Tootfinder

Labeled Plane Trees and Increasing Plane Trees
Lora R. Du, Kathy Q. Ji, Dax T. X. Zhang
https://arxiv.org/abs/2510.03039 https://arxiv.org/pdf/2510.03039…

Labeled Plane Trees and Increasing Plane Trees
This note is dedicated to presenting a polynomial analogue of $(n+1)!C_n=2^n(2n-1)!!$ (with $C_n$ as the $n$-th Catalan number) in the context of labeled plane trees and increasing plane trees, based on the definition of improper edges in labeled plane trees. A new involution on labeled plane trees is constructed to establish this identity, implying that the number of improper edges and the number of proper edges are equidsitributed over the set of labeled plane trees.

Filings: after EA's buyout, Saudi Arabia's PIF would own 93.4% of EA, implying it needs to put up ~$29B, while Silver Lake and Affinity would own 5.5% and 1.1% (Wall Street Journal)
https://www.wsj.com/business/deals/saudi-fund…

I've been seeing a term that fash coders use for themselves more and more:
"Builders."
(It's implying that people who don't agree with their fascist worldviews are "tearing down" society and the world and have nothing to contribute and are therefore expendable.)

@… The billboard was implying that ChatGPT is the broken engine right?
Right!?

Sensing-Secure ISAC: Ambiguity Function Engineering for Impairing Unauthorized Sensing
Kawon Han, Kaitao Meng, Christos Masouros
https://arxiv.org/abs/2510.02103 https://…

Sensing-Secure ISAC: Ambiguity Function Engineering for Impairing Unauthorized Sensing
The deployment of integrated sensing and communication (ISAC) brings along unprecedented vulnerabilities to authorized sensing, necessitating the development of secure solutions. Sensing parameters are embedded within the target-reflected signal leaked to unauthorized passive radar sensing eavesdroppers (Eve), implying that they can silently extract sensory information without prior knowledge of the information data. To overcome this limitation, we propose a sensing-secure ISAC framework that e…

Noisy Timing Behavior is a Feature of Central Compact Object Pulsars
K. I. Perez, E. V. Gotthelf, J. P. Halpern
https://arxiv.org/abs/2510.02233 https://ar…

Noisy Timing Behavior is a Feature of Central Compact Object Pulsars
We present a timing study of the three known central compact object (CCO) pulsars, isolated cooling neutron stars in supernova remnants, using Chandra, XMM-Newton and NICER observations spanning two decades. Relative to canonical young pulsars, CCOs are spinning down at a very slow rate $|\dot f| <10^{-15}$ s$^{-2}$, implying a surface dipole magnetic field strength $B_s < 10^{11}$ G that is too weak to account for their X-ray emitting hot spots. Two CCO pulsars with sufficiently long…

LatentEvolve: Self-Evolving Test-Time Scaling in Latent Space
Guibin Zhang, Fanci Meng, Guancheng Wan, Zherui Li, Kun Wang, Zhenfei Yin, Lei Bai, Shuicheng Yan
https://arxiv.org/abs/2509.24771

LatentEvolve: Self-Evolving Test-Time Scaling in Latent Space
Test-time Scaling (TTS) has been demonstrated to significantly enhance the reasoning capabilities of Large Language Models (LLMs) during the inference phase without altering model parameters. However, existing TTS methods are largely independent, implying that LLMs have not yet evolved to progressively learn how to scale more effectively. With the objective of evolving LLMs to learn ``how to scale test-time computation,'' we propose LatentEvolve, a self-evolving latent TTS framework inspired by…

I'm being a little mopey because Ranger the cat quit the family and ran off because of the "new" dog.
#caturday

A Refined Orbital Ephemeris for the Intermediate Polar FO Aquarii and Evidence for a Period Derivative
Peter Garnavich (Notre Dame), Jordan Tweddale (Notre Dame), Colin Littlefield (BAERI)
https://arxiv.org/abs/2509.22786

A Refined Orbital Ephemeris for the Intermediate Polar FO Aquarii and Evidence for a Period Derivative
We combine more than 40 years of eclipse timings of the intermediate polar FO Aqr and derive new orbital ephemerides. The eclipse times are best fit with a second order polynomial, implying an $8σ$ detection of a period derivative. The results show that the orbital period of FO Aqr is currently increasing, with a derivative of $\dot{P}=6.65\pm0.81\times10^{-11}$.

Source: Suno hit ~$150M in ARR from subscriptions to its app, up nearly 4x YoY; it has $10 and $30 per month subscription tiers, implying 5M subscribers (Stephanie Palazzolo/The Information)
https://www.theinformation.com/articles/mu

Music App Suno Nearly Quadruples Annual Recurring Revenue to $150 Million
You can count the number of breakout consumer AI applications on the fingers of one hand. There’s OpenAI’s ChatGPT and…that’s about it, at least so far.Suno, which helps people create music using conversational prompts, isn’t yet a breakout—but it could be soon. The company is generating around ...

#Wordle 1,621 4/6*
⬜⬜⬜⬜🟨 <1% of 225,353 (109)
⬜🟨🟨⬜⬜ 8% of 13 (12)
🟩🟩⬜🟩⬜ 0 of 2 (3)
🟩🟩🟩🟩🟩
WordleBot
Skill 90/99
Luck 47/99
It's interesting how you process the clues, different letters linking to others and implying placement.
Of the 3 words left 2 were past tense so really unlikely.

Finding rare classes in large datasets: the case of polluted white dwarfs from Gaia XP spectra
Xander Byrne, Amy Bonsor, Laura K. Rogers, Mariona Badenas-Agusti
https://arxiv.org/abs/2509.24487

Finding rare classes in large datasets: the case of polluted white dwarfs from Gaia XP spectra
The Gaia mission's third data release recorded low-resolution spectra for about 100 000 white dwarf candidates. A small subset of these spectra show evidence of characteristic broad Ca II absorption features, implying the accretion of rocky material by so-called polluted white dwarfs -- important probes of the composition of exoplanetary material. Several supervised and unsupervised data-intensive methods have recently been applied to identify polluted white dwarfs from the Gaia spectra. We pre…

(Note that Popehat does this in the OP.)
If you don’t do this, if you wander into arguing that has death was wrong because he had some redeeming qualities, then you’re basically implying that political violence •would• be OK against •someone• out there — just not against an outright fascist.
This does not seem like much of a noble principle to me.
A/3

The degrees of freedom of multiway junctions in three dimensional gravity
Avik Chakraborty, Tanay Kibe, Mart\'in Molina, Ayan Mukhopadhyay, Giuseppe Policastro
https://arxiv.org/abs/2509.20437

The degrees of freedom of multiway junctions in three dimensional gravity
We demonstrate that $n$-way junctions in three dimensional gravity correspond to coupled $n-1$ strings each satisfying the Nambu-Goto equation in the smoothened background, and with sources consisting of Monge-Ampère like terms which couple the strings. For $n\geq 3$, these $n-1$ degrees of freedom survive the tensionless limit implying that matter-like behavior can arise out of $pure$ gravity. We interpret these stringy degrees of freedom of gravitational junctions holographically in terms of…

Source: Suno hit ~$150M in ARR from subscriptions to its app, up nearly 4x YoY; it has $10 and $30 per month subscription tiers, implying 5M subscribers (Stephanie Palazzolo/The Information)
https://www.theinformation.com/articles/mu

Music App Suno Nearly Quadruples Annual Recurring Revenue to $150 Million
You can count the number of breakout consumer AI applications on the fingers of one hand. There’s OpenAI’s ChatGPT and…that’s about it, at least so far.Suno, which helps people create music using conversational prompts, isn’t yet a breakout—but it could be soon. The company is generating around ...

#DropoutTV

The Noise Boys Ride Again - Season 4 - Dropout
Josh, Zac, and Brennan name mobsters and try to hide their bald spots. Content Warning: Comedic Gags Implying Suicide - [2:00-3:13]

Brendan Carr says the FCC may need to pursue "remedies" against Jimmy Kimmel, if ABC doesn't discipline him, for implying Charlie Kirk's killer was a MAGA fan (Sean James/Mediaite)
https://www.mediaite.com/media/news/just…

JUST IN: Trump FCC Chair Threatens ABC With Punishment Over Jimmy Kimmel’s Charlie Kirk Comments
FCC Chair Brendan Carr threatened Jimmy Kimmel over his "concerted effort to lie to the American people" by claiming Charlie Kirk's killer was a Trump supporter

Dynamics of $\mathrm{CP}^{N-1}$ skyrmions
Seungho Lee, Hyojae Jeon, Jung Hoon Han
https://arxiv.org/abs/2509.17403 https://arxiv.org/pdf/2509.17403

Dynamics of $\mathrm{CP}^{N-1}$ skyrmions
We derive several exact results for the dynamics of CP$^{N-1}$ skyrmions with arbitrary $N$. Fractonic continuity equation is shown to hold for arbitrary CP$^{N-1}$ fluid implying the conservation of the topological charge and the dipole moment. Inclusion of the Gilbert damping modifies the continuity equation, resulting in the violation of the dipole moment conservation but not of the topological charge. Thiele's equation for the CP$^{N-1}$ skyrmion follows from the modified continuity equatio…

Nonlinear Heisenberg Limit via Uncertainty Principle in Quantum Metrology
Binke Xia, Jingzheng Huang, Yuxiang Yang, Guihua Zeng
https://arxiv.org/abs/2510.09216 https://

Nonlinear Heisenberg Limit via Uncertainty Principle in Quantum Metrology
The Heisenberg limit is acknowledged as the ultimate precision limit in quantum metrology, traditionally implying that root mean square errors of parameter estimation decrease linearly with the time T of evolution and the number N of quantum gates or probes. However, this conventional perspective fails to interpret recent studies of "super-Heisenberg" scaling, where precision improves faster than linearly with T and N. In this work, we revisit the Heisenberg scaling by leveraging the position-m…

Base Models Know How to Reason, Thinking Models Learn When
Constantin Venhoff, Iv\'an Arcuschin, Philip Torr, Arthur Conmy, Neel Nanda
https://arxiv.org/abs/2510.07364 https…

Base Models Know How to Reason, Thinking Models Learn When
Why do thinking language models like DeepSeek R1 outperform their base counterparts? Despite consistent performance gains, it remains unclear to what extent thinking models learn entirely new reasoning capabilities or repurpose pre-existing base model ones. In this work, we propose a hybrid model where we activate reasoning mechanisms in base models at the right time to elicit thinking-model-level reasoning chains, implying that thinking models exploit already existing capabilities. To ground o…

Revealing signals of higher-order nonlinear showers in particle-laser collisions
T. G. Blackburn, B. King, M. Samuelsson
https://arxiv.org/abs/2510.08679 https://

Revealing signals of higher-order nonlinear showers in particle-laser collisions
Several high power laser facilities are reaching field strengths where leading order strong-field quantum electrodynamical (QED) processes can be measured in the non-perturbative regime for the first time. At very high, as yet unobtainable in the laboratory, field strengths, the contribution of higher-order processes is predicted to dominate, implying a breakdown of current calculational methods. Focusing on nonlinear showers and considering currently available experimental parameters, we find …

On catastrophicity of convolutional codes and their encoders over $\Z_{p^r}$
Mohammed El Oued
https://arxiv.org/abs/2509.06670 https://arxiv.org/pdf/2509.0…

On catastrophicity of convolutional codes and their encoders over $\Z_{p^r}$
This paper investigates the existence of minimal $p$-encoders for convolutional codes over $\mathbb{Z}_{p^r}$, where $p$ is a prime. This addresses a conjecture from \cite{k}, which posits that every such code admits a minimal $p$-encoder, implying that all convolutional codes over $\mathbb{Z}_{p^r}$ are noncatastrophic when input sequences are restricted to coefficients in $\{0, \dots, p-1\}$. Our contributions include the introduction of a new polynomial invariant that characterizes free code…

On detection probabilities of link invariants
Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz, Victor L. Zhang
https://arxiv.org/abs/2509.05574 https://arxiv…

On detection probabilities of link invariants
We prove that the detection rate of n-crossing alternating links by link invariants insensitive to oriented mutation decays exponentially in n, implying that they detect alternating links with probability zero. This phenomenon applies broadly, in particular to quantum invariants such as the Jones or HOMFLYPT polynomials. We also use a big data approach to analyze several borderline cases (e.g. integral Khovanov or HOMFLYPT homologies), where our arguments almost, but not quite, apply, and we pr…

HiPERCAM and TESS observations of the rapidly rotating M7V star LP 89--187
Gavin Ramsay (Armagh Observatory,Planetarium), J. G. Doyle (Armagh), Stuart Littlefair (Sheffield), Vik Dhillon (Sheffield), David Alvarez Garcia (IAC)
https://arxiv.org/abs/2509.15941

HiPERCAM and TESS observations of the rapidly rotating M7V star LP 89--187
The discovery of a significant number of rapidly rotating low mass stars showing no or few flares in TESS observations was a surprise as rapid rotation has previously been taken as implying high stellar activity. Here we present TESS and HiPERCAM $u_{s}g_{s}r_{s}i_{s}z_{s}$ observations of one of these stars LP 89--187 which has a rotation period of 0.117 d. TESS data covering three sectors (64.6 d) only show three flares which have energies a few $\times10^{33}$ erg, whilst HiPERCAM observatio…

Harvesting chemical power from cyclic environments
Pranay Jaiswal, Ivar S. Haugerud, Hidde D. Vuijk, Christoph A. Weber
https://arxiv.org/abs/2510.10266 https://

Harvesting chemical power from cyclic environments
Life relies on a sophisticated metabolic molecular machinery that turns over high-energy molecules to evolve complex macromolecules and assemblies. At the molecular origin of life, such machinery was absent, implying the need for simple yet robust physical mechanisms to harvest energy from the environment and perform chemical work or produce chemical power. However, the mechanisms involved in harvesting energy from a macroscopic cyclic environment to drive chemical processes on the molecular sc…

Gap metrics for stationary point processes and quantitative convexity of the free energy
Martin Huesmann, Bastian M\"uller
https://arxiv.org/abs/2509.08659 https://

Gap metrics for stationary point processes and quantitative convexity of the free energy
In this article, we are interested in convexity properties of the free energy for stationary point processes on $\mathbb R$ w.r.t.\ a new geometry inspired by optimal transport. We will show for a rich class of pairwise interaction energies A) quantified strict convexity of the free energy implying uniqueness of minimizers B) existence of a gradient flow curve of the free energy w.r.t. the new metric converging exponentially fast to the unique minimizer. Examples for energies for which A …

An involution for trivariate symmetries of vincular patterns
Joanna N. Chen, Shishuo Fu, Jiang Zeng
https://arxiv.org/abs/2509.13097 https://arxiv.org/pdf/…

An involution for trivariate symmetries of vincular patterns
We provide a bijective proof of the equidistribution of two pairs of vincular patterns in permutations, thereby resolving a recent open problem of Bitonti, Deb, and Sokal (arXiv:2412.10214). Since the bijection is involutive, we also confirm their conjecture on the equidistribution of triple vincular patterns. Somewhat unexpectedly, we show that this involution is closed on the set of Baxter permutations, thereby implying another trivariate symmetries of vincular patterns. The proof of this sec…

Dissipative contributions to spin polarization
Matteo Buzzegoli
https://arxiv.org/abs/2509.04854 https://arxiv.org/pdf/2509.04854

Dissipative contributions to spin polarization
Utilizing the Zubarev non-equilibrium density operator method and a first-order gradient expansion, we provide a comprehensive classification of all possible spin polarization effects. A key finding is that, with the unique exception of those induced by the gradient of the spin potential, all first-order dissipative corrections are chiral, implying their dependence on parity-breaking interactions or chiral imbalance. The work also introduces new non-dissipative phenomena akin to the Spin Hall E…