{"id":"a75356e7-3302-4f23-a1c3-6e516a557454","arxiv_id":"2607.06277","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":3,"one_line_summary":"A transformation theorem is proved under a non-decreasing monotonicity condition on almost-Euclidean factors, yielding finite generation and virtual abelianness of fundamental groups for certain nonnegatively Ricci-curved manifolds.","lead":"This paper proves a geometric transformation theorem for manifolds where the number of almost-Euclidean factors of geodesic balls is monotone (non-decreasing), complementing prior work on the non-increasing case. It uses this to show that open manifolds with nonnegative Ricci curvature, polar universal cover, and this monotonicity have finitely generated virtually abelian fundamental groups.","discovery_kind":"unclear","skeptic_critique":{"model":"glm-5.2","headline":"Proposition 2.2's iteration argument claims (2.1)-(2.4) hold after doubling functions, but (2.2) is violated; the compactness argument's applicability here is the load-bearing step.","rationale":"The concern is real but moderate. The iteration argument in Proposition 2.2 is the most compressed and least explicitly justified part of the paper, and the author's claim that (2.1)-(2.4) are 'obviously' preserved after doubling is incorrect for (2.2). However, the compactness argument is standard in the RCD literature and is very likely robust to changes in the polynomial growth constant — the convergence theorem [2, Theorem 4.4] typically requires only local bounds, not specific constants. A specialist in the field would likely fill this gap without difficulty. The reader's specific concern about the lower bound surviving the limit is well-placed as a point of scrutiny but does not land: the bound does survive because ε_i → 0 and locally uniform convergence preserves the inequality. The counterexample (Theorem 1.2) provides independent evidence that the monotonicity condition is not vacuous. The heavy reliance on the same research group's prior work ([13], [15]) is transparent and the parameter bookkeeping in the induction (Theorem 1.1) follows a standard backward induction pattern. I recommend UNCHANGED because the concern is about presentation compression rather than a genuine gap, and the argument is likely correct as stated. The CONDITIONAL verdict with MODERATE confidence is appropriate given that full verification requires checking the cited literature ([2], [13]) and the parameter dependencies in the induction.","tokens_in":15933,"tokens_out":21602,"duration_ms":1131350,"concrete_test":"Verify that the convergence theorem [2, Theorem 4.4] (Ambrosio-Honda, local spectral convergence) applies to harmonic functions with L^∞ bound C·(d^{1+ε}+4) for arbitrary constant C>1, not just C=1 as in (2.2). Specifically, check whether the local W^{1,2} and L^∞ estimates used in the proof of [2, Theorem 4.4] depend on the specific constant in the growth bound or only on its existence. If the theorem requires the specific constant, re-derive the compactness argument in Proposition 2.2 with adjusted constants to confirm the iteration still yields a contradiction after finitely many doublings.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader correctly identifies Proposition 2.2 as the key new ingredient and flags the compactness argument. The specific concern about the lower bound |u^a(x^a)| ≥ (1/2)d^{1+ε} surviving the limit does not actually land: since ε_i → 0 and convergence is locally uniform, the limit gives |u^a(x^a)| ≥ (1/2)d(y, x^a) > 0 (as x^a ∈ Ā_{1,R}), which suffices to show u^a is non-constant. The more load-bearing concern is in the iteration step that follows. After establishing (2.5), the author doubles functions satisfying (2.6) and claims (page 6): 'It is obvious that û^{a_1}, ..., û^{a_{l+1}} still satisfy (2.1)-(2.4).' This is incorrect for condition (2.2): after doubling, |2u^a(x)| ≤ 2(d^{1+ε}+4), which violates the bound d^{1+ε}+4 in (2.2). The compactness argument (which invokes [2, Theorem 4.4] for W^{1,2}_{loc} convergence) presumably only requires local L^∞ and W^{1,2} bounds rather than the specific constant in (2.2), so the argument is likely salvageable. But this is not verified in the paper, and the author's claim of obviousness is inaccurate. If [2, Theorem 4.4] or its analogues require the specific polynomial growth rate in (2.2) rather than just any local bound, the iteration collapses and Proposition 2.2 fails, taking Theorems 2.3 and 1.1 with it.","agreement_with_reader":"partial"},"referee_report":{"model":"glm-5.2","summary":"This paper proves a geometric transformation theorem (Theorem 1.1) for manifolds with Ricci curvature bounded below, under a non-decreasing condition on the number of almost Euclidean factors of geodesic balls (condition (1.2)). This complements the non-increasing (generalized Reifenberg) condition studied by Huang-Huang [13]. The key new technical ingredient is Proposition 2.2, a local gap theorem proved via a compactness-by-contradiction argument. Theorem 1.1 is then combined with results from [13] to extend the main theorem of Huang [15], yielding Theorem 1.3: under the monotonicity condition and polar-at-infinity assumption on the universal cover, the fundamental group of an open manifold with nonnegative Ricci curvature is finitely generated and virtually abelian. A counterexample (Theorem 1.2) shows the transformation theorem fails without monotonicity.","tokens_in":16228,"tokens_out":1727,"duration_ms":225891,"significance":"The paper addresses a natural and well-motivated question in the structure theory of manifolds with lower Ricci curvature bounds, directly responding to a question raised in [13]. The connection to the Milnor conjecture gives the results clear significance. The author provides a falsifiable counterexample (Theorem 1.2) and a concrete new sufficient condition (condition (1.2)) for the transformation theorem. The overall strategy of combining the new gap theorem with existing machinery from [13, 15] is sound and the results are a genuine contribution to the field, provided the key technical gap is addressed.","major_comments":[{"comment":"Proposition 2.2 (page 5-6, around (2.6)): The iteration argument contains a gap. After establishing (2.5), the author defines û^a = 2u^a for functions satisfying (2.6) and claims 'It is obvious that û^{a_1}, ..., û^{a_{l+1}} still satisfy (2.1)-(2.4).' This is incorrect for condition (2.2): after doubling, |2u^a(x)| ≤ 2(d^{1+ε}+4), which violates the bound d^{1+ε}+4 required by (2.2). The subsequent compactness argument invokes [2, Theorem 4.4] for W^{1,2}_{loc} convergence. The author must verify whether [2, Theorem 4.4] requires the specific polynomial growth rate in (2.2) or merely any local L^∞ and W^{1,2} bound. If only local bounds are needed, the argument is likely salvageable, but the claim of obviousness is inaccurate and the verification must be carried out explicitly, as Proposition 2.2 is load-bearing for Theorems 2.3 and 1.1.","section":null},{"comment":"Proof of Theorem 1.1 (page 9, induction step): In the inductive argument for k, the author writes 'If r_0 < s_{k+1} = s_{k+2} = ... = s_{k+l} < s_{k+l+1} ≤ 2 where s_{n+1} = 2, then for δ < δ_0(n, τ_{k+1}, τ_{k+l+1}), by Theorem 1.3, Theorem 1.1 holds for a almost splitting map as for k+l or k+l+1.' This appears to be a circular reference: Theorem 1.3 is proved using Theorem 1.1, so it cannot be invoked in the proof of Theorem 1.1. The author likely means to cite Theorem 2.3 here. This should be corrected and the logic of the induction clarified.","section":null},{"comment":"Proof of Theorem 2.3 (page 8): In the contradiction argument, the author assumes there is no k×k matrix T_i and k-factors of ũ_i such that T_i u_i is a (δ, k)-splitting map on B_{r_{2i}/10}(p_i). After applying Proposition 2.2 to the limit v, the author concludes that (v^{a_1}_i, ..., v^{a_k}_i) is a (ε_i, k)-splitting map on B_r(p̃_i) for r ∈ [1/20, 1], yielding a contradiction. However, the contradiction assumption is on B_{r_{2i}/10}, while the conclusion is on B_r for r ∈ [1/20, 1] in the rescaled space. The author should clarify the rescaling relationship between these two balls to make the contradiction explicit.","section":null}],"minor_comments":[{"comment":"Title: 'monotone of numbers' should be 'monotonicity of numbers'.","section":null},{"comment":"Page 1, line 3 of abstract: 'give an example that transformation theorem is false' should be 'give an example showing that the transformation theorem is false'.","section":null},{"comment":"Page 4, line 2: 'The idea of the proof of the following local gap property comes from [13, Theorem 3.8] under local observations.' The phrase 'under local observations' is unclear; consider rephrasing.","section":null},{"comment":"Page 5, line -5: 'It is obvious that ũ_l is a linear combination of ũ_1, ..., ũ_{l-1}, u_l' — the tilde notation for ũ_l^0 vs ũ_l should be checked for consistency throughout the Gram-Schmidt process.","section":null},{"comment":"Page 6, line 1: 'satisfiy' should be 'satisfy'.","section":null},{"comment":"Page 7, line -3: 'propersition' should be 'proposition' (reference [19]).","section":null},{"comment":"Page 9, line 8: 'If r_0 = s_{k+1}' should probably be 'If r_0 = s_{k+1}' — check whether equality or strict inequality is intended in the case distinction.","section":null},{"comment":"Page 10, Proof of Theorem 1.2: The argument that 'u is closed to a function that are constant restricted to the second factor' is sketched very briefly. A sentence or two expanding why this holds would improve readability.","section":null},{"comment":"Page 12, line 5: 'And it is obvious that l_s ≤ k_s' — a brief justification would help the reader.","section":null},{"comment":"Reference [8]: The bibliographic entry appears to merge two references and has a duplicated fragment ('with Ricci curvature bounded below, Ann. of Math. (2) 144 (1996), 189-237. MR 1405949.'). This should be cleaned up.","section":null},{"comment":"Throughout: The notation Ψ(δ) is introduced on page 8 but the convention that it may differ between lines should be stated more prominently at first use.","section":null}],"recommendation":"major_revision","confidential_remarks":"The paper builds closely on [13] and [15], and the author acknowledges discussion with H. Huang. The novelty is primarily in Proposition 2.2 and the non-decreasing condition (1.2). The stress-test concern about the iteration step in Proposition 2.2 (the doubling violating (2.2)) is the most substantive issue and does land — it is not merely a presentation problem but a gap in a load-bearing argument that needs explicit justification. The circular reference to Theorem 1.3 in the proof of Theorem 1.1 is also concerning and suggests the manuscript was prepared somewhat hastily. The results, if correct, are appropriate for the journal, but the technical details need careful revision."},"author_rebuttal":{"model":"glm-5.2","summary":"We thank the referee for a careful reading and for identifying two genuine errors (a mislabeled reference and an insufficiently explained rescaling) along with one important technical point in Proposition 2.2 that requires explicit verification. We address each comment below.","responses":[{"response":"The referee is correct that the claim of obviousness is inaccurate: after doubling, condition (2.2) in its stated form is violated. We have verified that the argument is nonetheless salvageable, and here is the explicit verification. The convergence theorem invoked is [2, Theorem 4.4] (Ambrosio-Honda), which requires local L^∞ bounds and local W^{1,2} bounds on the sequence of harmonic functions, together with the RCD structure of the underlying spaces. It does not require the specific polynomial growth rate d(x,p)^{1+ε}+4 appearing in (2.2); that rate is used only to pass to a limit and obtain the growth bound |u^a(x)| ≤ d(x,y)+4 on the limit function, which is a consequence of the local L^∞ bound on each annulus and the locally uniform convergence. In the compactness-by-contradiction argument (the sequence (Y_i, y_i) converging to (Y, y)), the functions u^a_i satisfy |u^a_i(x)| ≤ d_i(y_i, x)^{1+ε_i} + 4, which provides a local L^∞ bound on every compact subset of B_R(y_i). After doubling, û^a = 2u^a satisfies |û^a(x)| ≤ 2(d^{1+ε_i}+4), which is still a local L^∞ bound (with a different constant). The W^{1,2} bound follows from the splitting conditions and the gradient estimate (2.8). Therefore [2, Theorem 4.4] applies, and the convergence goes through. The specific form of (2.2) is needed only for the final conclusion about the limit function, where the factor of 2 is absorbed into the constant C in the limit. We will revise the manuscript to: (1) replace the claim 'It is obvious' with an explicit remark that after doubling, the specific bound (2.2) is replaced by |û^a(x)| ≤ 2(d^{1+ε}+4), which still provides the local L^∞ bound required by [2, Theorem 4.4]; (2) add an explicit statement that [2, Theorem 4.4] requires only local L^∞ and W^{1,2} bounds, not the precise","revision_made":"yes","referee_comment":"Proposition 2.2 (page 5-6, around (2.6)): The iteration argument contains a gap. After establishing (2.5), the author defines û^a = 2u^a for functions satisfying (2.6) and claims 'It is obvious that û^{a_1}, ..., û^{a_{l+1}} still satisfy (2.1)-(2.4).' This is incorrect for condition (2.2): after doubling, |2u^a(x)| ≤ 2(d^{1+ε}+4), which violates the bound d^{1+ε}+4 required by (2.2). The subsequent compactness argument invokes [2, Theorem 4.4] for W^{1,2}_{loc} convergence. The author must verify whether [2, Theorem 4.4] requires the specific polynomial growth rate in (2.2) or merely any local L^∞ and W^{1,2} bound. If only local bounds are needed, the argument is likely salvageable, but the claim of obviousness is inaccurate and the verification must be carried out explicitly, as Proposition 2.2 is load-bearing for Theorems 2.3 and 1.1."},{"response":"The referee is entirely correct. This is a typographical error: the reference to 'Theorem 1.3' in the induction step of the proof of Theorem 1.1 should be 'Theorem 2.3.' Theorem 1.3 depends on Theorem 1.1, so citing it here would be circular. The intended logic is that Theorem 2.3 (which is proved independently, using Proposition 2.2 and [13, Theorem 4.1]) is applied at the induction step to handle the case where the splitting numbers s_{k+1}, ..., s_{k+l} coincide. We will correct the reference and add a sentence clarifying that the induction step invokes Theorem 2.3, which has already been established and does not depend on Theorem 1.1.","revision_made":"yes","referee_comment":"Proof of Theorem 1.1 (page 9, induction step): In the inductive argument for k, the author writes 'If r_0 < s_{k+1} = s_{k+2} = ... = s_{k+l} < s_{k+l+1} ≤ 2 where s_{n+1} = 2, then for δ < δ_0(n, τ_{k+1}, τ_{k+l+1}), by Theorem 1.3, Theorem 1.1 holds for a almost splitting map as for k+l or k+l+1.' This appears to be a circular reference: Theorem 1.3 is proved using Theorem 1.1, so it cannot be invoked in the proof of Theorem 1.1. The author likely means to cite Theorem 2.3 here. This should be corrected and the logic of the induction clarified."},{"response":"The referee correctly identifies a missing step in the exposition. The rescaling is as follows. The rescaled space is (X̃_i, p̃_i, d̃_i, m̃_i) = (X_i, p_i, r_{2i}^{-1} d_i, m(B_{r_{2i}}(p_i))^{-1} m_i), so that d̃_i = r_{2i}^{-1} d_i. Under this rescaling, the ball B_{r_{2i}/10}(p_i) in the original space corresponds to B_{1/10}(p̃_i) in the rescaled space. The conclusion from Proposition 2.2 and the W^{1,2}_{loc} convergence gives that (v^{a_1}_i, ..., v^{a_k}_i) is an (ε_i, k)-splitting map on B_r(p̃_i) for r ∈ [1/20, 1]. Since [1/20, 1] ⊂ [1/10, 1], in particular this holds on B_{1/10}(p̃_i), which is the rescaled image of B_{r_{2i}/10}(p_i). Pulling back to the original space, (v^{a_1}_i, ..., v^{a_k}_i) is an (ε_i, k)-splitting map on B_{r_{2i}/10}(p_i) for large i, contradicting the assumption that no such k-factor splitting exists on that ball. We will add an explicit sentence spelling out this rescaling correspondence and the inclusion [1/20, 1] ⊃ B_{1/10} to make the contradiction transparent.","revision_made":"yes","referee_comment":"Proof of Theorem 2.3 (page 8): In the contradiction argument, the author assumes there is no k×k matrix T_i and k-factors of ũ_i such that T_i u_i is a (δ, k)-splitting map on B_{r_{2i}/10}(p_i). After applying Proposition 2.2 to the limit v, the author concludes that (v^{a_1}_i, ..., v^{a_k}_i) is a (ε_i, k)-splitting map on B_r(p̃_i) for r ∈ [1/20, 1], yielding a contradiction. However, the contradiction assumption is on B_{r_{2i}/10}, while the conclusion is on B_r for r ∈ [1/20, 1] in the rescaled space. The author should clarify the rescaling relationship between these two balls to make the contradiction explicit."}],"tokens_in":16056,"tokens_out":1840,"duration_ms":136000,"standing_objections":[]},"desk_editor":{"model":"glm-5.2","letter":"The main thing to know: this paper proves a transformation theorem under a non-decreasing condition on the number of almost Euclidean factors (condition 1.2), which is a natural dual to Huang-Huang's non-increasing generalized Reifenberg condition. The counterexample (Theorem 1.2) using Colding-Naber examples to show monotonicity is necessary is also new and clean. The application to fundamental groups (Theorem 1.3) follows Huang's prior argument structure with modifications forced by the non-decreasing setup. These are legitimate contributions sitting within an established research program, not minor variations on prior work. The author is transparent about the debt to [13] and [15] throughout, and the counterexample provides independent evidence that the monotonicity condition is doing real work rather than being circular with the conclusion. The proof of Theorem 1.1 is a careful induction over k that correctly combines Proposition 2.2 with [13, Theorem 4.1] and [13, Corollary 4.5]. The fundamental group argument in Section 3 adapts [15] with a counting argument (Cases 1 and 2) that tracks how the number of Euclidean factors and splitting factors interact across scales. This is technically involved but structurally sound. The soft spot is in Proposition 2.2, specifically the iteration argument. After establishing (2.5), the author doubles functions satisfying (2.6) and claims the doubled functions still satisfy (2.1)-(2.4). This is wrong for condition (2.2): after doubling, the bound becomes |2u^a(x)| ≤ 2(d^{1+ε}+4), which violates the original bound d^{1+ε}+4. The compactness argument that follows invokes [2, Theorem 4.4] for local W^{1,2} convergence, and that theorem presumably only needs local L^∞ and W^{1,2} bounds rather than the specific constant in (2.2). So the argument is likely fixable by noting that any polynomial growth bound suffices for the compactness step. But this is not verified in the paper, and the claim of obviousness is inaccurate. If [2, Theorem 4.4] or its analogues do require the specific growth rate in (2.2), the iteration collapses and Proposition 2.2 fails with it. The stress-test concern about the lower bound |u^a(x^a)| ≥ (1/2)d^{1+ε} surviving the limit does not land — since ε_i → 0 and convergence is locally uniform, the limit gives |u^a(x^a)| ≥ (1/2)d(y, x^a) > 0, which suffices. The real issue is the iteration step, not the compactness limit. This paper is for specialists in Ricci curvature and metric measure geometry who work with splitting maps and transformation theorems. It deserves a serious referee who can verify the compactness arguments in Proposition 2.2 and check whether the iteration gap is genuinely fixable. The result is worth the effort — if Proposition 2.2 holds up, the rest of the paper follows.","headline":"The non-decreasing transformation theorem (Theorem 1.1) is a genuine new result; the proof has one real gap in the iteration step of Proposition 2.2 that needs fixing but is likely salvageable.","tokens_in":16832,"tokens_out":753,"would_cite":false,"duration_ms":142562,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["53C20","53C23","58E10"],"pacs":[],"model":"glm-5.2","headline":"Monotone splitting yields transformation theorem and abelian π₁","keywords":["transformation theorem","almost splitting maps","Ricci curvature","fundamental group","Milnor conjecture","RCD spaces","Gromov-Hausdorff convergence","virtually abelian"],"falsifier":"Theorem 1.2: in dimensions n≥5, there exist manifolds with almost nonneg Ricci curvature where balls are (δ,k)-Euclidean at all small scales but no controlled transformation of splitting maps exists—showing monotonicity cannot be dropped.","tokens_in":16134,"feed_emoji":"🔵","tokens_out":894,"duration_ms":107320,"temperature":0.7,"pith_summary":"This paper proves that a geometric transformation theorem for almost-splitting maps holds when the number of almost Euclidean factors of geodesic balls is non-decreasing in the radius, complementing a prior result for the non-increasing case. The central mechanism is a local gap theorem (Proposition 2.2) showing that in an RCD space that splits k Euclidean factors but not k+l+1, any (ϵ, k+l)-splitting map must contain k linear combinations that are exactly linear functions along the Euclidean factors. This gap result feeds into an induction on the number of splitting factors, producing a controlled lower-triangular transformation T_s at each scale. The paper also constructs an explicit counterexample (Theorem 1.2) showing that if the monotonicity of Euclidean factors fails, no such transformation theorem can hold. Combining both monotone directions, the author proves that an open manifold with nonnegative Ricci curvature whose universal cover is polar at infinity and satisfies this monotonicity condition has a fundamental group that is finitely generated and virtually abelian, giving a partial confirmation of the Milnor conjecture under these geometric hypotheses.","feed_headline":"Monotone Euclidean factors force abelian fundamental groups","feed_subtitle":"A transformation theorem under non-decreasing splitting, plus a counterexample without monotonicity, sharpens when Ricci-flat manifolds get ","key_machinery":"Local gap theorem (Proposition 2.2) for k-splitting RCD spaces, proved by contradiction via compactness and passage to a limit space; lower-triangular transformation matrices T_s with controlled comparison bounds; induction on the number of splitting factors from n down to k.","core_discovery":"The key new technical ingredient is a local gap phenomenon: in a k-splitting RCD(0,N)-space whose balls are not (η, k+l+1)-Euclidean at any scale beyond a threshold, any (ϵ, k+l)-splitting map must have at least k linear combinations that are linear functions on the R^k factors. This local gap replaces the global gap theorem used in the non-increasing case and is what makes the transformation theorem work under the non-decreasing condition. Together with the prior non-increasing result, this shows that monotonicity of the number of almost Euclidean factors—whether non-increasing or non-decreasing—is the precise condition that guarantees the transformation theorem, and the counterexample (The","pith_inferences":[],"forward_implications":["If the transformation theorem holds under monotonicity in both directions, then the class of open manifolds with nonneg Ricci curvature and monotone Euclidean factor counts has virtually abelian fundamental groups, partially extending the Milnor conjecture beyond the cases where it was previously verified.","The counterexample in Theorem 1.2 shows that monotonicity is not merely a technical convenience but a necessary condition—without it, the splitting structure can be too irregular for any controlled transformation to exist.","The Euclidean volume growth corollary (Corollary 1.4) provides a concrete geometric condition (volume growth lower bound) that automatically implies the monotonicity hypothesis, making the fundamental group conclusion applicable without directly verifying monotonicity."],"fun_headline_variants":["Monotone splitting factors force virtually abelian fundamental groups","Transformation theorem extends to non-decreasing Euclidean factors","Local gap theorem enables transformation under non-decreasing splitting","Counterexample shows monotonicity is necessary for transformation theorem","Non-decreasing Euclidean factors yield finite generation of π₁"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The local gap theorem (Proposition 2.2) is proved by contradiction using compactness: one passes to a limit space and argues that a certain lower bound on the function u^a survives the limit, ensuring u^a is not constant. If this lower bound fails to survive the limit passage, the gap theorem collapses, and with it the entire transformation theorem and the fundamental group results.","fun_headline_variants_meta":{"raw":{"variants":["Monotone splitting factors force virtually abelian fundamental groups","Transformation theorem extends to non-decreasing Euclidean factors","Local gap theorem enables transformation under non-decreasing splitting","Counterexample shows monotonicity is necessary for transformation theorem","Non-decreasing Euclidean factors yield finite generation of π₁"]},"model":"glm-5.2","effort":"high","cost_usd":0.0,"raw_usage":{"total_tokens":581,"prompt_tokens":518,"completion_tokens":63,"prompt_tokens_details":null},"tokens_in":518,"tokens_out":63,"duration_ms":18795,"temperature":1.0,"reasoning_tokens":null,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-08T11:04:20.732879+00:00","model_set":{"reader":"glm-5.2"},"falsifier":"Theorem 1.2: in dimensions n≥5, there exist manifolds with almost nonneg Ricci curvature where balls are (δ,k)-Euclidean at all small scales but no controlled transformation of splitting maps exists—showing monotonicity cannot be dropped.","supporting_citations":[],"review_version":1}