Tootfinder

A recursive approach for the determination of the nice sections of width three having a 4-crown stack as retract
Frank a Campo
https://arxiv.org/abs/2510.05640 https://

A recursive approach for the determination of the nice sections of width three having a 4-crown stack as retract
The characterization of the finite minimal automorphic posets of width three is still an open problem. Niederle has shown that this task can be reduced to the characterization of the nice sections of width three having a non-trivial tower of nice sections as retract. In our article, we characterize those of them which have a 4-crown stack as retract and we develop a recursive approach for their determination. We apply the approach on a sub-class $\mathfrak{N}_2$ of nice sections of width three …

Series C, Episode 04 - Dawn of the Gods
DAYNA: Orac with delusions of grandeur, Zen unable to control the ship. I'd say we've a lot of little problems on our hands.
AVON: Course deflection is zero zero five. Speed Standard by five and increasing. I'd say we have one large problem on our hands.
https://blake.torpidit…

ReasonEmbed: Enhanced Text Embeddings for Reasoning-Intensive Document Retrieval
Jianlyu Chen, Junwei Lan, Chaofan Li, Defu Lian, Zheng Liu
https://arxiv.org/abs/2510.08252 http…

ReasonEmbed: Enhanced Text Embeddings for Reasoning-Intensive Document Retrieval
In this paper, we introduce ReasonEmbed, a novel text embedding model developed for reasoning-intensive document retrieval. Our work includes three key technical contributions. First, we propose ReMixer, a new data synthesis method that overcomes the triviality problem prevalent in previous synthetic datasets, enabling large-scale production of 82K high-quality training samples. Second, we design Redapter, a self-adaptive learning algorithm that dynamically adjusts training each sample's weight…

An approach using geometric diagrams to generic Bell inequalities with multiple observables
Junghee Ryu, Jinhyoung Lee, Hoon Ryu
https://arxiv.org/abs/2510.05622 https://…

An approach using geometric diagrams to generic Bell inequalities with multiple observables
We extend the generic Bell inequalities suggested by Son, Lee, and Kim [Phys. Rev. Lett. 96, 060406 (2006)] to incorporate multiple observables for tripartite systems and introduce a geometric methodology for calculating classical upper bounds of the inequalities. Our method transforms the problem of finding the classical upper bounds into identifying constraints in linear congruence relations. Using this approach, we derive the upper bounds for scenarios with three and four observables per par…

This piece by @… is more than three years old but it contains plenty of good points about digital continuity and contingency.
https://shkspr.mobi/blog/2022/06/ive-l

I've locked myself out of my digital life
Imagine… Last night, lightning struck our house and burned it down. I escaped wearing only my nightclothes. In an instant, everything was vaporised. Laptop? Cinders. Phone? Ashes. Home server? A smouldering wreck. Yubikey? A charred chunk of gristle. This presents something of a problem. In order to recover my digital life, I need to be able to log in to things. This means I need to know my u…

Oof, fuck microsoft.
But also, there's no reason to use permissive licenses any more. "Open source" has taken over the world. We no longer have to work with billion-dollar companies in order to get our stuff used. Now we need to protect ourselves from being taken advantage of by them.
https://

At least he understood the location and extent of our problem. Not great on the solution side, but we will be workshopping that... https://bird.makeup/users/macfarlanenews/statuses/1969117630578540785

Scott MacFarlane
ALERT: Justice Dept will seek minimum 30-year prison term for Nicholas Roske, the California man who pleaded guilty in attempt to assassinate Justice Brett Kavanugh Feds argue Roske was targeting UP TO THREE justices for assassination COURT FILING: https://storage.courtlistener.com/recap/gov.uscourts.mdd.514255/gov.uscourts.mdd.514255.98.0.pdf

https://hemaks.org/posts/why-your-obsession-with-code-linting-is-excessive/
Consider these questions when evaluating your linting setup:
- Does this rule prevent actual bugs? If not, consider removing it.
- Would a new team member understand …

The hereditariness problem for the \v{C}ern\'y conjecture
Emanuele Rodaro, Riccardo Venturi
https://arxiv.org/abs/2509.17992 https://arxiv.org/pdf/2509…

The hereditariness problem for the Černý conjecture
This paper addresses the lifting problem for the Černý conjecture: namely, whether the validity of the conjecture for a quotient automaton can always be transferred (or "lifted") to the original automaton. Although a complete solution remains open, we show that it is sufficient to verify the Černý conjecture for three specific subclasses of reset automata: radical, simple, and quasi-simple. Our approach relies on establishing a Galois connection between the lattices of congruences and ideal…

Risk Comparisons in Linear Regression: Implicit Regularization Dominates Explicit Regularization
Jingfeng Wu, Peter L. Bartlett, Jason D. Lee, Sham M. Kakade, Bin Yu
https://arxiv.org/abs/2509.17251

Risk Comparisons in Linear Regression: Implicit Regularization Dominates Explicit Regularization
Existing theory suggests that for linear regression problems categorized by capacity and source conditions, gradient descent (GD) is always minimax optimal, while both ridge regression and online stochastic gradient descent (SGD) are polynomially suboptimal for certain categories of such problems. Moving beyond minimax theory, this work provides instance-wise comparisons of the finite-sample risks for these algorithms on any well-specified linear regression problem. Our analysis yields three …

Goldman-Turaev formality from the Kontsevitch integral
Dror Bar-Natan, Zsuzsanna Dancso, Tamara Hogan, Jessica Liu, Nancy Scherich
https://arxiv.org/abs/2509.20983 https://

Goldman-Turaev formality from the Kontsevitch integral
We present a new solution to the formality problem for the framed Goldman--Turaev Lie bialgebra, constructing Goldman-Turaev homomorphic expansions (formality isomorphisms) from the Kontsevich integral. Our proof uses a three dimensional derivation of the Goldman-Turaev Lie biaglebra arising from a low-degree Vassiliev quotient -- the {\em emergent} quotient -- of tangles in a thickened punctured disk, modulo a Conway skein relation. This is in contrast to Massuyeau's 2018 proof using braids. A…

Fast and Compact Sketch-Based Dynamic Connectivity
Quinten De Man, Qamber Jafri, Daniel Delayo, Evan T. West, Michael A. Bender, David Tench
https://arxiv.org/abs/2509.14433 htt…

Fast and Compact Sketch-Based Dynamic Connectivity
We study the dynamic connectivity problem for massive, dense graphs. Our goal is to build a system for dense graphs that simultaneously answers connectivity queries quickly, maintains a fast update throughput, and a uses a small amount of memory. Existing systems at best achieve two of these three performance goals at once. We present a parallel dynamic connectivity algorithm using graph sketching techniques that has space complexity $O(V \log^3 V)$ and query complexity $O(\log V/\log\log V)$…