Tootfinder

Transform Mozilla from a company to a democratically run collective and see how long management will still be overpaid and hires rentier capitalists.
https://social.cryptography.dog/@ansuz/115746707589261530

Inside the Biggest Sting Operation Ever (with Michael Bobbitt) https://www.404media.co/inside-the-biggest-sting-operation-ever-with-michael-bobbitt/

Rewriting Systems on Arbitrary Monoids
Eduardo Magalh\~aes
https://arxiv.org/abs/2601.10564 https://arxiv.org/pdf/2601.10564 https://arxiv.org/html/2601.10564
arXiv:2601.10564v1 Announce Type: new
Abstract: In this paper, we introduce monoidal rewriting systems (MRS), an abstraction of string rewriting in which reductions are defined over an arbitrary ambient monoid rather than a free monoid of words. This shift is partly motivated by logic: the class of free monoids is not first-order axiomatizable, so "working in the free setting" cannot be treated internally when applying first-order methods to rewriting presentations.
To analyze these systems categorically, we define $\mathbf{NCRS_2}$ as the 2-category of Noetherian Confluent MRS. We then prove the existence of a canonical biadjunction between $\mathbf{NCRS_2}$ and $\mathbf{Mon}$.
Finally, we classify all Noetherian Confluent MRS that present a given fixed monoid. For this, we introduce Generalized Elementary Tietze Transformations (GETTs) and prove that any two presentations of a monoid are connected by a (possibly infinite) sequence of these transformations, yielding a complete characterization of generating systems up to GETT-equivalence.
toXiv_bot_toot

NFL Fan Misery Index after Week 17, plus record nights in the NBA https://www.nytimes.com/athletic/6924583/2025/12/29/nfl-week-17-fan-misery-index-the-pulse/