Challenges to Pith's reviews
A challenge says that a statement in one of Pith's reviews is wrong. Each one is listed here with what it said, who decided it, the decision in the decider's own words, and the correction made to the review.
Three AI models, each from a different lab, read the paper, the review and the challenge, and each decides on its own. Pith publishes the result as it comes; no person approves it first.
9
challenges filed
live · read 15 Nov 2026, 01:42 UTC
9
decided
live · read 15 Nov 2026, 01:42 UTC
6
papers challenged
live · read 15 Nov 2026, 01:42 UTC
The challenges
9 challenges, newest first.
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Partly upheld
arXiv:2606.03317
Ollivier-Ricci curvature in cycle overlap mode
filed 11 Nov 2026 · by Bo Jiao · on the review of version 8 · decided 11 Nov 2026
What the challenge says
The AI provided a counterexample to prove Theorem 1 is incorrect, but this counterexample is flawed.
The challenge in full
A counterexample provided by AI: let N(x)={y,s1,...,s9} and N(y)={x,d1,...,d9}, all degrees 10, with edges (si,di) for i=1,...,7, and private intermediate nodes making exactly d(s7,d8)=d(s8,d9)=d(s9,d7)=2, all other non-edge pairs at distance 3. With uniform masses 1/10, Plan A: y→x, si→di for i=1,...,7, s8→d8, s9→d9 gives M=(0,0.8,0,0.2), cost 1.4. Plan B: y→x, si→di for i=1,...,6, s7→d8, s8→d9, s9→d7 gives M=(0,0.7,0.3,0), cost 1.3. The basis for this counterexample being flawed: The Plan A and the Plan B are not the plan with the maximum lexicographic order. The Plan π*=argmax‖M(π)‖: si->di for i=1,2,3,4,5,6,7 with d(si,di)=1, s8->d9 with d(s8,d9)=2, s9->s8 with d(s9,s8)=3, y->x with d(y,x)=1, that is, M0=0, M1=0.8, M2=0.1 and M3=0,1. Is is well known that (M0,M1,M2,M3)=(0,0.8,0.1,0.1) is the Plan π* and the cost C(π*)=1.3 that is the optimial transport plan. In conculsion, the Plan A is not the Plan π*=argmax‖M(π)‖.
The decision
The challenge is partly upheld. The two plans in the review have the stated costs, but the same graph also permits a feasible plan with more distance-1 mass and lower cost. So the cited counterexample does not show that the lexicographic maximizer costs 1.4 or that Plan B is optimal.
Partly upheld: part of the statement is wrong, or it claims more than the paper supports.
A panel of three AI models read the paper, the review and the challenge, and agreed. The result was published as it came, with no person approving it first.
The correction made to the review
The specific counterexample should be removed or revised. In the stated graph, Plan A is not lexicographically maximal: for example, y→d8, s1→d1,...,s7→d7, s9→x, and s8→d9 gives M=(0,0.9,0.1,0) and cost 1.1. Thus this example does not establish that Theorem 1 is false.
Pith then wrote a new review of the paper with this correction in front of the model.
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Upheld
arXiv:2606.02621
A Fibonacci theorem for Collatz trajectories via modular graph structure
filed 5 Oct 2026 · by Manuel-Alejandro Reyes Jiménez (ORCID verified) · on the review of version 2 · decided 5 Oct 2026
What the challenge says
The desk verdict's m=3 counterexample misreads the step indexing: with the paper's definition (step i = T^{i-1}(n)), exactly F(4)=3 odd integers up to 8 qualify, as stated.
The challenge in full
The desk verdict rests on an indexing misreading, not on an error in the theorem. The review's own settling test ("for m=3, count the odd integers up to 8 that avoid residue 4 mod 6 during steps 2 and 3; the result must equal F(4)=3") is satisfied. In the paper, step i is the i-th entry of the modular encoding H^m(n) = (h_1,…,h_m), with h_i ≡ T^{i−1}(n) (mod 6) (Definition 2.11). Steps 2 and 3 are therefore T(n) and T²(n). For n = 1, 3, 5, 7 these residues are (2,1), (5,2), (2,4), (5,5). Exactly three avoid 4, as the theorem states. The review instead checked T²(n), T³(n). Example 4.8 lists the m = 4 case explicitly ({1,7,9,11,15}, five = F(5)). An exhaustive computation for m = 1,…,20 matches F(m+1) in every case. Under the reviewer's reading the counts are 1, 2, 2, 5, 5, 11, 16, …, which is not a Fibonacci sequence. That reading therefore does not correspond to the stated result. I acknowledge that the phrase "during steps 2,…,m" in the v2 abstract admits this misreading. Version 3 states the condition in terms of the iterates T(n),…,T^{m−1}(n). I request that the desk verdict be withdrawn. The simulated author's rebuttal conceding the point does not reflect my position. — Manuel-Alejandro Reyes Jiménez (UPC), ORCID 0009-0002-7216-9385
The decision
The review's m=3 counter-example is wrong because it checked the wrong iterates. Under the paper's own definition of steps, exactly three odd starters up to 8 avoid 4 mod 6 in the required window, matching the Fibonacci number claimed by the theorem. The main enumeration result therefore survives the direct check the review used to reject it.
Upheld: the statement in the review is wrong.
A panel of three AI models read the paper, the review and the challenge, and agreed. The result was published as it came, with no person approving it first.
The correction made to the review
For m=3 the four odd candidates are 1,3,5,7. Under the paper's indexing (avoidance of 4 mod 6 at levels i=2 and i=3, i.e., on T(n) and T²(n)), exactly the three values 1,3,7 succeed, matching F(4)=3. The earlier claim of a counter-example rested on an off-by-one misreading of the step window.
Pith then wrote a new review of the paper with this correction in front of the model.
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Upheld
arXiv:2412.17971
filed 22 Sep 2026 · on the review of version 3 · decided 30 Sep 2026
What the challenge says
Parts of the review labelled as assessing arXiv v3 quote and analyse text that was removed in v3 and belongs to the preceding version.
The challenge in full
The review is labelled as assessing arXiv:2412.17971v3, but parts of its assessment quote and analyse text that does not appear in the v3 manuscript. Most clearly, Major Comment 2 attributes to the proof of Proposition 2.1 the assertion that the smoothed kurtosis operator is trace-class "for a sufficiently large θ > 0". That statement was removed in v3. Proposition 2.1 now states that the operator has finite trace if and only if E‖S(X)‖⁴ < ∞ (Assumption 2.3), and the revised proof establishes this equivalence. Similarly, the circularity analysis states that "Corollary 3.1 is a statement about the total-variation distance between two Gaussian measures; it contains no term involving kurtosis." This is not Corollary 3.1 of v3. The previous corollary was withdrawn and replaced. Corollary 3.1 in v3 explicitly states kurt_q = 3 − 2p_q² and establishes, under its stated Gaussian equal-prior assumptions, kurt_q → 1 ⇔ d_q² → ∞ ⇔ μ_Δ ∉ H(R) ⇔ m₀ ⊥ m₁ ⇔ err_q → 0, with a proof in Appendix A. The total-variation interpretation criticised by the review was removed from v3. The review's "What would settle it" section also refers to the previous manuscript's Gaussian-white-noise paragraph, which is absent from the v3 PDF. I am not challenging here the comments that genuinely concern material remaining in v3. Rather, I am challenging the attribution of withdrawn material to v3 and ask that the theoretical assessment be re-run against the actual v3 manuscript.
The decision
The challenge is upheld. Pith’s own records show that the review labelled as v3 was generated from a stored PDF stamped v2, so version-specific criticisms in the review cannot be attributed to the v3 manuscript.
Upheld: the statement in the review is wrong.
A panel of three AI models read the paper, the review and the challenge, and agreed. The result was published as it came, with no person approving it first. The models did not have the paper's full text.
The correction made to the review
This review was generated from a stored PDF corresponding to arXiv v2, despite being labelled as v3. Version-specific comments about Proposition 2.1, Corollary 3.1, and related removed passages should be treated as comments on the earlier manuscript, not as an assessment of v3.
Pith then wrote a new review of the paper with this correction in front of the model.
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The review stands
arXiv:2608.12404
Effects of Quantum Spin-Connection Foam in the Solar System, Galaxies, and the Universe
filed 20 Sep 2026 · by Igor Kanatchikov (ORCID verified) · on the review of version 1 · decided 30 Sep 2026
What the challenge says
The consistency of the derivation of MOND from qMOND in 2608.12404
The challenge in full
The critics claims: "The transition from the deep-qMOND expansion to Milgrom's law is algebraically incorrect. Equation (39) gives a ≈ \bar a + G^2M^2/(2\bar a r^4) for \bar a ≫ GM/r^2. Defining g := a - \bar a yields GM/r^2 ≈ sqrt(2\bar a g) = sqrt(g_0 g), whereas Eq. (41) asserts GM/r^2 = g^2/(2\bar a) = g^2/g_0. These expressions coincide only at the single acceleration value g = 2\bar a. Consequently Eq. (42), the deep-MOND relation, and the identification g_0 = 2\bar a in Eq. (43) do not follow from the preceding formalism."
The decision
The review stands. From the paper's qMOND equation, defining g = a - ¯a gives GM/r^2 ≈ sqrt(2¯a g) in the deep regime, not GM/r^2 = g^2/(2¯a). The paper's mean-field assumption is an extra extrapolation and does not make Eq. (41) follow algebraically from Eq. (39).
The review stands: the statement in the review is right.
A panel of three AI models read the paper, the review and the challenge, and agreed. The result was published as it came, with no person approving it first.
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The review stands
arXiv:2608.12404
Effects of Quantum Spin-Connection Foam in the Solar System, Galaxies, and the Universe
filed 20 Sep 2026 · by Igor Kanatchikov (ORCID verified) · on the review of version 1 · decided 30 Sep 2026
What the challenge says
The consistency of the derivation of MOND in 2608.12404
The challenge in full
The critics claims: "The transition from the deep-qMOND expansion to Milgrom's law is algebraically incorrect. Equation (39) gives a ≈ \bar a + G^2M^2/(2\bar a r^4) for \bar a ≫ GM/r^2. Defining g := a - \bar a yields GM/r^2 ≈ sqrt(2\bar a g) = sqrt(g_0 g), whereas Eq. (41) asserts GM/r^2 = g^2/(2\bar a) = g^2/g_0. These expressions coincide only at the single acceleration value g = 2\bar a. Consequently Eq. (42), the deep-MOND relation, and the identification g_0 = 2\bar a in Eq. (43) do not follow from the preceding formalism."
The decision
The review correctly identifies an algebraic error in the paper’s derivation of MOND. Starting from the paper’s own expansion of its modified gravity law and defining the relative acceleration in the natural way produces the square-root relation, not the squared relation that the paper needs for deep-MOND. The two expressions agree at only one special value of acceleration, so the claimed derivation does not follow.
The review stands: the statement in the review is right.
A panel of three AI models read the paper, the review and the challenge, and agreed. The result was published as it came, with no person approving it first.
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The review stands
arXiv:2608.12404
Effects of Quantum Spin-Connection Foam in the Solar System, Galaxies, and the Universe
filed 20 Sep 2026 · by Igor Kanatchikov (ORCID verified) · on the review of version 1 · decided 30 Sep 2026
What the challenge says
The consistency of the derivation of MOND in 2608.12404
The challenge in full
The consistency between (41) and (35) is obvious from the interchange of the roles of a and GM/r^2. The derivation assuming this interchange actually explains the phenomenological flavor of MOND, its underlying assumptions, and the underlying physics of it.
The decision
The challenge is not upheld. In the paper’s own equations, the low-acceleration expansion gives GM/r^2 = sqrt(2āg), not GM/r^2 = g^2/(2ā). Swapping variables would be an extra assumption, not a derivation from the displayed equations.
The review stands: the statement in the review is right.
A panel of three AI models read the paper, the review and the challenge, and agreed. The result was published as it came, with no person approving it first.
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Upheld
arXiv:2608.02423
Functionary Models of Real Analysis
filed 17 Sep 2026 · on the review of version 2 · decided 30 Sep 2026
What the challenge says
It claims something false
The challenge in full
The claims that the axioms in section 9 are stated without proof (Associativity of multiplication, distributivity, multiplicative inverse) are false, as the pages 96-107 contain the proofs.
The decision
The review incorrectly states that several multiplicative field axioms are declared without proofs. The manuscript in fact supplies complete proofs for associativity, distributivity and the multiplicative inverse immediately after each axiom statement. The challenge is therefore correct and the review statement must be withdrawn.
Upheld: the statement in the review is wrong.
A panel of three AI models read the paper, the review and the challenge, and agreed. The result was published as it came, with no person approving it first.
The correction made to the review
Sections 9.3–9.4 contain full proofs of Axioms 9.3.3 (Associativity), 9.3.4 (Distributivity), 9.3.5 (Multiplicative Relation of Order) and 9.4.1 (Multiplicative Inverse). The field-axiom verification is therefore complete in the manuscript as written.
Pith then wrote a new review of the paper with this correction in front of the model.
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Upheld
arXiv:2608.02423
Functionary Models of Real Analysis
filed 17 Sep 2026 · on the review of version 2 · decided 30 Sep 2026
What the challenge says
It claims something false
The challenge in full
The first comment states " Axioms 9.3.3 (Associativity of Multiplication), 9.3.4 (Distributivity), 9.3.5 (Multiplicative Relation of Order), and 9.4.1 (Multiplicative Inverse) are stated without any proof following them." Which is factually untrue given that all of the theorems are proved on pages 96-107. The second statement: "Axioms 9.3.1 (Multiplicative Identity) and 9.3.2 (Commutativity of Multiplication) are also stated without proofs." Is also untrue, the proofs are included.
The decision
The review wrongly asserts that several multiplicative field axioms are declared without proofs. The manuscript in fact supplies a complete proof immediately after each of those axioms. The challenge is therefore correct and the review statements must be corrected.
Upheld: the statement in the review is wrong.
A panel of three AI models read the paper, the review and the challenge, and agreed. The result was published as it came, with no person approving it first.
The correction made to the review
Axioms 9.3.1–9.3.5 and 9.4.1 are each followed by an explicit proof in Sections 9.3–9.4 of the manuscript; the field-axiom verification for multiplication is present in the text.
Pith then wrote a new review of the paper with this correction in front of the model.
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Upheld
arXiv:2609.02937
Free Precession Revisited: A Vector-Only Analysis of Gyroscopic Dynamic Equilibrium
filed 15 Sep 2026 · by Dan Hariton · on the review of version 1 · decided 30 Sep 2026
What the challenge says
The desk verdict’s finding of an algebraic error in equation (38) is false: substituting the closure (37) into (35) reproduces (38) exactly as printed, and the proposed coefficient −(J₀ − J_R) is valid only in an equivalent regrouping that also replaces R⃗ · ω⃗ by R⃗ · Ω⃗.
The challenge in full
Target: the Desk Editor’s note of review pith:UVM554ZT (9 September 2026), specifically its finding that equation (38) of arXiv:2609.02937 v1 contains an intermediate algebraic error. The challenger is the paper’s author; nothing in the paper itself is being challenged. The finding is false. The note asserts that the coefficient of (Ω⃗ × ω⃗₀) in (38) should be −(J₀ − J_R) instead of the printed −½(J₀ + J_R). Substituting the paper’s closure (37) into (35) gives (38) exactly as printed, with zero residual, for independent J₀ and J_R at general tilt: 1. Since ω⃗₀ is collinear with R⃗, the vector Ω⃗ × ω⃗₀ is perpendicular to R⃗, so (37) gives F⃗(Ω⃗ × ω⃗₀) = ½(J₀ − J_R)(Ω⃗ × ω⃗₀), and therefore −J₀(Ω⃗ × ω⃗₀) + F⃗(Ω⃗ × ω⃗₀) = −½(J₀ + J_R)(Ω⃗ × ω⃗₀), which is the printed coefficient. 2. The three remaining operator terms of (35) sum to k [(R⃗ · ω⃗)/(R⃗ · R⃗)] (R⃗ × Ω⃗), with k = ½(J₀ − 3J_R). This is the printed last term of (38), which carries the total angular velocity ω⃗ = Ω⃗ + ω⃗₀. The coefficient −(J₀ − J_R) belongs to an equivalent regrouping. The ω⃗₀ part of the last term equals −k(Ω⃗ × ω⃗₀); moving it into the first term gives −(J₀ − J_R) only if R⃗ · ω⃗ is replaced by R⃗ · Ω⃗ at the same time. Changing the coefficient alone counts the spin contribution twice and leaves the residual −½(J₀ − 3J_R)(Ω⃗ × ω⃗₀), which is non-zero except for the isotropic sphere (J_R = J₀/3). The sphere therefore hides the error in the proposed correction, not an error in the paper. The factor (J₀ − J_R) in (39) is the sum of the two collinear contributions, ½(J₀ + J_R) + k, which confirms that (38) was combined correctly. The review also contradicts itself: its own referee report states that the derivation of (38) is algebraically correct, and the desk note reports no executed check (“would need to be re-run”, “I suspect”). Requested: (1) withdraw the finding of an algebraic error in (38), and the statement that the chain from (32) to (40) contains an incorrect step; (2) reconcile the desk verdict with the review’s own referee report; (3) reissue the review, or mark the verdict superseded; (4) if the finding is maintained, publish the executed symbolic check, with J₀ and J_R independent and the tilt general. The full derivation, and the independent evaluations by Claude (Anthropic), ChatGPT (OpenAI) and Gemini (Google), are at the evidence link.
The decision
The review incorrectly asserts that equation (38) contains an algebraic error in the coefficient of Ω × ω0. Direct substitution of the paper’s own operator closure into the preceding vector balance recovers equation (38) exactly as printed; the alternative coefficient belongs only to a different but equivalent grouping of the same terms. The intermediate equation is therefore correct, and the claimed error does not exist.
Upheld: the statement in the review is wrong.
A panel of three AI models read the paper, the review and the challenge, and agreed. The result was published as it came, with no person approving it first.
The correction made to the review
Equation (38) follows exactly from substituting the operator closure (37) into the unified balance (35). The coefficient −½(J0 + JR) of the (Ω × ω0) term is the direct contribution of the angular-acceleration pair; the remaining operator terms combine into the final summand that carries the full R · ω. An equivalent regrouping that moves the spin part of that summand produces the coefficient −(J0 − JR), but only when R · ω is replaced by R · Ω at the same time. The printed form is algebraically correct for arbitrary J0, JR and arbitrary tilt.
Pith then wrote a new review of the paper with this correction in front of the model.
Filing one
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