9 citations · 37 across the 17 of their papers we have counts for
22 papers
Proving at Scale for Universal Algebra
João Araújo, Jan Hůla, Mikoláš Janota +2
We introduce SemiBase, a project that computes and formally certifies finite identity bases for small semigroups. Deciding finite basability is undecidable for finite algebras and…
Leiden Declaration on Artificial Intelligence and Mathematics
Jarod Alper, Michael Barany, Alain Chavarri Villarello +13
This declaration calls for action to address the challenges posed by the use of artificial intelligence within mathematics research. Technological developments have repeatedly tran…
Efficient Record-and-Replay Arithmetic for Quantum Elliptic-Curve Point Addition
Jieyi Long, Theodore Pender, Zhao Huang +33
We study reversible secp256k1 point-addition circuits developed through ECDSA.Fail for Shor's elliptic-curve discrete-logarithm algorithm. Two complementary constructions improve r…
Mirror, Mirror on the Wall: Prompt Echoing in Small Instruct Language Models
Inez Okulska, Bartosz Naskręcki, Jan Piotrowski +1
Prompt echoing is a recognized failure mode of instruct language models, in which a model instead of generating a response, mirrors the provided prompt, even though it did not rece…
ECDSA.Fail: Open Autoresearch for Optimizing Elliptic-Curve Point Addition in Shor's Algorithm
Jieyi Long, Theodore Pender, Zhao Huang +33
We propose Open Autoresearch, a paradigm in which humans and AI agents publish evaluator-verified improvements to a public leaderboard. We instantiate it in ECDSA.Fail, optimizing…
Key Recovery from Residue-Confined Errors in Pradhan CRT-RLWE
Lukasz Olejnik, Bartosz Naskrecki
We show that the CRT-FHE scheme of Pradhan et al.\ is insecure for laws within its assumed error distribution range. The secret key follows from the public key by a single ring inv…
AI Grinding for Fun and Cryptanalysis
Lukasz Olejnik, Bartosz Naskrecki
We present an autonomous cryptanalysis workflow in which agents generate, test, and refine hypotheses before human review. The autonomous stage returns reproducible candidates with…
Direction-aware topological descriptors for elastic stiffness tensor prediction in porous materials
Rafał Topolnicki, Michał Bogdan, Jakub Malinowski +3
Classical topological descriptors used in topological data analysis (TDA) are invariant under permutations of spatial axes and therefore cannot represent the loading direction, whi…
On the geography of log-surfaces
Bartosz Naskręcki, Piotr Pokora
This survey focuses on the geometric problem of log-surfaces, which are pairs consisting of a smooth projective surface and a reduced non-empty boundary divisor. In the first part,…
Common valuations of division polynomials
Bartosz Naskręcki, Matteo Verzobio
In this note we prove a formula for the cancellation exponent between division polynomials and associated with a sequence of points…
Diophantine triples and K3 surfaces
Matija Kazalicki, Bartosz Naskręcki
A Diophantine -tuple with elements in the field is a set of non-zero (distinct) elements of with the property that the product of any two distinct elements is one le…
Geometry of the del Pezzo surface y^2=x^3+Am^6+Bn^6
Julie Desjardins, Bartosz Naskręcki
In this paper, we give an effective and efficient algorithm which on input takes non-zero integers and and on output produces the generators of the Mordell-Weil group of th…
Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell--Yan scattering
Marco Besier, Dino Festi, Michael Harrison +1
We study a K3 surface, which appears in the two-loop mixed electroweak-quantum chromodynamic virtual corrections to Drell--Yan scattering. A detailed analysis of the geometric Pica…
Primitive divisors of elliptic divisibility sequences over function fields with constant j-invariant
Bartosz Naskręcki, Marco Streng
We prove an optimal Zsigmondy bound for elliptic divisibility sequences over function fields in case the -invariant of the elliptic curve is constant. In more detail, given an e…
The generalized Fermat equation with exponents 2, 3, n
Nuno Freitas, Bartosz Naskrecki, Michael Stoll
We study the Generalized Fermat Equation , to be solved in coprime integers, where is prime. Using modularity and level lowering techniques, the problem…
On a certain hypergeometric motive of weight 2 and rank 3
Bartosz Naskrecki
We study a family of hypergeometric motives attached to a pair of tuples , . To each such motive we can attach a system of --adic reali…
Divisibility sequences of polynomials and heights estimates
Bartosz Naskręcki
In this note we compute a constant that bounds the number of non--primitive divisors in elliptic divisibility sequences over function fields of any characteristic. We improve a…
Distribution of Mordell--Weil ranks of families of elliptic curves
Bartosz Naskręcki
We discuss the distribution of Mordell--Weil ranks of the family of elliptic curves where are coprime polynomials that parametrize the proj…
Mordell-Weil ranks of families of elliptic curves parametrized by binary quadratic forms
Bartosz Naskręcki
We prove results on the Mordell--Weil rank of elliptic curves parametrized by binary quadratic forms . We express our explicit lower bounds…
Mordell-Weil ranks of families of elliptic curves associated to Pythagorean triples
Bartosz Naskręcki
We study the family of elliptic curves parametrized by Pythagorean triples . We prove that for a generic triple the lower bound of the rank of the Mo…
On higher congruences between cusp forms and Eisenstein series
Bartosz Naskręcki
In this paper we present several finite families of congruences between cusp forms and Eisenstein series of higher weights at powers of prime ideals. We formulate a conjecture whic…
Infinite family of elliptic curves of rank at least 4
Bartosz Naskrecki
We investigate -ranks of the elliptic curve : where is a rational parameter. We prove that for infinitely many values of the rank of…