Tootfinder

Zero to 100: By the numbers look at Cowboys' preseason loss to Ravens https://www.dallascowboys.com/news/zero-to-100-by-the-numbers-look-at-cowboys-preseason-loss-to-ravens

Class numbers of Imaginary bicyclic biquadratic number fields
Anuj Jakhar, Ravi Kalwaniya, Mahesh Kumar Ram
https://arxiv.org/abs/2509.13153 https://arxiv.…

Class numbers of Imaginary bicyclic biquadratic number fields
For any fixed positive integer $n$, we provide a method to compute all imaginary bicyclic biquadratic number fields with class number $n$, along with their class group structures, using the list of all imaginary quadratic number fields whose class numbers divide $2n$. We apply this method to list all imaginary bicyclic biquadratic number fields with class numbers $4$, $6$ and $7$. We also present the class group structure of each subfield of these fields.

This works, right? I mean, sure the numbers are reversed but the time makes sense to most people this way!
And yes you are looking at a backwards clock through a mirror in my bathroom.

Make paint-by-number pictures in R: #rstats

GitHub - cj-holmes/paintr: Create paint by numbers images
Create paint by numbers images. Contribute to cj-holmes/paintr development by creating an account on GitHub.

Zero to 100: By the numbers look at Cowboys' preseason loss to Ravens https://www.dallascowboys.com/news/zero-to-100-by-the-numbers-look-at-cowboys-preseason-loss-to-ravens

I love little programming katas like this where the theoretical solution is kinda obvious but the implementation needs many things to wrap your head around.
Here: sum to numbers as strings (that will possibly exceed the max value of your numeric data type).
https://www.codewars.com/kata/5324945e2ece

Best versions:
Keynote: 2013-14
Pages: 2005-13
Numbers: 2013-14.
Conclusion: Mac icons have been crap since 2014.
[ducks] https://mastodon.social/@BasicAppleGuy/115050148901528749

BasicAppleGuy (@BasicAppleGuy@mastodon.social)
Attached: 3 images macOS Icon History iWork Suite: Keynote, Pages, & Numbers

Watch: Numbers to know for Raiders-Chiefs Week 7 https://www.raiders.com/video/watch-numbers-to-know-for-raiders-chiefs-week-7

On the non-zero Love numbers of magnetic black holes
David Pere\~niguez, Edgars Karnickis
https://arxiv.org/abs/2509.12418 https://arxiv.org/pdf/2509.12418…

On the non-zero Love numbers of magnetic black holes
Black holes are believed to possess vanishing Love numbers, which implies that they do not deform in the presence of external tides. This fact has been verified in a number of scenarios, that involve tides of bosonic fields of various natures (e.g. scalar, electromagnetic and gravitational), and has triggered active research in trying to identify the underlying reason. Surprisingly, two counterexamples have been found recently. The first, concerns charged-field tides on electrically-charged bla…

'murcans: I can't make it to protests today (health issue) but please go to there in numbers.
https://www.nokings.org/#map

North Carolina Elections Chief Demands Voters' Full Social Security Numbers From DMV (Yunior Rivas/Democracy Docket)
https://www.democracydocket.com/news-alerts/north-carolina-elections-chief-demands-voters-full-social-security-numbers-from-dmv/
http://www.memeorandum.com/251016/p148#a251016p148

Hacker group Scattered LAPSUS$ Hunters posts alleged names, phone numbers, and addresses of hundreds of DHS, ICE, FBI, and DOJ officials in a mass doxxing event (Joseph Cox/404 Media)
https://www.404media.co/hackers-dox-hundreds-of-dhs-ice-fbi-and-doj-officials…

Hackers Dox Hundreds of DHS, ICE, FBI, and DOJ Officials
Scattered LAPSUS$ Hunters—one of the latest amalgamations of typically young, reckless, and English-speaking hackers—posted the apparent phone numbers and addresses of hundreds of government officials, including nearly 700 from DHS.

Applying Hurlbert's Linear Optimization Technique to Establish Bounds on Pebbling Numbers
Lingwen Li
https://arxiv.org/abs/2509.11024 https://arxiv.org…

Applying Hurlbert's Linear Optimization Technique to Establish Bounds on Pebbling Numbers
This paper explores the application of Hurlbert's Linear Optimization Technique to determine bounds on pebbling numbers. By applying Hurlbert's weight functions and optimization methods, we derive upper bounds for specific graph families. The study provides a comprehensive analysis of these bounds and contributes to a broader understanding of pebbling numbers in graph theory. In particular, the weight function lemma is applied to calculate upper bounds for graphs such as the Petersen graph, the…

https://www.404media.co/hackers-dox-hundreds-of-dhs-ice-fbi-and-doj-officials/
Hackers Dox Hundreds of DHS, ICE, FBI, and DOJ Officials

Hackers Dox Hundreds of DHS, ICE, FBI, and DOJ Officials
Scattered LAPSUS$ Hunters—one of the latest amalgamations of typically young, reckless, and English-speaking hackers—posted the apparent phone numbers and addresses of hundreds of government officials, including nearly 700 from DHS.

TRUMP: We're gonna have numbers like nobody has ever seen before [obvious lie]
MacCALLUM: When do you think we're gonna see that? Recent Fox polling showed 52% said the economy is worse under this administration
TRUMP: Fox polling is the worst polling
**'Get yourself a new pollster!' Fed-up Trump bashes Fox News' own surveys during interview** - Raw Story
https://www.rawstory.com/donald-trump-fox-news-2674008561/

The BBC and UK's other public sector broadcasters call for new regulations to force platforms such as YouTube to give them a fairer deal and more prominence (Michael Savage/The Guardian)
https://www.theguardian.com/media/2025/sep…

European police bust network selling thousands of phone numbers to scammers https://therecord.media/europe-sim-farms-raided-latvia-austria-estonia

Protests from american cities, where people just take over entire streets.. and then protest pics from the suburbs, where people are standing on sidewalks waving signs. This despite large numbers where they COULD take over the streets.
Just another reminder of how badly we've built our public spaces..

Protest numbers data from Harvard's Crowd Counting Consortium (Ash Center) -- part of the Nonviolent Action Lab
#resist

A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz Hankel Determinants II
Roozbeh Gharakhloo, Alexander Its
https://arxiv.org/abs/2509.12345 https://

A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz+Hankel Determinants II
In this article, we continue the development of the Riemann-Hilbert formalism for studying the asymptotics of Toeplitz+Hankel determinants with non-identical symbols, which we initiated in \cite{GI}. In \cite{GI}, we showed that the Riemann-Hilbert problem we formulated admits the Deift-Zhou nonlinear steepest descent analysis, but with a special restriction on the winding numbers of the associated symbols. In particular, the most natural case, namely zero winding numbers, is not allowed. A pri…

If you render numbers like this 1,005 €, in a financial app, with no other references, and it's possible to a pay fraction of a cent, you absolutely should stop.
Write 1,005.00 or 1005. Otherwise I have no idea if I'm gonna pay a euro or a thousand.
This post is brought to you by Trade Republic.

On manifolds homeomorphic to spheres
Somnath Basu, Sachchidanand Prasad
https://arxiv.org/abs/2509.13008 https://arxiv.org/pdf/2509.13008

On manifolds homeomorphic to spheres
We prove a result analogous to Reeb's theorem in the context of Morse-Bott functions: if a closed, smooth manifold $M$ admits a Morse-Bott function having two critical submanifolds $S^k$ and $S^l$ ($k \neq l$), then $M$ has dimension $k+l+1$ and is homeomorphic to the standard sphere $S^{k+l+1}$ but not necessarily diffeomorphic to it. We also prove similar results for projective spaces over the real numbers, complex numbers and quaternions.

#cornell #lacrosse had a historic season this year winning the NCAA championship; Apr 26 was the last game of the regular season at Schoellkopf Field against Dartmouth, the Big Red won 10-8; № 15 attack CJ Kirst passes to № 1 attack Michael Long

A Canonical Bijection Between Finite-Decimal Real Numbers and Natural Numbers with Constant-Time Enumeration Formulas
S. K. Rithvik
https://arxiv.org/abs/2508.10750 https://

A Canonical Bijection Between Finite-Decimal Real Numbers and Natural Numbers with Constant-Time Enumeration Formulas
We present an explicit bijection between finite-decimal real numbers and natural numbers ($\mathbb{N} = \{1, 2, 3, ...\}$) using a systematic 4-tuple parametrization with closed-form mathematical formulas for enumeration. Our enumeration system provides complete indexing of all real numbers with terminating decimal representations through the parametrization $(\text{sign}, N_1, N_2, N_3)$. Both forward and inverse mappings execute in O(1) constant time, achieved through closed-form lexicographi…

https://vancouver.citynews.ca/2025/10/07/these-numbers-show-how-2-years-of-war-have-devastated-palestinian-lives-in-gaza/

These numbers show how 2 years of war have devastated Gaza
Numbers alone cannot capture the toll the Israel-Hamas war has taken on the Gaza Strip.

Real-time vacuum-state quantum random number generator on a chip
Guan-Ru Qiao, Bing Bai, Zi-Xuan Weng, Han-Shen Chen, Wei Zheng, Zhi-Yuan Zheng, You-Qi Nie, Jun Zhang, Jian-Wei Pan
https://arxiv.org/abs/2509.13105

Real-time vacuum-state quantum random number generator on a chip
Quantum random number generators (QRNGs) produce true random numbers, which are guaranteed by the fundamental principles of quantum physics. Miniaturization of QRNGs is crucial for a wide range of communication and cryptography applications. Here, we first report a fully functional QRNG chip based on vacuum-state fluctuations, with dimensions of 16.6 mm x 7.8 mm. The quantum entropy source, which is achieved via hybrid photonic integration with a SiO2 waveguide, generates raw quantum random num…

The thing about arrest quotas is that the important arrests
— folks committing or organizing crimes
— don't tell you where they are.
So if you want to hit your numbers, you need lots of basically law-abiding people you can punish.
-- @joedudekjd.bsky.social

Stephen Miller’s Quota Likely Drove Korean Arrests In Immigration Raid
When ICE agents arrested over 300 Korean workers at a Georgia battery plant, a daily immigrant arrest quota was likely on their minds.

Sensitive details about Trump-Putin summit revealed in discarded government documents, NPR reports: https://benborges.xyz/2025/08/16/sensitive-details-about-trumpputin-summit.html

Thom-Milnor bounds for smooth manifolds
Saugata Basu, Antonio Lerario, Matteo Testa
https://arxiv.org/abs/2509.14079 https://arxiv.org/pdf/2509.14079

Thom-Milnor bounds for smooth manifolds
We prove a smooth analogue of the classical Thom-Milnor bound, showing that the Betti numbers of the zero set of a smooth map on a compact Riemannian manifold can be controlled by a condition number computed from its first jet. This extends previous results in the Euclidean setting by Lerario and Stecconi [J. Singul., 2021]. As a key step, we generalize the Thom-Milnor bound to polynomial maps on a nonsingular real algebraic variety, improving the dependence on the degree. Finally, inspired by …

Towards an Embodied Composition Framework for Organizing Immersive Computational Notebooks
Sungwon In, Eric Krokos, Kirsten Whitley, Chris North, Yalong Yang
https://arxiv.org/abs/2509.13291

Towards an Embodied Composition Framework for Organizing Immersive Computational Notebooks
As immersive technologies evolve, immersive computational notebooks offer new opportunities for interacting with code, data, and outputs. However, scaling these environments remains a challenge, particularly when analysts manually arrange large numbers of cells to maintain both execution logic and visual coherence. To address this, we introduce an embodied composition framework, facilitating organizational processes in the context of immersive computational notebooks. To evaluate the effectiven…

Trump's war on numbers (Erica Pandey/Axios)
https://www.axios.com/2025/08/18/trump-jobs-report-dc-crime-data
http://www.memeorandum.com/250818/p6#a250818p6

A little arts and crafts project with some help from @….
We 'fixed' a colleagues wall clock. Will they notice? 😉

Stoimenow matchings avoiding multiple Catalan patterns simultaneously
Shuzhen Lv, Sergey Kitaev
https://arxiv.org/abs/2509.12726 https://arxiv.org/pdf/2509…

Stoimenow matchings avoiding multiple Catalan patterns simultaneously
Motivated by Vassiliev's knot invariants, Stoimenow introduced a special class of matchings, now known as Stoimenow matchings. These matchings have since been linked to various combinatorial structures enumerated by the Fishburn numbers. In a recent paper, a problem posed by Bevan et al. was addressed concerning the identification of subsets of Stoimenow matchings counted by the Catalan numbers. Five such subsets were presented, each defined by the avoidance of a single pattern, referred to as …

Anomaly cancellation for a $U(1)$ factor
Ben Gripaios, Khoi Le Nguyen Nguyen
https://arxiv.org/abs/2508.11583 https://arxiv.org/pdf/2508.11583

Anomaly cancellation for a $U(1)$ factor
We use methods of arithmetic geometry to solve the abelian local anomaly cancellation conditions for a four-dimensional gauge theory whose Lie algebra has a single $\mathfrak{u}_1$ summand, assuming that a solution exists. The resulting polynomial equations in the integer $\mathfrak{u}_1$ charges define a projective cubic hypersurface over the field of rational numbers. Generically, such a hypersurface is (by a theorem of Kollár) a unirational variety, making it possible to find a finitely-man…

Quantum entropy and cardinality of the rational numbers
Kaushik Ghosh
https://arxiv.org/abs/2509.12972 https://arxiv.org/pdf/2509.12972

Quantum entropy and cardinality of the rational numbers
We compare two methods for evaluating cardinality of the Cartesian product $N \times N$ of the set of natural numbers $N$. The first is used to explain the thermodynamics of black body radiation by using convergent functions on $N \times N$. Cardinality of $N \times N$ enters through the partition function that acts as the normalization constant of a probability distribution over $N \times N$. Here, $N \times N$ is given a greater cardinality than $N$. The expression of the partition function a…

Quasinormal modes and tidal Love numbers of covariant effective quantum black holes with cosmological constant
Yunlong Liu, Xiangdong Zhang
https://arxiv.org/abs/2509.12013 http…

Quasinormal modes and tidal Love numbers of covariant effective quantum black holes with cosmological constant
This paper systematically investigates the quasinormal modes (QNMs) and tidal Love numbers of covariant quantum-modified black holes (BHs) within two cosmological constant-dependent metric frameworks. By deriving axial/polar perturbation equations and employing pseudospectral methods (for QNMs) and numerical integration (for Love numbers), we quantify the quantum parameter $ζ$'s influence. We find that, higher overtones exhibit enhanced $ζ$ sensitivity. Solution 1 maintains purely imaginary Q…

"The secret of numbers" is an excellent short video about the sense of numbers and quantities in humans and animals.
Overall, the "Be Smart" #YouTube channel is just excellent.
#learning

AI-based satellite survey offers independent assessment of migratory #wildebeest numbers in the Serengeti: https://academic.oup.com/pnasnexus/article/4/9/pgaf264/8249339?login=false -> AI satellite survey challenges long-standing estimates of Serengeti wildebeest numbers: https://www.ox.ac.uk/news/2025-09-10-ai-satellite-survey-challenges-long-standing-estimates-serengeti-wildebeest-numbers

Extremal Betti numbers of certain two-dimensional monomial ideals
Nguyen Quang Loc, Nguyen Cong Minh, Phan Thi Thuy
https://arxiv.org/abs/2510.12149 https://

Extremal Betti numbers of certain two-dimensional monomial ideals
In this paper, we shall provide explicit formulas for the extremal Betti numbers of $R/I$, where $I$ is the defining ideal of certain weighted hyperplanes in $\Bbb{P}^{n-1}$ and $R$ is the polynomial ring in $n$ indeterminates over a field. As a consequence, we completely classify such ideals which are pseudo-Gorenstein as in sense of V. Ene, J. Herzog, T. Hibi and S. S. Madani.

TyDe 2025: Szumi Xie presenting "The conatural numbers form an exponential commutative semiring"
https://conf.researchr.org/details/icfp-splash-2025/tyde-2025-papers/9/The-conatural-numbers-form-an…

Tropical bird numbers plummet due to more days of extreme heat, study finds https://news.mongabay.com/short-article/2025/09/tropical-bird-numbers-plummet-due-to-more-days-of-extreme-heat-study-finds/

Tropical bird numbers plummet due to more days of extreme heat, study finds
Tropical bird populations are crashing as temperatures soar. That’s according to a new study that found abundances of tropical birds were 25-38% lower than they would be without human-driven climate change and the rising temperatures it has caused. This temperature impact on birds is greater than declines attributed to deforestation. “It’s a staggering decrease. Birds […]

Recurrence relations for harmonic and derangement numbers
Taekyun Kim, Dae san Kim, Jongkyum Kwon, Kyo-Shin Hwang
https://arxiv.org/abs/2509.10404 https://…

Recurrence relations for harmonic and derangement numbers
We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the underlying structure of these numbers but also highlight the effectiveness of elementary techniques in discovering new mathematical properties. The findings have potential applications in various fields where these numbers appear, including combinatorics, probabi…

Relaminarization of turbulent puffs in pipe flow
Basheer A. Khan, Shai Arogeti, Oriel Shoshani, Alexander Yakhot
https://arxiv.org/abs/2509.12663 https://a…

Relaminarization of turbulent puffs in pipe flow
This study examines the relaminarization of turbulent puffs in pipe flow using highly resolved direct numerical simulations at Reynolds numbers of 1880, 1900, and 1920. The exponential decay of the total energy of streamwise velocity fluctuations and the weak dependence of the decay rate on the Reynolds number were verified. In the cross-section of the laminar-turbulent interface at the trailing edge of the puff, an analysis of the spatio-temporal evolution of the streamline patterns reveals a …

"If you’re thinking all of this looks a lot like Musk trying to juice his #Tesla sales numbers—and therefore his Tesla stock share price—by playing a shell game with his own companies, you’re not alone. It isn’t quite the same as the disastrous special purpose entities that ultimately brought energy company #Enron

Cybertruck sales are so bad Musk is selling them to ... himself
You wanna see a dead body? Third-quarter sales numbers for Tesla’s misbegotten Cybertruck are in, and it is definitely spooky season for tech titan Elon Musk, who moved only 5,385 of the hideous ...

Zero to 100: Difference making numbers from Cowboys Week 2 win https://www.dallascowboys.com/news/zero-to-100-difference-making-numbers-from-cowboys-week-2-win

Semi-simple partition algebras as centralizers of representations for rook monoids
Volodymyr Mazorchuk, Shraddha Srivastava
https://arxiv.org/abs/2509.14044 https://

Semi-simple partition algebras as centralizers of representations for rook monoids
Let $\mathcal{P}_k(δ)$, where $k$ is a positive integer and $δ$ some complex parameter, be the classical partition algebra over the complex numbers. In the case when $δ=n$, it is well-known that the algebra $\mathcal{P}_k(δ)$ is the centralizer of the symmetric group $S_n$ acting on the $k$-fold tensor space of the natural representation of $S_n$, for $n\geq 2k$. The algebra $\mathcal{P}_k(δ)$ is semi-simple for generic values of $δ$. In this paper, we show that semi-simple partition alge…

trying to find out which way round indians wrote their numbers over 1000 years ago, and as always the answer is “it’s complicated”
https://en.wikipedia.org/wiki/Bhāskara_I#Representation_of_numbers
hindu-arabic numbers have always been big-end-on-left rega…

This is an interesting study in how local conditions skew your perceptions, I'm actually surprised how *low* the numbers are, but I see in Denmark EVs are much higher than the rest of the EU, who also clearly have some catching up to do...
https://ec.social-network.europa.eu/@EUCommission/115354274303487490
EUCommission@ec.social-network.europa.eu - 👋 Watt’s up, Europe?
 
The numbers of electric vehicles sold in Europe in 2024 are in:
 
⚡ 1.45 million new battery-only EVs registered
📈 32% growth in the total electric fleet
🚗 Nearly 6 million e-vehicles on the road
🔋 13.6% of all new car registrations are electric
 
Europe is accelerating full throttle to a clean future.  
 
Read more: https://link.europa.eu/cNKjkh

u wot m8
"""
First install the version of this crate corresponding to the Fibonacci number you want to use:
cargo add fibonacci-numbers@186 --rename fib186
Then you can use the VALUE constant to get its value:
assert_eq!(fib186::VALUE, 332825110087067562321196029789634457848);
"""
https://

"‘We’re winning a battle’: Mexico’s jaguar numbers up 30% in conservation drive"
#Mexico #Jaguar #Animals

Frenkel anomaly on co-ordination numbers in liquid CO2 at 100 and 1000 bar studied by Monte Carlo simulation using Kihara potential model
Koji Kobashi
https://arxiv.org/abs/2510.11029

Frenkel anomaly on co-ordination numbers in liquid CO2 at 100 and 1000 bar studied by Monte Carlo simulation using Kihara potential model
An issue concerning the Frenkel line of liquid CO2 is that its location has not been unequivocally determined. So far, reliable Frenkel lines were identified from velocity autocorrelation functions (VAFs) computed by Molecular Dynamic simulations; however VAFs cannot be directly verified experimentally. By contrast, the co-ordination numbers (CNs) can be measured experimentally by X-ray and neutron scattering or computed by Monte Carlo (MC) simulation, and thus provide an alternative means of d…

Pew: Trump has lost 30% of his young 2024 voters | Weekly roundup for August 17, 2025 (G. Elliott Morris/Strength In Numbers)
https://www.gelliottmorris.com/p/pew-trump-has-lost-30-of-his-young
http://www.memeorandum.com/250817/p26#a250817p26

"The tech platforms that promised to transform our attention spans succeeded, but only superficially. They created a new, much worse way of creating culture. A universe of dumbasses talking to other dumbasses, measured by numbers that don’t make sense and don’t reflect anything other than passive screen time."
(Original title: The Great Dumbening)

The Great Dumbening
Read to the end for it’s Tronin’ time

There was a time in the not-so-distant past when we could have avoided incredible harm to incredible numbers of people here in the US simply by giving the absolute stink eye to people spouting deranged fascist crap, by saying “ugh, wtf, get out of here” instead of finding ways to describe fascism politely enough to give it equal time in the news.
I don’t know what’s coming. I hope for the best; I fear the worst. But shunning and shaming sound so, so, so much better than even the best-case scenarios that follow from here.

Quantum Time Crystals and Interacting Chiral Gauge Theories in Atomic BECs III: Role of the Page-Wootters mechanism
Patrik \"Ohberg, Ewan M. Wright
https://arxiv.org/abs/2508.11245

Quantum Time Crystals and Interacting Chiral Gauge Theories in Atomic BECs III: Role of the Page-Wootters mechanism
We build the case that our published chiral soliton model [Phys. Rev. Lett. 124, 250402 (2019)] can lead to a genuine quantum time crystal for smaller atom numbers. To do this we compare results from the chiral soliton model with exact numerical solutions for the ground state of the three-particle Schrödinger equation in the limit that the spatial profile of the soliton is largely independent of its center-of-mass motion. The connection between the two approaches is found via the Page-Wootters…

Proof-Carrying Numbers (PCN): A Protocol for Trustworthy Numeric Answers from LLMs via Claim Verification
Aivin V. Solatorio
https://arxiv.org/abs/2509.06902 https://

Proof-Carrying Numbers (PCN): A Protocol for Trustworthy Numeric Answers from LLMs via Claim Verification
Large Language Models (LLMs) as stochastic systems may generate numbers that deviate from available data, a failure known as \emph{numeric hallucination}. Existing safeguards -- retrieval-augmented generation, citations, and uncertainty estimation -- improve transparency but cannot guarantee fidelity: fabricated or misquoted values may still be displayed as if correct. We propose \textbf{Proof-Carrying Numbers (PCN)}, a presentation-layer protocol that enforces numeric fidelity through mechanic…

When the optometrist's aide asks you to read the bottom line of the card, she doesn't mean the small imprint of the card number and edition.
She was very confused, thought I couldn't read the text and numbers at all.

Replaced article(s) found for math.GM. https://arxiv.org/list/math.GM/new
[1/1]:
- A note on solitary numbers
Sagar Mandal
https://arxiv.o…

Signature 0 toric varieties, wall crossings, and cross polytope-like structures
Soohyun Park
https://arxiv.org/abs/2509.13296 https://arxiv.org/pdf/2509.13…

Signature 0 toric varieties, wall crossings, and cross polytope-like structures
We describe the structure of simplicial locally convex fans associated to even-dimensional complete toric varieties with signature 0. They belong to the set of such toric varieties whose even degree Betti numbers yield a gamma vector equal to 0. The gamma vector is an invariant of palindromic polynomials whose nonnegativity lies between unimodality and real-rootedness. It is expected that the cases where the gamma vector is 0 form ``building blocks'' among those where it is nonnegative. This me…

Papers with U.S. State Department markings, found Friday morning in the business center of an Alaskan hotel, revealed previously undisclosed and potentially sensitive details about the Aug. 15 meetings between President Donald Trump and Russian President Vladimir V. Putin in Anchorage.
Eight pages, that appear to have been produced by U.S. staff and left behind accidentally, shared precise locations and meeting times of the summit and phone numbers of U.S. government employees

Topological Levinson's theorem and corrections at thresholds: the full picture in a quasi-1D example
T. T. Nguyen, D. Parra, S. Richard
https://arxiv.org/abs/2509.12684 http…

Topological Levinson's theorem and corrections at thresholds: the full picture in a quasi-1D example
Various threshold effects are investigated on a discrete quasi-1D scattering system. In particular, one of these effects is to add corrections to Levinson's theorem. We explain how these corrections are due to the opening or to the closing of channels of scattering, and how these contributions can be computed as partial winding numbers on newly introduced operators. Embedded thresholds, thresholds associated with changes of spectral multiplicity, and doubly degenerate thresholds are exhibited a…

Poincar\'{e} Polynomials and Curvature Operators of Symmetric Spaces
Peter Petersen, James Stanfield
https://arxiv.org/abs/2508.11236 https://arxiv.org…

Poincaré Polynomials and Curvature Operators of Symmetric Spaces
We compute explicit formulas for the curvature operators and Poincaré polynomials of all compact irreducible symmetric spaces. We can easily derive the Poincaré polynomials using quantum numbers, giving a formula that mirrors the known formula for the Euler characteristic. For the curvature operators, we show that their maximum eigenvalue is always bounded above by the Einstein constant, with equality attained precisely by the Hermitian symmetric spaces.

How the #Perseids 2025 performed: global activity profiles from two video networks and radio echos place a single pretty pronounced peak around 23:00 and 18:00 UTC on 12 August, respectively, perhaps probing different dust populations. Visual data (not shown) have the peak around 21:00 UTC but nearly level activity until 2:00 UTC on 13 August: see https://skyweek.wordpress.com/2025/08/04/allgemeines-live-blog-ab-dem-4-august-2025/#Aug16 for the sources and more numbers.

Watch: Numbers to know for Raiders-Chargers Week 2 https://www.raiders.com/video/watch-numbers-to-know-for-raiders-chargers-week-2-nfl

Catalan numbers and a conjecture on the maximum composition length of a Kac module
Ian M. Musson
https://arxiv.org/abs/2509.10868 https://arxiv.org/pdf/250…

Catalan numbers and a conjecture on the maximum composition length of a Kac module
We prove a conjecture on the maximum number of composition factors of a Kac module for the Lie superalgebra $\fg=\fgl(r|r)$. The proof uses some elementary facts about continuous functions.

New York fines auto insurers $19M over major data breaches
https://www.fingerlakes1.com/2025/10/14/auto-insurance-data-breach-ny-fines/

New York fines auto insurers $19M over major data breaches | Fingerlakes1.com
New York State has fined eight major auto insurance companies over $19 million after an investigation uncovered major cybersecurity failures that exposed the personal data of residents, including driver’s license numbers and birthdates. The settlement—announced October 14, 2025—follows a wide-ranging investigation led by Superintendent Adrienne Harris of the New York Department of Financial Services (DFS).… MoreNew York fines auto insurers $19M over major data breaches

"Tropical bird numbers plummet due to more days of extreme heat, study finds"
#Birds #Climate #ClimateChange

Tropical bird numbers plummet due to more days of extreme heat, study finds
Tropical bird populations are crashing as temperatures soar. That’s according to a new study that found abundances of tropical birds were 25-38% lower than they would be without human-driven climate change and the rising temperatures it has caused. This temperature impact on birds is greater than declines attributed to deforestation. “It’s a staggering decrease. Birds […]

Frobenius manifold for the nodal quiver
Atsuki Nakago, Yuuki Shiraishi, Atsushi Takahashi
https://arxiv.org/abs/2509.12722 https://arxiv.org/pdf/2509.12722…

Frobenius manifold for the nodal quiver
Starting from the Weierstrass elliptic function, we study the associated Frobenius structure, incorporating the perspective of derived categories, particularly that of homological mirror symmetry. Given a deformation of the Weierstrass elliptic function, we construct a primitive form normalized to be compatible with the period map for integral cycles, and obtain a Frobenius structure whose Frobenius potential is defined over the rational numbers. We also construct a Frobenius structure using el…

this is exceedingly silly https://docs.rs/crate/fibonacci-numbers/latest/source/Cargo.toml

Gauss and p-adic numbers
Franz Lemmermeyer
https://arxiv.org/abs/2510.11559 https://arxiv.org/pdf/2510.11559

Gauss and p-adic numbers
In his notebooks, Gauss recorded various calculations with "infinite congruences". These infinite congruences are p-adic numbers; Gauss computes a square root of $5$ in the $11$-adic integers in order to find an $11$-adic approximation to a quadratic Gauss sum, computes a nontrivial square root of $1$ in $10$-adic integers, and computes the $10$-adic logarithms of small natural numbers.

Seed-dispersing animals are in decline, impacting forests and the climate: Study https://news.mongabay.com/short-article/2025/08/seed-dispersing-animals-are-in-decline-impacting-forests-and-the-climate-study/

Seed-dispersing animals are in decline, impacting forests and the climate: Study
A lot of attention has been paid to the decrease in bee populations and other pollinators, but a recent review article makes the case that we should be equally alarmed by the declining numbers of seed-dispersing animals, which are crucial for growing healthy forests. “Both are important and should be taken into account in restoration […]

To cover a permutohedron
Bochao Kong, Ji Zeng
https://arxiv.org/abs/2509.13877 https://arxiv.org/pdf/2509.13877

To cover a permutohedron
The permutohedron $P_n$ of order $n$ is a polytope embedded in $\mathbb{R}^n$ whose vertex coordinates are permutations of the first $n$ natural numbers. It is obvious that $P_n$ lies on the hyperplane $H_n$ consisting of points whose coordinates sum up to $n(n+1)/2$. We prove that if the vertices of $P_n$ are contained in the union of $m$ affine hyperplanes different from $H_n$, then $m\geq n$ when $n \geq 3$ is odd, and $m \geq n-1$ when $n \geq 4$ is even. This confirms a recent conjecture o…

Giants Now: Numbers to know for Giants-Cowboys https://www.giants.com/news/numbers-to-know-week-2-giants-cowboys-malik-nabers-russell-wilson-bobby-okereke-dak-prescott-ceedee-lamb

Fermionic Love number of Reissner-Nordstr\"om black holes
Xiankai Pang, Yu Tian, Hongbao Zhang, Qingquan Jiang
https://arxiv.org/abs/2510.10036 https://

Fermionic Love number of Reissner-Nordström black holes
The tidal deformation of compact objects, characterised by their Love numbers, provides insights into the internal structure of neutron stars and black holes. While bosonic tidal Love numbers vanish for black holes in general relativity, it has been recently revealed that fermionic tidal perturbations can induce non-zero Love numbers for Kerr black holes. In this paper, we investigate the response of the Reissner-Nordström black hole to the fermionic Weyl field. As a result, we find that the c…

Transcendence Meets Normality: Construction of Transcendentally Normal Numbers
Chokri Manai
https://arxiv.org/abs/2508.09319 https://arxiv.org/pdf/2508.093…

Transcendence Meets Normality: Construction of Transcendentally Normal Numbers
In this work, we study real numbers $x$ for which $p(x)$ is (absolutely) normal for every non-constant integer-valued polynomial $p$. We call such numbers transcendentally normal. We prove that almost every real number is transcendentally normal and provide an explicit construction of such a number, based on Sierpinski's covering method and novel ideas involving the so-called stretch function. In the next step, we transform this construction into an algorithm that computes the digits of a t-nor…

Generalizations of the Crossing Lemma
Geza Toth
https://arxiv.org/abs/2509.14074 https://arxiv.org/pdf/2509.14074…

Generalizations of the Crossing Lemma
The crossing number of a graph is the minimum number of crossings over all of its drawings on the plane. The Crossing Lemma, proved more than 40 years ago, is a tight lower bound on the crossing number of a graph in terms of the number of vertices and edges. It is definitely the most important inequality on crossing numbers. We review some generalizations and applications of the Crossing Lemma.

White House announces federal worker layoffs as government shutdown nears third week
No official numbers have been announced but treasury, HHS, DHS and education departments among agencies confirming cuts
https://www.theguardian.com…

Local structure of classical sequences, regular sequences, and dynamics
Sawian Jaidee, Patrick Moss, Thomas Ward
https://arxiv.org/abs/2508.11054 https://a…

Local structure of classical sequences, regular sequences, and dynamics
We introduce the notions of local realizability at a prime and algebraic realizability of an integer sequence. After discussing this notion in general we consider it for the Euler numbers, the Bernoulli denominators, and the Bernoulli numerators. This gives, for example, a dynamical characterization of the Bernoulli regular primes. Algebraic realizability of the Bernoulli denominators is shown at every prime, giving a different perspective on the great diversity of congruences satisfied by this…

Trump nominates Jan 6 "bystander" to produce better job numbers (Don Moynihan/Can We Still Govern?)
https://donmoynihan.substack.com/p/trump-nominates-jan-6-bystander-to
http://www.memeorandum.com/250815/p22#a250815p22

Zero to 100: Cowboys preseason opener by the numbers https://www.dallascowboys.com/news/zero-to-100-cowboys-preseason-opener-by-the-numbers

Some Structures arising from the Farey Fractal
Shai Haran
https://arxiv.org/abs/2509.10959 https://arxiv.org/pdf/2509.10959

Some Structures arising from the Farey Fractal
This work explores new arithmetic and combinatorial structures arising from the interplay between Farey-type graphs, Fibonacci expansions, and operadic constructions. We introduce Fibonadic numbers, defined as an inverse limit under the Zeckendorf shift, equipped with a metric, order, and commutative rig structure. A normalization lemma provides canonical representatives, while quotients of the non-zero Fibonadic numbers under shifts and it's fundamental domain covering the circle via phi-value…

Zero to 100: Cowboys preseason opener by the numbers https://www.dallascowboys.com/news/zero-to-100-cowboys-preseason-opener-by-the-numbers

On a remark of Serre
Katie Ahrens, Jon Grantham
https://arxiv.org/abs/2508.11048 https://arxiv.org/pdf/2508.11048…

On a remark of Serre
Inspired by a remark of Serre, we extend the search for primes $p$ such that the maximum Hasse bound for the number of points on an elliptic curve over $\mathbb{F}_{p^5}$ is not achieved. We then give a list of all $q<10^{70}$ such that the Hasse bound is not achieved over $\mathbb{F}_{q}$. We explore the heuristics for how many such numbers should exist in each case. Finally, look at similar criteria for genus $2$ and $3$ curves.

Formulas and asymptotics of hypergraph Catalan numbers
Eva-Maria Hainzl
https://arxiv.org/abs/2508.08865 https://arxiv.org/pdf/2508.08865

Formulas and asymptotics of hypergraph Catalan numbers
Tree walks are a class of closed walks on a complete graph constrained to span trees. In this work, we focus on a special subclass called $k$-tours, which were recently introduced by Gunnells and are enumerated by the hypergraph Catalan numbers $ c_n^{(k)}$. Gunnells conjectured an asymptotic formula for $c_n^{(k)}$ which we confirm through an alternative approach to their enumeration. As it turns out, the asymptotic growth is governed by the number of $k$-tours on star-like trees.

3 numbers to know from the new NBC News Decision Desk Poll: From the Politics Desk (NBC News)
https://www.nbcnews.com/politics/politics-news/3-numbers-know-nbc-news-decision-desk-poll-politics-desk-rcna229943
http://www.memeorandum.com/250908/p134#a250908p134

Several expressions for degenerate harmonic numbers and some related numbers
Taekyun Kim, Dae san Kim, Kyo-Shin Hwang
https://arxiv.org/abs/2508.01189 https://

Several expressions for degenerate harmonic numbers and some related numbers
Many authors have recently studied the degenerate harmonic numbers. This paper makes two main contributions. First, we derive several explicit expressions for these numbers, which are a degenerate version of the ordinary harmonic numbers. We also examine the degenerate harmonic numbers of order m and find an expression for them. Second, we investigate some related numbers that are closely connected to the degenerate harmonic numbers of order m, which reduce to the degenerate harmonic numbers wh…

Recurrence Relations for Some Integer Sequences Related to Ward Numbers
Aleks \v{Z}igon Tankosi\v{c}
https://arxiv.org/abs/2508.04754 https://arxiv.org/pdf…

Recurrence Relations for Some Integer Sequences Related to Ward Numbers
In this paper, we give recurrence relations and identities for some integer sequences related to Ward numbers such as Ward-Lah numbers, varied Ward numbers and binomial Ward numbers. Most of the sequences are entered in the On-Line Encyclopedia of Integer Sequences. We give triangular recurrence relations, horizontal recurrence relations, exponential generating functions and some recurrence relations of higher order obtained by using Sister Celine's general algorithm.

The zero blocking numbers of grid graphs
Hau-Yi Lin, Wu-Hsiung Lin, Gerard Jennhwa Chang
https://arxiv.org/abs/2508.09873 https://arxiv.org/pdf/2508.09873

The zero blocking numbers of grid graphs
In a zero forcing process, vertices of a graph are colored black and white initially, and if there exists a black vertex adjacent to exactly one white vertex, then the white vertex is forced to be black. A zero blocking set is an initial set of white vertices in a zero forcing process such that ultimately there exists a white vertex. The zero blocking number is the minimum size of a zero blocking set. This paper gives the exact value of the zero blocking number of grid graphs.

On Diophantine equations involving intersection of Thabit and Williams numbers base $b$ and some ternary recurrent sequences
Bibhu Prasad Tripathy, Asutosh Satapathy, Utkal Keshari Dutta, Bijan Kumar Patel
https://arxiv.org/abs/2510.12145

On Diophantine equations involving intersection of Thabit and Williams numbers base $b$ and some ternary recurrent sequences
Let $\mathcal{P}_{n}$ be the $n$-th Padovan number, $E_{n}$ be the $n$-th Perrin number and $N_{n}$ be the $n$-th Narayana's cows number. Let $b$ be a positive integer such that $b \geq 2$. In this paper, we study the Diophantine equations \[ \mathcal{P}_{n} = (b \pm 1)\cdot b^{l} \pm 1, \] \[ E_{n} = (b \pm 1)\cdot b^{l} \pm 1, \] and \[ N_{n} = (b \pm 1)\cdot b^{l} \pm 1, \] in non-negative integers $n, b$ and positive integer $l$. As a result, we determine the Padovan, Perrin…

Counting Salem numbers arising from arithmetic hyperbolic orbifolds
Michelle Chu, Plinio G. P. Murillo, Otto Romero, Lola Thompson
https://arxiv.org/abs/2508.08003 https://

Counting Salem numbers arising from arithmetic hyperbolic orbifolds
The relationship between Salem numbers and short geodesics has been fruitful in quantitative studies of arithmetic hyperbolic orbifolds, particularly in dimensions 2 and 3. In this article, we push these connections even further. The primary goals are: (1) to bound the proportion of Salem numbers of degree up to $n+1$ in the commensurability class of classical arithmetic lattices in any odd dimension $n$; (2) to improve lower bounds for the strong exponential growth of averages of multiplicitie…

A decomposition of graph a-numbers
Suyuong Choi, Younghan Yoon
https://arxiv.org/abs/2508.06855 https://arxiv.org/pdf/2508.06855

A decomposition of graph a-numbers
We study the $a$-sequence $(a_0(G), a_1(G), \cdots)$ of a finite simple graph $G$, defined recursively through a combinatorial rule and known to coincide with the sequence of rational Betti numbers of the real toric variety associated with $G$. In this paper, we establish a combinatorial and topological decomposition formula for the $a$-sequence. As an application, we show that the $a$-sequence is monotone under graph inclusion; that is, $a_i(G) \geq a_i(H)$ for all $i \geq 0$ whenever $H$ is…

Complete characterization of $2$-near perfect numbers with exactly 2 prime factors
Richard Fearon, Henry Foushee, Benjamin Porosoff, Alexander Skula, Joshua Zelinsky, Kyle Zhang
https://arxiv.org/abs/2508.06651

Complete characterization of $2$-near perfect numbers with exactly 2 prime factors
Let $σ(n)$ be the sum of the positive divisors of $n$. A positive integer $n$ is said to be $2$-near perfect when $σ(n)=2n+d_1+d_2$, where $d_1$ and $d_2$ are distinct positive divisors of $n$. We show that there are no odd $2$-near perfect numbers with exactly two prime factors, and that all even $2$-near perfect numbers (i.e. those of the form $2^kp^m$, where $p$ is an odd prime) belong to a specific family, provided that $m$ is at least 3. In combination with prior work, these results prod…

Hurwitz--Lerch Type Families of Poly-Bernoulli and Poly-Cauchy Numbers and Polynomials with Parameters $(\alpha,a)$
Noel B. Lacpao, Roberto B. Corcino
https://arxiv.org/abs/2508.06766

Hurwitz--Lerch Type Families of Poly-Bernoulli and Poly-Cauchy Numbers and Polynomials with Parameters $(α,a)$
This study introduces $(α,a)$-parameterized Hurwitz-Lerch type poly-Bernoulli and poly-Cauchy numbers and polynomials, extending classical sequences through the Hurwitz-Lerch zeta function. We derive generating functions, recurrences, and explicit formulas, revealing deeper structures and connections with zeta functions and polylogarithms. The results enrich existing theory and open new directions in analytic number theory and combinatorics.

Conjectures about Primes and Cyclic Numbers
Joel E. Cohen
https://arxiv.org/abs/2508.08335 https://arxiv.org/pdf/2508.08335

Conjectures about Primes and Cyclic Numbers
A positive integer $n$ is defined to be cyclic if and only if every group of size $n$ is cyclic. Equivalently, $n$ is cyclic if and only if $n$ is relatively prime to the number of positive integers less than $n$ that are relatively prime to $n$. Because every prime number is cyclic, it is natural to ask whether a (proved or conjectured) property of primes extends to cyclic numbers. I review proved or conjectured properties of primes (including some new conjectures about primes) and propose ana…

Restricted Jacobi permutations
Alyssa G. Henke, Kyle R. Hoffman, Derek H. Stephens, Yongwei Yuan, Yan Zhuang
https://arxiv.org/abs/2509.11494 https://arxiv…

Restricted Jacobi permutations
Jacobi permutations, introduced by Viennot in the context of Jacobi elliptic functions, are counted by the Euler numbers $E_{n}$ appearing in the series expansion $\sec x+\tan x=\sum_{n=0}^{\infty}E_{n}x^{n}/n!$. We conduct a systematic study of pattern avoidance in Jacobi permutations, achieving a complete enumeration of Jacobi permutations avoiding a prescribed set of length 3 patterns. In the case of a single pattern restriction, we obtain refined enumerations with respect to several permuta…

Superior Highly Composite Numbers and the Explicit Upper Bound of Generalized Divisor Functions
Lee-Peng Teo
https://arxiv.org/abs/2508.06764 https://arxiv…

Superior Highly Composite Numbers and the Explicit Upper Bound of Generalized Divisor Functions
For $k\geq 2$, we give a detailed exposition of the superior $k$-highly composite numbers. We then consider the function \[f_k(n)=\frac{\log d_k(n)\log\log n}{\log k\log n},\quad n\geq 3\] which has a maximum value $λ(k)$ at a superior $k$-highly composite number. We develop an efficient algorithm to compute $λ(k)$ and the positive integer $N_{\max}(k)$ where $f_k$ achieves the value $λ(k)$. The results for $2\leq k\leq 100$ are tabled.

Folkman's theorem and the primes
David J. Fern\'andez-Bret\'on
https://arxiv.org/abs/2509.12025 https://arxiv.org/pdf/2509.12025

Folkman's theorem and the primes
We provide two new proofs of the infinitude of prime numbers, using the additive Ramsey-theoretic result known as Folkman's theorem (alternatively, one can think of these proofs as using Hindman's theorem). This adds to the existing literature deriving the infinitude of primes from Ramsey-type theorems.

On pairs of triangular numbers whose product is a perfect square and pairs of intervals of successive integers with equal sums of squares
Vladimir Gurvich, Mariya Naumova
https://arxiv.org/abs/2508.06598

On pairs of triangular numbers whose product is a perfect square and pairs of intervals of successive integers with equal sums of squares
A number $N$ is a triangular number if it can be written as $N = t(t + 1)/2$ for some nonnegative integer number $t$. A triangular number $N$ is called square if it is a perfect square, that is, $N = d^2$ for some integer number $d$. Square triangular numbers were characterized by Euler in 1778 and are in one-to-one correspondence with the so-called near-isosceles Pythagorean triples $(k,k+1,l)$, where $k^2 + (k+1)^2 = l^2$. A quadratic number is the product $Π= Π(k,j) = k(k+1)(k+j)(k+j+1)$ f…

Narayana numbers that are products of two Fibonacci numbers
Japhet Odjoumani
https://arxiv.org/abs/2508.02688 https://arxiv.org/pdf/2508.02688

Narayana numbers that are products of two Fibonacci numbers
Let $\{N_m\}_{m\ge0}$ be the Narayana's cows sequence given by $N_0=0$, $N_1=1=N_2=1$ and \[ N_{m+3}=N_{m+2}+N_m,\quad \text{ for }\; m\geq 0 \] and let $\{F_n\}_{n\ge0}$ be the Fibonacci sequence. In this paper we solve explicitely the Diophantine equation \[ N_m=F_nF_k, \] in positive unknowns $m,\,n$ and $k$. That is, we find the non-zero narayana numbers that are products of two Fibonacci numbers.

Repdigits as Product of Consecutive Shifted Tribonacci Numbers
Pranabesh Das, Salah Eddine Rihane, Alain Togb\'e
https://arxiv.org/abs/2509.09578 https://

Repdigits as Product of Consecutive Shifted Tribonacci Numbers
A repdigit is a positive integer that has only one distinct digit in its decimal expansion, i.e., a number has the form $d(10^m-1)/9$ for some $m\geq 1$ and $1 \leq d \leq 9$. Let $\left(T_n\right)_{n\ge0}$ be the sequence of Tribonacci. This paper deals with the presence of repdigits in the products of consecutive shifted Tribonacci numbers.