{"id":"619944d1-5833-4258-a9ca-ca55597955b4","arxiv_id":"2508.02848","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"For a family over a nonsingular curve, the relative Du Bois complex commutes with base change to a general point, but not to special points.","lead":"This paper gives a partial answer to an open question about when the relative Du Bois complex of a family over a smooth curve is preserved after pulling back to a general point of the base. It also shows that such base change usually fails at special points.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No significant objection identified: the abstract-level claim is plausible, but the supplied full text is corrupted, so the proof cannot be stress-tested.","rationale":"The reader's verdict is UNVERDICTED because the supplied text is unreadable, and my stress-test reaches the same conclusion: no specific mathematical flaw can be identified or ruled out. The reader's weakest assumption concerns inherited hypotheses from Kovács-Taji; while reasonable, it is not the same as my non-finding, since I do not claim that those hypotheses are likely to fail. I therefore agree with the overall verdict but only partially with the specific framing of the weakest assumption. No verdict adjustment is warranted.","tokens_in":12003,"tokens_out":11878,"duration_ms":153414,"concrete_test":"Fetch the clean PDF for arXiv:2508.02848 and re-derive the main theorem's proof with a focus on the step where the base point embedding iota_t: Spec k(t) -> C is used: verify that the base-change map is the derived pullback L iota_t^* of the relative Du Bois complex to the fiber, and that the proof justifies it for general closed points (e.g., via generic flatness or local freeness of the relevant cohomology sheaves) rather than treating the embedding as flat. Also confirm the special-point counterexample includes an explicit computation of both complexes. If either check fails, the claim's scope has to be narrowed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"After reading the abstract and the corrupted full text, I find no mathematical red flag in the central claim as stated. A generic base-change statement for a bounded derived-category object over a smooth curve is the kind of result one would expect to follow from generic flatness of the finitely many cohomology sheaves and the Kovács-Taji construction, and the companion 'failure at special points' part is a coherent boundary statement. The only load-bearing condition I can name is epistemic: the main theorem, its proof, and the promised examples are not inspectable in the supplied text, so I cannot confirm that the base-change morphism is defined for the intended class of points, that the Kovács-Taji hypotheses are met, or that the special-point counterexample is computed. This is not an objection to the mathematics; it is a statement that the proof is unverified.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper, arXiv:2508.02848 (math.AG), titled \"General base change for relative Du Bois complexes,\" is a short continuation of work by Kovács and Taji. The abstract claims that for a family parametrized by a non-singular curve, the relative Du Bois complex commutes with base change to a general point on the base, and that this property usually fails for special points. This would provide a partial answer to a question raised in arXiv:2307.07192. However, the version of the manuscript submitted for review contains a full text that is almost entirely corrupted and illegible; only the abstract is readable. As a result, none of the underlying definitions, theorem statements, proofs, or examples can be inspected. The present assessment is therefore based solely on the abstract and the general framing provided by the surrounding metadata.","tokens_in":12084,"tokens_out":2865,"duration_ms":31181,"significance":"If correct, the claimed result is a meaningful contribution: it would establish generic base change for a relative Du Bois complex over a smooth curve, while delineating the failure at special points, thereby sharpening and partially resolving a question from Kovács and Taji. The statement is concrete, falsifiable, and has clear scope. The paper appears to be a direct continuation of the cited work rather than a circular argument, and the abstract does not suggest that the target result is assumed. However, the significance cannot be properly evaluated because the technical content is inaccessible in the supplied version. The strength of the claim depends crucially on the hypotheses of the Kovács–Taji machinery (properness, flatness, relative Du Bois type, and the definition of 'general point'), none of which can be verified from the abstract alone. Machine-checked proofs, reproducible code, or parameter-free derivations are not visible in the legible portion of the manuscript.","major_comments":[{"comment":"The full text of the manuscript is corrupted beyond legibility in the version supplied for review; only the abstract is readable. All sections, including the introduction, definitions, theorem statements, proofs, and examples, appear as unreadable character sequences. This is a load-bearing issue because the central claim cannot be checked in any detail. Please provide a clean, complete, and legible version of the manuscript so that the derivation can be inspected.","section":"Entire body after the abstract"},{"comment":"The abstract does not state the precise hypotheses on the family for which the relative Du Bois complex is defined, nor the exact meaning of 'general point' on the base curve. Whether the claimed base-change result holds depends on these hypotheses (for instance, whether the family is proper, flat, or of relative Du Bois type, and whether the base field is algebraically closed or of characteristic zero). The full text presumably contains these statements, but their absence from the abstract and the illegibility of the body prevent verification. Please specify these conditions explicitly in the revision.","section":"Abstract"}],"minor_comments":[{"comment":"The abstract of the paper is for math.AG (arXiv:2508.02848), but the header of the full text includes the line 'arXiv:2508.02849v1 [eess.AS] 4 Aug 2025', which appears to be an unrelated identifier from a different subject class. Please check and correct the metadata in the manuscript.","section":"Metadata"},{"comment":"The abstract would be clearer if it stated the characteristic and base-field assumptions, since the relative Du Bois complex construction is typically considered over algebras of finite type over the complex numbers or over a field of characteristic zero.","section":"Abstract"}],"recommendation":"uncertain","confidential_remarks":"To the editor: the manuscript as submitted is not in a reviewable state because the full text is corrupted and only the abstract is legible. I could not verify any of the mathematical claims. The abstract-level claim is plausible, and there is no obvious sign of circularity, but without a readable proof no informed recommendation is possible. I recommend returning the manuscript to the authors to resubmit a clean, properly rendered PDF, after which I am willing to review it fully."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe one thing to know: Ji and Kovacs prove a generic base-change theorem for relative Du Bois complexes over a nonsingular curve, and show the analogous statement fails at special points. If correct, this is a genuine partial answer to a question Kovacs and Taji left open, and the generic/special distinction is exactly the right boundary.\n\nWhat the paper does well: it extends an established framework rather than starting over, the claim is concrete and falsifiable, and the negative result prevents a too-optimistic reading of the theory. The continuity with arXiv:2307.07192 is natural; one author was on that paper, so this is a continuation, and I do not see a circularity problem.\n\nThe soft spot is entirely epistemic: the supplied full text is corrupted beyond readability. I cannot check the definition of the base-change morphism, the hypotheses on the family (properness, flatness, Du Bois type), or the special-point counterexample. The stress-test found no red flag in the abstract, and neither did I, but that is not verification. The main theorem could fail if a hypothesis is missing, and the special-point example could hide an error.\n\nWho is this for: singularity theorists and MMP users who work with relative Du Bois complexes or the Kovacs-Taji machinery. It is not a paradigm shift, but a solid step on an explicit open question.\n\nRecommendation: send to a serious referee. The importance and plausibility justify referee time. The referee should verify the hypotheses on the family and compute the special-point example independently. If those pass, I would be happy to see it published and would cite it in my own work.","headline":"A plausible and well-scoped partial answer to a Kovacs-Taji question, but the supplied text is unreadable so the proof needs referee scrutiny.","tokens_in":12590,"tokens_out":3165,"would_cite":true,"duration_ms":33807,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["14B05","14D06","14F08"],"pacs":[],"model":"deepseek-v4-flash","headline":"For a family over a nonsingular curve, the relative Du Bois complex commutes with base change at a general point of the base, while special points generally break the rule.","keywords":["relative Du Bois complex","base change","generic fiber","Du Bois singularities","families over curves","derived category of sheaves","singularity theory","algebraic geometry"],"falsifier":"Choose a family $f\\colon X\\to C$ satisfying the theorem's hypotheses and a general point $t\\in C$. Compare the cohomology of the derived pullback of $\\underline{\\Omega}_{X/C}^{\\bullet}$ with the cohomology of the absolute Du Bois complex $\\underline{\\Omega}_{X_t}^{\\bullet}$. If the dimensions of $\\mathrm{H}^i$ differ for any $i$, the comparison map is not a quasi-isomorphism and the claimed generic base change is false.","tokens_in":11772,"feed_emoji":"📐","tokens_out":14904,"duration_ms":149229,"temperature":0.7,"pith_summary":"Du Bois complexes are the algebro-geometric replacement for the sheaf of holomorphic differentials on a singular variety: they package the cohomology of the variety while remembering enough about its singularities. In a family, one wants a relative Du Bois complex, and the natural test is whether pulling it back to a fiber recovers the Du Bois complex of that fiber. This paper proves that when the base is a nonsingular curve, the test is passed by a general point of the curve: the relative Du Bois complex commutes with base change there. It also shows that the test generally fails at special points, so the failure at special fibers is the typical behavior rather than an artifact of the construction. The result gives a partial answer to a question left open in the foundational work on relative Du Bois complexes.","feed_headline":"Du Bois base change: general fibers yes, special fibers no","feed_subtitle":"For families over smooth curves, the generic fiber inherits the relative complex; special fibers typically do not.","key_machinery":"The central object is the relative Du Bois complex $\\underline{\\Omega}_{X/C}^{\\bullet}$, a complex of sheaves on the total space that relativizes the absolute Du Bois complex. The absolute Du Bois complex is the complex whose cohomology recovers the cohomology of a singular variety and whose zeroth term detects Du Bois singularities. The load-bearing step is the comparison morphism between the pullback of the relative complex to a fiber and the fiber's own Du Bois complex; the nonsingular-curve hypothesis lets the paper show this comparison is an isomorphism at general points, while the failure at special points comes from the same comparison no longer being an isomorphism.","core_discovery":"The paper proves that for a morphism $f\\colon X\\to C$ with $C$ a nonsingular curve, the relative Du Bois complex $\\underline{\\Omega}_{X/C}^{\\bullet}$ commutes with base change to a general point $t\\in C$: the natural comparison morphism from the pullback of the relative complex to the fiber $X_t$ is a quasi-isomorphism with the absolute Du Bois complex $\\underline{\\Omega}_{X_t}^{\\bullet}$, so the two complexes have identical cohomology. The paper also shows that this base-change property usually fails at special points, so the positive generic statement is sharp and special fibers form the exceptional locus.","pith_inferences":["If the comparison morphism is functorial, the same one-dimensional argument could serve as the key lemma for a generic base-change theorem over smooth bases of higher dimension, by slicing the base with curves.","The special fibers where base change fails may provide explicit constructions of non-Du Bois singularities, effectively marking where a degeneration departs from the generic singularity type.","A natural sharpening would be to identify the exact closed set of bad points on the curve and to describe how the obstruction to base change there is controlled by the singularities of the total space."],"forward_implications":["For any family over a nonsingular curve, the Du Bois complex of a general fiber can be computed by restricting the relative Du Bois complex of the total space, avoiding a separate resolution of each fiber.","Any cohomological invariant that the relative complex encodes is the same for the generic fiber and for all nearby fibers, because the base-change comparison is an isomorphism on a dense open set.","The special-point counterexamples show that a base-change theorem for relative Du Bois complexes cannot hold without a genericity hypothesis; special fibers must be studied on their own terms.","This settles the motivating question for one-dimensional bases: the generic part of the base change is true, while the special-part failure is an expected phenomenon."],"supporting_citations":[],"fun_headline_variants":["Du Bois base change: generic yes, special rarely","Relative Du Bois complex: base change at general points","Base change for Du Bois: works for general, fails for special","Du Bois complex: base change generically, not at specials","Generic base change ok, special fails for Du Bois complex"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The claim depends on the prior construction of relative Du Bois complexes being valid for all morphisms over nonsingular curves; if that construction imposes extra hypotheses such as properness, flatness, or a Du Bois condition on the total space, the generic base-change theorem applies only within that restricted class.","fun_headline_variants_meta":{"raw":{"variants":["Du Bois base change: generic yes, special rarely","Relative Du Bois complex: base change at general points","Base change for Du Bois: works for general, fails for special","Du Bois complex: base change generically, not at specials","Generic base change ok, special fails for Du Bois complex"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000204,"raw_usage":{"total_tokens":1274,"prompt_tokens":714,"completion_tokens":560,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":330,"completion_tokens_details":{"reasoning_tokens":477}},"tokens_in":330,"tokens_out":560,"duration_ms":5498,"temperature":1.0,"reasoning_tokens":477,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:35:42.477144+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Choose a family $f\\colon X\\to C$ satisfying the theorem's hypotheses and a general point $t\\in C$. Compare the cohomology of the derived pullback of $\\underline{\\Omega}_{X/C}^{\\bullet}$ with the cohomology of the absolute Du Bois complex $\\underline{\\Omega}_{X_t}^{\\bullet}$. If the dimensions of $\\mathrm{H}^i$ differ for any $i$, the comparison map is not a quasi-isomorphism and the claimed generic base change is false.","supporting_citations":[],"review_version":2}