spin, and glide). I think that claim is likely true as a description of the Gaia data. But the cosmological interpretation—redshift-dependent net rotation of the universe—is not supported by the paper's own validation. The stress-test concern lands: the ML classifier includes astrometric gof_al, so the bins can be selected on astrometric quality, not just redshift. The Fig. 5 median check only tests the first moment, not the spatial structure of systematics. The filter test (G<19.8, 3-sigma clip) reduces all prominent coefficients by ~40%, which shows the fitted patterns are fragile. The reduced chi-square near 2 means formal errors are understated, so the quoted S/N values are optimistic. And the bin leakage is not \"several percent\"—73.6% correct classification means ~26% mixing, which is substantial and weakens the claim that leakage only dilutes the signal (mixing could also create selection patterns).\n\nNone of this is fatal to the paper as a methods contribution. The VSH software, the redshift catalog, and the differential approach are useful. The author deserves credit for flagging the systematics interpretation so explicitly. But a reader should not come away thinking the universe's rotation has been detected. This is a provisional measurement with a dominant systematic-error explanation that remains to be excluded.\n\nWho is this for? Astrometrists working on Gaia systematics, and cosmologists interested in dipole/rotation constraints will both want to cite it. It deserves peer review—the referees should push for a reshuffled-redshift null test, error bars absorbing excess variance, and a systematics model that breaks the gof_al–bin coupling. But this is a solid paper that should be engaged with, not desk-rejected.","headline":"A careful, honestly hedged differential VSH analysis of quasar proper motions that finds suggestive redshift-dependent signals, but the classifier–astrometry coupling and the paper's own filter tests leave the cosmological interpretation unproven.","tokens_in":30427,"tokens_out":1792,"would_cite":true,"duration_ms":21198,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The proper motions of a million distant quasars, split by redshift, show significant differences in global spin and drift patterns—formally a net rotation of the universe that changes with cosmic epoch, though hidden Gaia systematics…","keywords":["quasar proper motions","Gaia DR3","vector spherical harmonics","machine learning redshifts","cosmological principle","cosmic rotation","secular aberration","anisotropic cosmology"],"falsifier":"Restrict the analysis to the spectroscopic SDSS footprint, where redshifts are exact, and reweight the redshift bins so the joint distributions of astrometric goodness-of-fit, photometric excess factor, $G$, and $W2$ magnitude are identical across bins, then recompute the degree-3 VSH fits. If the first-degree differences between $z\\in[1,2]$ and $z\\in[2,3]$ survive the classifier-matched samples, they cannot be a selection artifact of hidden systematics; if they vanish, the cosmological rotation interpretation is excluded. A complementary test is to inject the measured classifier-dependent covariance noise into a simulated isotropic proper motion field and see whether the observed differential coefficients reappear.","tokens_in":29329,"feed_emoji":"🌌","tokens_out":15081,"duration_ms":155535,"temperature":0.7,"pith_summary":"The paper asks whether the tiny apparent sideways drifts of distant quasars—the proper motions measured at the microarcsecond level by the Gaia mission—depend on cosmic epoch. The author predicts redshifts for 1.57 million Gaia reference-frame quasars with a neural network trained on spectroscopic redshifts, splits them into bins at $z=1$--$2$, $2$--$3$, and $>3$, and fits a 30-term vector spherical harmonic model to each bin's global proper motion field. Comparing the fits, the only significant differences (signal-to-noise $S/N>3$) are in three first-degree terms: two rigid spins and one polar glide, all between the $z=1$--$2$ and $z=2$--$3$ bins. Formally that is what a universe with a net rotation that changes with cosmic epoch would look like, and it would extend a violation of the cosmological principle into the time domain. The author immediately notes that unseen systematic errors in Gaia astrometry, correlated with the redshift classifiers, are the more mundane explanation; independent Quaia redshifts and the known Galactic aberration dipole are used as checks.","feed_headline":"Quasar proper motions reveal a redshift-dependent cosmic spin","feed_subtitle":"Microarcsecond drift differences between redshift epochs formally challenge the cosmological principle.","key_machinery":"The central object is the vector spherical harmonic (VSH) decomposition of a tangential vector field on the celestial sphere, a complete orthonormal basis of vector functions that splits any smooth proper motion pattern into electric (divergence-type) and magnetic (curl-type) components. Fitted to degree 3 (30 functions) by weighted least squares on cell-averaged proper motions, the low-degree magnetic terms directly represent rigid rotations of the whole field and the electric terms represent dipole glides, so comparing coefficients between redshift bins converts the question of whether the tangential kinematic structure changes with epoch into a small set of scalar differences. The other load-bearing piece is the neural-network redshift predictor, which converts six photometric and Gaia metadata classifiers into predicted redshifts and makes the coarse redshift binning possible for a sample without full spectroscopic coverage.","core_discovery":"The central claim is that the large-scale proper motion field of quasars is not kinematically the same at different cosmological epochs. In a vector spherical harmonic decomposition to degree 3, the $2