{"id":"a29d9eaf-5368-4d57-af3b-8573421a8263","arxiv_id":"2508.10276","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"The submission pairs a differential-geometry abstract on Lie groupoid weightings with an unrelated astrophysics manuscript, leaving the claimed results unsupported by the provided text.","lead":"The abstract promises a study of multiplicative weightings for Lie groupoids and Lie algebroids. The attached full text is an unrelated galaxy morphology survey, so the mathematical results cannot be checked from the material submitted.","discovery_kind":"unclear","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Full text is an unrelated DEVILS astro-ph paper (arXiv:2508.10285); none of the abstract's definitions, theorems, or proofs appear, so the central claim cannot be checked.","rationale":"The reader identified the same weakness: the abstract and body are different papers, so the core results cannot be checked. I agree. The concern is load-bearing because every stated theorem—three equivalent characterizations, differentiation, integration, classification along units—depends on constructions (especially the weighted deformation space) that are absent. There is no way to test the mathematics from this submission. I am not claiming the authors are dishonest or that the mathematical results are false; the evidence is a text mismatch, and the embedded arXiv ID confirms the body belongs to 2508.10285. Because the fault is missing content rather than a demonstrated contradiction, the reader's UNVERDICTED status should be preserved. One verification step—fetching the real 2508.10276 source and checking for the expected terms—would settle whether this is simply a submission error or a genuinely absent paper body.","tokens_in":32436,"tokens_out":3221,"duration_ms":29657,"concrete_test":"Download the actual source/PDF for arXiv:2508.10276 directly from arXiv and search for 'weighted deformation space', 'Lie filtration', 'infinitesimally multiplicative', and 'multiplicative weighting'. If the retrieved text contains definitions and proofs matching the abstract, re-run the review on that text. If the retrieved body is still the DEVILS paper (or lacks those terms), the abstract-body mismatch is confirmed and the central claim has no supporting derivation in the submission.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim in the abstract is a mathematical equivalence/classification: multiplicative weightings of a Lie groupoid are characterized three ways (structure maps, graph of multiplication, weighted deformation space), differentiate to infinitesimally multiplicative weightings, and integrate along wide Lie subalgebroids; along units they are classified by Lie filtrations of the Lie algebroid. For this claim to be supported, the paper must at minimum define the weighted deformation space and prove the equivalence of the three characterizations. The submitted full text contains none of this: it begins 'MNRAS 000, 1–23 (2025) ... DEVILS: Evolution of the Morphology-Density Relation' and carries the arXiv header '2508.10285v1 [astro-ph.GA] 14 Aug 2025'. There is no Lie groupoid, no filtration, no deformation space, and no theorem statement matching the abstract. This is not an internal flaw in a derivation; it is a total absence of the derivation from the submission. Per the review rule, this is an explicit missing-support flag located in the full-text title/abstract and embedded arXiv identifier. The strongest claim is therefore ungrounded in the supplied material; the correct status is unverdictable, not a demonstrated mathematical error.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The abstract advertises a mathematical paper on multiplicative weightings for Lie groupoids and Lie algebroids: three equivalent definitions of multiplicative weighting (via structure maps, via the graph of multiplication, and via a weighted deformation space), a differentiation/integration theorem for infinitesimally multiplicative weightings along wide Lie subalgebroids, and a classification of multiplicative weightings along units by Lie filtrations of the Lie algebroid. The submitted full text, however, is an unrelated astrophysics paper, 'DEVILS: Evolution of the Morphology-Density Relation' (arXiv:2508.10285, astro-ph.GA), with no mathematical definitions, theorem statements, or proofs. None of the claims in the abstract are supported by the supplied manuscript.","tokens_in":32622,"tokens_out":2254,"duration_ms":27481,"significance":"If the advertised results are correct, they would constitute a substantial contribution to the differential geometry of Lie groupoids and Lie algebroids, notably the classification of multiplicative weightings by Lie filtrations and the integration theorem along wide subalgebroids. However, because the submitted full text contains none of the promised mathematics, the significance cannot be assessed from this submission. There are no machine-checked proofs, reproducible derivations, or verifiable statements to credit.","major_comments":[{"comment":"The full text is not the manuscript described in the abstract. It is titled 'DEVILS: Evolution of the Morphology-Density Relation', carries the header 'arXiv:2508.10285v1 [astro-ph.GA] 14 Aug 2025', and discusses galaxy morphology in MNRAS style. The abstract announces a math.DG paper (arXiv:2508.10276) on multiplicative weightings. This is a total absence of the claimed mathematical content, not a presentation issue. Every mathematical claim in the abstract is therefore unsupported.","section":"Full text, p.1 (title and arXiv header)"},{"comment":"The central equivalence claim—that multiplicative weightings can be characterized by the structure maps, by the graph of multiplication, and by the weighted deformation space—requires at minimum the definition of a multiplicative weighting, the construction of the weighted deformation space, and proofs of the equivalences. None of these appear anywhere in the full text. The classification of multiplicative weightings along units in terms of Lie filtrations is likewise stated only in the abstract.","section":"Abstract, 'three equivalent definitions ... weighted deformation space'"},{"comment":"The claims that multiplicative weightings differentiate to infinitesimally multiplicative weightings and that infinitesimally multiplicative weightings integrate along wide Lie subalgebroids are stated without any definitions, hypotheses, or proof. The full text contains no numbered theorems, no equations, and no mathematical notation matching the abstract. This is an explicit missing-support flag for every substantive assertion of the paper.","section":"Abstract, differentiation and integration claims"}],"minor_comments":[],"recommendation":"reject","confidential_remarks":"This appears to be a submission error or an integrity problem: the arXiv identifier on the full text (2508.10285) does not match the identifier in the abstract (2508.10276), and the subject matter is entirely different. No mathematical evaluation is possible from the supplied file. If the intended manuscript exists, it should be submitted as a fresh, correct file; the present submission cannot be meaningfully revised."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the one thing you should know: this submission is not a math paper. The abstract describes substantive work on multiplicative weightings for Lie groupoids and algebroids, but the full text is a DEVILS astronomy paper on the morphology-density relation, with its own arXiv number (2508.10285). There are zero definitions, theorems, or proofs from the abstract in the body.\n\nCredit where it's due: the abstract is specific and promising. It extends Loizides and Meinrenken's weighted-manifold theory, offers three equivalent characterizations of multiplicative weightings, states a classification along units in terms of Lie filtrations, and claims an integration theorem along wide Lie subalgebroids. If a manuscript matching that abstract exists and works, it is a solid subfield contribution for people working on weightings, groupoids, and geometric mechanics. The citation to Loizides and Meinrenken is appropriate, not a red flag.\n\nBut the soft spot here is not soft. The central claims—the classification and the integration result—depend on constructions like the weighted deformation space, and the body does not contain any of them. This is not a gap in a derivation; it is a total absence of the derivation. The stress-test note has it right, and I agree with the reader's call: the correct status is unverdictable, not \"mathematically wrong.\" The mismatch looks like an upload or compilation error rather than deliberate deception, so I wouldn't level an integrity accusation. But it means the submitted document is not a paper in the relevant sense.\n\nWould I send this to peer review? As submitted, no. A serious editor should desk-reject this file and invite the author to resubmit the correct full text. The abstract alone is not enough to referee, and there is nothing to check. If the real manuscript arrives, then it absolutely deserves a careful referee—someone who knows the weighted-manifold literature should look hard at the three characterizations and the wide-subalgebroid integration claim.\n\nMy take for the reading group: skip this one unless you want a five-minute case study in submission integrity. I won't cite it in the next year because I can't verify the content. If the author puts up the correct PDF, I'll be glad to look again.\n\nRecommendation: tell the editor to bounce it back, ask for the intended manuscript, and then treat that version as a normal submission for full review.","headline":"The abstract is a real-looking math paper; the body is an unrelated galaxy-evolution paper—nothing here is refereeable as submitted.","tokens_in":33112,"tokens_out":2247,"would_cite":false,"duration_ms":26375,"reading_group":"no","serious_thinker":"unclear","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["22A22","53D17","58H05"],"pacs":[],"model":"deepseek-v4-flash","headline":"Multiplicative weightings on a Lie groupoid correspond, along the groupoid's units, to Lie filtrations of its Lie algebroid — a dictionary between global multiplicative geometry and infinitesimal filtered algebra.","keywords":["weightings","Lie groupoids","Lie algebroids","multiplicative weighting","Lie filtrations","integration problem","weighted deformation space","homological vector fields"],"falsifier":"Open the submitted full text and look for the weighted deformation space construction or the classification of multiplicative weightings along the units by Lie filtrations; neither appears, since the body is an unrelated extragalactic-survey paper. Mathematically, the classification would be refuted by a Lie groupoid whose units carry an infinitesimally multiplicative weighting whose underlying subbundle filtration is not compatible with the Lie bracket of the algebroid — the claimed bijection would then assign a non-Lie filtration to a genuine weighting.","tokens_in":32277,"feed_emoji":"🪜","tokens_out":14410,"duration_ms":133392,"temperature":0.7,"pith_summary":"This paper develops the differential geometry of weightings — structures that assign growth orders to directions, encoded as filtrations of functions or sections — for vector bundles, Lie groupoids, and Lie algebroids, extending the existing theory of weighted manifolds. It defines weighted submanifolds, weighted immersions and embeddings with normal-form theorems, develops linear weightings for vector bundles, and gives three equivalent definitions of a multiplicative weighting on a Lie groupoid: through its structure maps, through the graph of its multiplication, and through the weighted deformation space. Its central results are that multiplicative weightings differentiate to infinitesimally multiplicative weightings, that the integration problem is solved along wide Lie subalgebroids, and that along the units of the groupoid multiplicative weightings are classified by Lie filtrations of the Lie algebroid. A sympathetic reader would care because this turns a global, geometric compatibility question into finite, checkable algebraic data at the infinitesimal level — the standard shape of a Lie-theoretic correspondence.","feed_headline":"Weightings on Lie groupoids are classified by Lie filtrations","feed_subtitle":"Along the units, groupoid weightings are the same thing as Lie filtrations of the algebroid.","key_machinery":"A Lie filtration of a Lie algebroid — a filtration of the underlying vector bundle by subbundles that is compatible with the Lie bracket — is the object that classifies multiplicative weightings along the units. The other load-bearing construction is the weighted deformation space of the groupoid, a one-parameter family of spaces that supplies the third equivalent characterization of multiplicative weightings and mediates between the global and infinitesimal pictures. The differentiation/integration correspondence is carried by the two further characterizations of infinitesimally multiplicative weightings, in terms of linear Poisson structures and in terms of homological vector fields.","core_discovery":"On its own terms, the paper claims that multiplicative weightings differentiate faithfully: a multiplicative weighting of a Lie groupoid induces an infinitesimally multiplicative weighting of its Lie algebroid, and conversely, along wide Lie subalgebroids, every infinitesimally multiplicative weighting integrates to a multiplicative one. Along the units of the groupoid, the structure unwinds to a Lie filtration of the Lie algebroid — a filtration of the underlying vector bundle compatible with the Lie bracket — so the global weighting data is classified by such filtrations. Infinitesimally multiplicative weightings are characterized two further ways, by linear Poisson structures and by homol","pith_inferences":["The classification along the units suggests a broader principle the paper leaves implicit: multiplicative groupoid structures are governed by filtered infinitesimal data, so other filtration types (by rank, by ideals, by growth rate) may correspond to further classes of groupoid weightings.","The homological-vector-field characterization points to a concrete follow-up: if an infinitesimally multiplicative weighting is equivalently a graded structure on the algebroid's cochain complex, then the general integration problem becomes the question of extending the associated graded data to a compatible Q-structure.","The paper's sufficient condition for the general integration problem invites a boundary test: constructing an infinitesimally multiplicative weighting along a non-wide subalgebroid that fails the condition — or proving none exists — would show how close the result is to a full classification.","The submitted full text is an unrelated galaxy-morphology paper, so the abstract's constructions and proofs cannot be located in the body; the mathematical claims are not checkable from this submission as received."],"forward_implications":["Along the units, multiplicative weightings of a Lie groupoid are in one-to-one correspondence with Lie filtrations of its Lie algebroid, so the global classification reduces to filtered data on the infinitesimal object.","Every infinitesimally multiplicative weighting on a wide Lie subalgebroid integrates to a multiplicative weighting of the groupoid, providing a large existence guarantee for the integration problem.","A weighting is multiplicative if and only if it satisfies any of three equivalent conditions — compatibility with the structure maps, weightedness of the multiplication graph, or descent from the weighted deformation space — so the condition can be checked in the most convenient presentation.","Infinitesimally multiplicative weightings are recognized equivalently as linear Poisson structures and as homological vector fields, linking weightings to Poisson geometry and graded-manifold theory.","Weighted submanifolds, weighted immersions, and weighted embeddings admit normal forms, giving local models for weighted geometry and for weighted morphisms, which are also characterizable via graphs and via weighted paths."],"supporting_citations":[],"fun_headline_variants":["Multiplicative weightings classified by Lie filtrations","Lie filtrations encode groupoid weightings","Weighted groupoids: integration along wide subalgebroids","From Lie groupoids to algebroids: weightings as filtrations"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The load-bearing premise is that the weighted deformation space construction exists with the properties needed to make the three characterizations of a multiplicative weighting equivalent — and that the submitted full text (which is in fact an unrelated galaxy-survey paper) contains the abstract's theorems.","fun_headline_variants_meta":{"raw":{"variants":["Multiplicative weightings classified by Lie filtrations","Lie filtrations encode groupoid weightings","Weighted groupoids: integration along wide subalgebroids","From Lie groupoids to algebroids: weightings as filtrations"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000329,"raw_usage":{"total_tokens":1710,"prompt_tokens":818,"completion_tokens":892,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":562,"completion_tokens_details":{"reasoning_tokens":823}},"tokens_in":562,"tokens_out":892,"duration_ms":8945,"temperature":1.0,"reasoning_tokens":823,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T20:32:18.731278+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Open the submitted full text and look for the weighted deformation space construction or the classification of multiplicative weightings along the units by Lie filtrations; neither appears, since the body is an unrelated extragalactic-survey paper. Mathematically, the classification would be refuted by a Lie groupoid whose units carry an infinitesimally multiplicative weighting whose underlying subbundle filtration is not compatible with the Lie bracket of the algebroid — the claimed bijection would then assign a non-Lie filtration to a genuine weighting.","supporting_citations":[],"review_version":1}