category_name_readable: Functional Analysis

comments: 45 pages. Various improvements of the presentation, and an error in the proof of Theorem 19 is corrected

Location of Error: Theorem 19

title_extracted_from_tex: On coarse geometry of separable dual Banach spaces


category_name_readable: Logic

comments: In this version, the erroneous Proposition 6.10 is corrected

Location of Error: Proposition 6.10

Liscence: arXiv.org - Non-exclusive license to distribute

title_extracted_from_tex: Categories of orthosets and adjointable maps


category_name_readable: Algebraic Topology

comments: 43 pages, 4 figures. Corrected an error in the proof of Theorem B. Moved the section on interval decomposability to another preprint. Some terminology has been renamed. Other minor changes

Location of Error: Theorem B

Liscence: CC BY-SA 4.0

title_extracted_from_tex: Poset functor cocalculus and applications to topological data analysis


category_name_readable: Analysis of PDEs

comments: Corrected a major error in the proof of Theorem 3.1 and revised other flawed proofs

Location of Error: Theorem 3.1

title_extracted_from_tex: Connecting SPDE to SGMs


category_name_readable: Group Theory

comments: 19 pages. Fixes a mistake in the proof of Theorem 1.2, by refining the definition of balanced Artin groups

Location of Error: Theorem 1.2

title_extracted_from_tex: On the $\Sigma^1$ and $\Sigma^2$-invariants of Artin groups


category_name_readable: Commutative Algebra

comments: Removed redundant and incorrect proof of Lemma 2.3, updated introduction

Location of Error: Lemma 2.3

title_extracted_from_tex: Rational Invariants of even degree polynomials under the orthogonal group


category_name_readable: Optimization and Control

comments: We find a counterexample to illustrate that Theorem 5 (iii) and (iv) are incorrect

Location of Error: Theorem 5

title_extracted_from_tex: Comments and extensions on ``State-equivalent form and minimum-order compensator design for rectangular descriptor systems''


category_name_readable: Differential Geometry

comments: I find that there is a mistake in the proof of Theorem 2.2, I give a new proof in this version

Location of Error: Theorem 2.2

title_extracted_from_tex: Singularity of mean curvature flow with bounded mean curvature and Morse index


category_name_readable: Combinatorics

comments: I thank Nathan Bowler for pointing out a critical mistake at the end of my claimed proof of Theorem 2.1. The set ${^*}A \cap {^*}\mathbb{I}$ is not necessarily contained in its internal star extension as it was claimed in the last line of that proof. The purported proofs of both conjectures had this issue. An expository article growing out of the correct parts of this work will be posted soon

Location of Error: Theorem 2.1

title_extracted_from_tex: Matroid intersection and packing/covering conjectures are true in the class of finitary matroids


category_name_readable: Number Theory

comments: Fixed proof of Lemma 8, other minor changes

Location of Error: Lemma 8

title_extracted_from_tex: Non-isomorphic abelian varieties with the same arithmetic


comments: 25 pages, comments welcome; version 2 includes the addition of a section on Dedekind domains and the correction of an error in Proposition 5.1 of version 1

Location of Error: Proposition 5.1

title_extracted_from_tex: Profinite Rigidity over Noetherian Domains


category_name_readable: Dynamical Systems

comments: Lemma 4.1 has been corrected after N. Tedesco pointed out a mistake in the calculations. The main results are unchanged

Location of Error: Lemma 4.1

title_extracted_from_tex: Finite codimension stability of invariant surfaces


category_name_readable: Data Structures and Algorithms

comments: Appeared at ICALP 2025. Fixed small mistake in Lemma 20

Location of Error: Lemma 20

title_extracted_from_tex: Light Edge Fault Tolerant Graph Spanners


comments: Version 2: fixed statement and proof of Lemma 3.5. 33 pages, 10 figures. Comments are welcome!

Location of Error: Lemma 3.5

title_extracted_from_tex: Rectification of dendroidal left fibrations


comments: An inaccuracy in the proof of Theorem 5.1 (6) has been fixed

Location of Error: Theorem 5.1

title_extracted_from_tex: Equationally separable classes of groups


category_name_readable: Probability

comments: Correction of the speed of convergence in Theorem 4.5

Location of Error: Theorem 4.5

title_extracted_from_tex: Empirical distribution of ancestral lineages in populations with density-dependent interactions


comments: 14 pages, 1 figure, Minor corrections to Theorem 1.5 and Lemma 2.1

Location of Error: Theorem 1.5, Lemma 2.1

title_extracted_from_tex: Power-free palindromes and reversed primes


category_name_readable: K-Theory and Homology

comments: 73 pages. Proposition 3.3 was corrected and references were added

Location of Error: Proposition 3.3

title_extracted_from_tex: magnetic Equivariant K-theory


category_name_readable: Rings and Algebras

comments: 29 pages, 1 table. Corrected Theorem 4.8, added Corollary 4.9, added Table 1, added Proposition 7.12 and modified remarks in the last section. Many other typo corrected

Location of Error: Theorem 4.8

title_extracted_from_tex: Central series' and ($n$)-isoclinism of skew left braces


category_name_readable: Complex Variables

comments: The proof of Lemma 5 is incorrect: we do not have $H(M_\mathcal S)\subset M_\infty$ since $M_\infty$ is defined by 2 equations and $Im(w)=0$ has not be considered in the proof. This affects the main result, and we do not know whether it is true

Location of Error: Lemma 5

title_extracted_from_tex: real algebraic surfaces biholomorphically equivalent but not algebraically equivalent


comments: 21 Pages. Corrected a statement in Lemma 2.2 to address a minor gap in the proof from the previous version

Location of Error: Lemma 2.2

title_extracted_from_tex: Sharp stability for critical points of the Sobolev inequality in the absence of bubbling


comments: 16 pages, corrected version with substantial modifications, Theorem 1.2 in the former version was not correct and has changed, new coauthor

Location of Error: Theorem 1.2

title_extracted_from_tex: Nonnegativity of signomials with Newton simplex over convex sets


category_name_readable: Metric Geometry

comments: 9 pages; substantial revisions throughout, including removing Lemma 4.3, which was in error, adding Theorem 1.3, and correcting the bounds in the main theorem

Location of Error: Lemma 4.3, main theorem

title_extracted_from_tex: DISTORTION FROM SPHERES INTO EUCLIDEAN SPACE


category_name_readable: Geometric Topology

comments: 14 pages, 1 figure, comments are welcome! v2 : corrected gap in proof of Proposition 4.3, updated reference to recent preprint by C. Lecuire (arXiv:2510.07087)

Location of Error: Proposition 4.3

title_extracted_from_tex: Bending parameterization of one-sided degenerated Kleinian surface groups


comments: The previous proof of proposition 3 was incorrect, the hypotheses of proposition 3 (ii) have been narrowed to allow a correct proof. It does not change the conclusions we draw of the proposition. The introduction was reformulated in a (hopefully) clearer way

Location of Error: Proposition 3

title_extracted_from_tex: Regular version of the inverse Galois problem for skew fields


comments: We have corrected the statement and argument of Proposition 4.1(b). Comments are welcome

Location of Error: Proposition 4.1(b)

title_extracted_from_tex: Quasilinear problems with mixed local-nonlocal operator and concave-critical nonlinearities: Multiplicity of positive solutions


category_name_readable: Algebraic Geometry

comments: 76 pages. I have corrected the errors in the version 1. Theorem 3.4 and Corollary 3.5 were not true as they are. There is a counterexample to Corollary 3.5 with $p=q=0,$ given by the harmonic function $r^{2-2n}.$ Also Lemma 6.5 was not really proved

Location of Error: Theorem 3.4, Corollary 3.5, Lemma 6.5

title_extracted_from_tex: Deformations of Compact Calabi--Yau Conifolds


comments: We fix a gap in the proofs of Theorem 2.3 and 2.4 by imposing an additional technical assumption, 18 pages

Location of Error: Theorem 2.3, Theorem 2.4

title_extracted_from_tex: Quantitative Halmos-Savage theorems and robust large financial markets


comments: 47 pages. Comments are welcome. There is a mistake in Lemma 5.7 of the previous version, which implies that the energy reduction result holds only for manifolds that are both non-umbilic. Consequently, we can establish an energy reduction criterion that may help prevent topology loss, rather than a non-existence result

Location of Error: Lemma 5.7

title_extracted_from_tex: Non-existance of minimizers for Fourth order Willmore energy


comments: 29 pages. v3 is a substantial rewrite of the paper. Versions 1 and 2 contain a fatal error in Lemma 3.11 (old numbering), so the main claims of those versions are invalid as stated. This version gives a revised symmetry result and includes results for expanders

Location of Error: Lemma 3.11

title_extracted_from_tex: Uniqueness of asymptotically cylindrical steady gradient Ricci solitons


category_name_readable: Representation Theory

comments: Clarified the notion of cuts vs. gradings. Removed the incorrect Proposition 2.15 (v2) and adapted affected proofs. 28 pages. Comments welcome!

Location of Error: Proposition 2.15

title_extracted_from_tex: $2$-representation infinite algebras from non-abelian subgroups of $\SL_3$ \text{Part I: Extensions of abelian groups}


comments: 22 pages; V2: corrected a mistake in Lemma 4.1 of v1; definitive version, to appear in Forum of Mathematics Sigma

Location of Error: Lemma 4.1

title_extracted_from_tex: Rank jumps and Multisections of elliptic fibrations on K3 surfaces


comments: 10 pages; The statement and proof of Lemma 8 have been revised and corrected, Proof of Theorem 1 is rewritten

Location of Error: Lemma 8

title_extracted_from_tex: A generalization of Dumas irreducibility criterion


comments: In this version, Theorem 2 and its proof have been corrected

Location of Error: Theorem 2

title_extracted_from_tex: $n$-Valued Groups, Kronecker Sums, and Wendt's $(x, y, z)$-Matrices


comments: Lemma 4.2 in v1 is wrong. We modify the proof of Theorem 4.1

Location of Error: Lemma 4.2

title_extracted_from_tex: Variation of Tannaka groups of perverse sheaves in family