Tootfinder

"Instead of calculators, we could sit at exams with certain books on our desks, filled with logarithm and trigonometry tables, featuring formulae for algebra, calculus, and geometry. French-speaking Swiss students might remember the ubiquitous “Formulaire et Tables” of the “Commissions romandes de mathématiques, de physique et de chimie”, published by the Éditions du Tricorne, that many generations of Swiss students used during their exams."

Banning, Adopting, Reckoning
Last month, OpenAI, the company (in)famous for their ChatGPT product, released a course called "ChatGPT Foundations for K-12 Educators", an event that has raised more than a few eyebrows, and even some outrage. We must have a serious conversation about the value of a bullshit generator in the context of teaching programming skills to new generations.

Divisibility criteria and coefficient formulas for cyclotomic polynomials
Laura De Carli, Maurizio Laporta
https://arxiv.org/abs/2508.02722 https://arxiv.o…

Divisibility criteria and coefficient formulas for cyclotomic polynomials
We establish necessary and sufficient conditions for a polynomial to be divisible by a cyclotomic polynomials and derive new formulas involving Ramanujan sums as an application of our results. Additionally, we provide new insights into the coefficients of cyclotomic polynomials and we propose a recursive relation between the coefficients of two cyclotomic polynomials whose indexes differ by a prime factor.

This https://arxiv.org/abs/2505.19412 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries
The Cardy-Rabinovici model is a toy model of the lattice $U(1)$ gauge theories to study various oblique confinement states associated with the nonzero $θ$ angles. We reformulate the $2$d version of this model using the modified Villain lattice formalism, and we establish the exact $θ$ periodicity for the Witten effect and the strong-weak duality at the finite lattice spacings. We then study the phase structure of this model based on the duality, symmetry and anomaly, and the perturbative reno…

Cooperation and the Design of Public Goods
J. Carlos Mart\'inez Mori, Alejandro Toriello
https://arxiv.org/abs/2506.05251 https://

Cooperation and the Design of Public Goods
We consider the cooperative elements that arise in the design of public goods, such as transportation policies and infrastructure. These involve a variety of stakeholders: governments, businesses, advocates, and users. Their eventual deployment depends on the decision maker's ability to garner sufficient support from each of these groups; we formalize these strategic requirements from the perspective of cooperative game theory. Specifically, we introduce non-transferable utility, linear product…

This https://arxiv.org/abs/2305.17915 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the First Cohomology of Infinitesimal Poisson Algebras
For the so-called infinitesimal Poisson algebras encoding first-order jets of Poisson submanifolds, we provide a description of their first cohomology in terms of intrinsic cohomologies of the underlying Poisson submanifold. We establish a natural mapping from their first cohomology to the first Poisson cohomology of the corresponding Poisson submanifold. Moreover, we formulate necessary and sufficient conditions for the vanishing of the first cohomology of infinitesimal Poisson algebras. Final…

Encoding Peano Arithmetic in a Minimal Fragment of Separation Logic
Sohei Ito, Makoto Tatsuta
https://arxiv.org/abs/2507.00465 https://

Encoding Peano Arithmetic in a Minimal Fragment of Separation Logic
This paper investigates the expressive power of a minimal fragment of separation logic extended with natural numbers. Specifically, it demonstrates that the fragment consisting solely of the intuitionistic points-to predicate, the constant 0, and the successor function is sufficient to encode all $Π^0_1$ formulas of Peano Arithmetic (PA). The authors construct a translation from PA into this fragment, showing that a $Π^0_1$ formula is valid in the standard model of arithmetic if and only if i…

This https://arxiv.org/abs/2407.17708 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The index of lattice Dirac operators and $K$-theory
We mathematically show an equality between the index of a Dirac operator on a flat continuum torus and the $η$ invariant of a lattice Dirac operator known as the Wilson Dirac operator with a negative mass when the lattice spacing is sufficiently small. Unlike the standard approach, our formulation using $K$-theory does not require modified chiral symmetry on the lattice. We prove that a one-parameter family of continuum massive Dirac operators and the corresponding Wilson Dirac operators belon…

Caustic fringes for wave dark matter
Andrew Eberhardt, Lam Hui
https://arxiv.org/abs/2506.02400 https://arxiv.org/pdf/2506.02400

Caustic fringes for wave dark matter
Wave dark matter is composed of particles sufficiently light that their de Broglie wavelength exceeds the average inter-particle separation. A typical wave dark matter halo exhibits granular substructures due to wave interference. In this paper, we explore the wave interference effects around caustics. These are locations of formally divergent density in cold collisionless systems. Examples include splashback in galaxy clusters, and tidal shells in merging galaxies, where the pile-up of dark ma…

Unique equilibrium states for Viana maps with small potentials
Kecheng Li
https://arxiv.org/abs/2508.00136 https://arxiv.org/pdf/2508.00136

Unique equilibrium states for Viana maps with small potentials
We investigate the thermodynamic formalism for Viana maps-skew products obtained by coupling an expanding circle map with a slightly perturbed quadratic family on the fibers. For every Hölder potential $φ$ whose oscillation is below an explicit threshold, we show that an equilibrium state not only exists but is unique and satisfies an upper level-2 large-deviation principle. All of these conclusions persist under sufficiently small perturbations of the reference map.

Free Askey--Wilson functionals and geometric last passage percolation on a strip
Wlodek Bryc, Kamil Szpojankowski, Jacek Wesolowski
https://arxiv.org/abs/2506.01879

Free Askey--Wilson functionals and geometric last passage percolation on a strip
Barraquand, Corwin, and Yang arXiv:2306.05983 established that geometric last passage percolation (LPP) on a strip of $\mathbb{Z}^2$ has a unique stationary measure. Building on this, Barraquand arXiv:2409.08927 derived explicit contour integral formulas for the model's multipoint probability generating function. In this paper, we introduce free Askey--Wilson functionals and use them to extend these generating function formulas. Our framework yields explicit expressions valid over a broader ran…