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On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers
Ritesh Dwivedi, Rohit Yadav
https://arxiv.org/abs/2506.01830 https://

On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers
We define a sequence of positive integers recursively, where each term is determined as follows: starting with a given positive integer, if the term is odd, the next is the sum of its positive divisors; if the term is even, the subsequent term is half the term. It is conjectured that the sequence eventually reaches one for all initial values. In this paper, we classify a family of integers for which this conjecture holds.

Selbst wenn die #Erderwärmung langfristig wieder unter 1,5 °C fällt, bleiben viele #Gletscherverluste unumkehrbar.
Bei einem vorübergehenden Temperaturanstieg auf 3 °C verlieren #Gletscher

Irreversible glacier change and trough water for centuries after overshooting 1.5 °C - Nature Climate Change
How mountain glaciers will react to temporarily overshooting 1.5 °C of warming is poorly understood. Here the authors show irreversible global glacier loss for centuries after overshoot, implying long-term reductions in glacial water resources with amplified impacts in regions where glaciers regrow.

Particle-in-Cell Simulations of Burning ICF Capsule Implosions
Johannes J. van de Wetering, Justin R. Angus, W. Farmer, V. Geyko, D. Ghosh, D. Grote, C. Weber, G. Zimmerman
https://arxiv.org/abs/2506.02273

Particle-in-Cell Simulations of Burning ICF Capsule Implosions
Anomalies observed in the neutron spectral shift of high-yield shots at the National Ignition Facility (NIF) suggest the presence of suprathermal ions, implying that kinetic effects play a significant role in burning inertial confinement fusion (ICF) plasmas. Furthermore, recent measurements of reaction-in-flight (RIF) neutrons offer a direct probe of the stopping power in the burning fuel region of high energy alpha particles and up-scattered fuel ions. We have developed the particle-in-cell c…

This https://arxiv.org/abs/2506.01830 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers
We define a sequence of positive integers recursively, where each term is determined as follows: starting with a given positive integer, if the term is odd, the next is the sum of its positive divisors; if the term is even, the subsequent term is half the term. It is conjectured that the sequence eventually reaches one for all initial values. In this paper, we classify a family of integers for which this conjecture holds.

Random Utility with Aggregated Alternatives
Yuexin Liao, Kota Saito, Alec Sandroni
https://arxiv.org/abs/2506.00372 https://arxiv.org…

Random Utility with Aggregated Alternatives
This paper studies when discrete choice data involving aggregated alternatives such as categorical data or an outside option can be rationalized by a random utility model (RUM). Aggregation introduces ambiguity in composition: the underlying alternatives may differ across individuals and remain unobserved by the analyst. We characterize the observable implications of RUMs under such ambiguity and show that they are surprisingly weak, implying only monotonicity with respect to adding aggregated …

This https://arxiv.org/abs/2412.16772 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCY_…

Assessing Social Alignment: Do Personality-Prompted Large Language Models Behave Like Humans?
The ongoing revolution in language modeling has led to various novel applications, some of which rely on the emerging social abilities of large language models (LLMs). Already, many turn to the new cyber friends for advice during the pivotal moments of their lives and trust them with the deepest secrets, implying that accurate shaping of the LLM's personality is paramount. To this end, state-of-the-art approaches exploit a vast variety of training data, and prompt the model to adopt a particula…

This https://arxiv.org/abs/2310.03697 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Onset of dark energy from cosmological scalarization and gravitational wave speed
This study investigates the emergence of dark energy during the matter-dominated era through spontaneous cosmological scalarization in the scalar-Ricci-Gauss-Bonnet model.Our model aligns with the conjecture that the speed of gravitational waves at low redshifts is nearly equal to the speed of light, implying that the Gauss-Bonnet invariant does not directly contribute to late-time acceleration and suggesting that scalarization begins in the radiation-dominated era. The Gauss-Bonnet coupl…

Asteroids fail to retain cometary impact signatures
Sarah Joiret, Guillaume Avice, Ludovic Ferri\`ere, Zo\"e M. Leinhardt, Simon Lock, Alexandre Mechineau, Sean N. Raymond
https://arxiv.org/abs/2507.00753

Asteroids fail to retain cometary impact signatures
A bombardment of comets is thought to have occurred in the inner solar system as a result of a dynamical instability among the giant planets after gas disk dispersal. Vesta, the second largest asteroid in the main asteroid belt, likely differentiated before gas disk dispersal, implying its crust witnessed the cometary bombardment. The composition of HED meteorites, which represent fragments of Vesta's crust, could therefore have been altered by cometary impacts. Here we combine noble gas mass s…

On the conjecture of Kashuba and Mathieu about free Jordan algebras
Vladimir Dotsenko, Irvin Roy Hentzel
https://arxiv.org/abs/2507.00437 https://

On the conjecture of Kashuba and Mathieu about free Jordan algebras
Kashuba and Mathieu proposed a conjecture on vanishing of Lie algebra homology, implying a description of the $GL_d$-module structure of the free $d$-generated Jordan algebra. Their conjecture relies on a functorial version of the Tits--Kantor--Koecher construction that builds Lie algebras out of Jordan algebras. In this note, we summarize new intricate computational data concerning free Jordan algebras and explain why, despite a lot of overwhelmingly positive evidence, the conjecture of Kashub…

An anomalous particle-exchange mechanism for two isolated Bose gases merged into one
Q. H. Liu
https://arxiv.org/abs/2506.22478 https://

An anomalous particle-exchange mechanism for two isolated Bose gases merged into one
In an isolated ideal Bose system with a fixed energy, the number of microstates depends solely on the configurations of bosons in excited states, implying zero entropy for particles in the ground state. When two such systems merge, the resulting entropy is less than the sum of the individual entropies. This entropy decrease is numerically shown to arise from an effectively but anomalous exchange of particles in excited states, where $\overline{N}!/(\overline{N}_{1}!\overline{N}_{2}!)<1$. Here, …

I'm not sure which is worse: the idea that the folks setting this up didn't realize what they were implying...
... Or that they knew exactly what they were doing.

Replaced article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Conditions implying annular chaos
Alejandro Passeggi, Fabio Armando Tal

gcor: A Python Implementation of Categorical Gini Correlation and Its Inference
Sameera Hewage
https://arxiv.org/abs/2506.19230 https://

gcor: A Python Implementation of Categorical Gini Correlation and Its Inference
Categorical Gini Correlation (CGC), introduced by Dang et al. (2020), is a novel dependence measure designed to quantify the association between a numerical variable and a categorical variable. It has appealing properties compared to existing dependence measures, such as zero correlation mutually implying independence between the variables. It has also shown superior performance over existing methods when applied to feature screening for classification. This article presents a Python implementa…

The JWST/AURORA Survey: Multiple Balmer and Paschen Emission Lines for Individual Star-forming Galaxies at z=1.5-4.4. I. A Diversity of Nebular Attenuation Curves and Evidence for Non-Unity Dust Covering Fractions
Naveen A. Reddy, Alice E. Shapley, Ryan L. Sanders, Michael W. Topping, Richard S. Ellis, Max Pettini, Gabriel Brammer, Fergus Cullen, Natascha M. Forster Schreiber, Ali A. Khostovan, Derek J. McLeod, Ross J. McLure, Desika Narayanan, Pascal A. Oesch, Anthony J. Pahl, Charles…

The JWST/AURORA Survey: Multiple Balmer and Paschen Emission Lines for Individual Star-forming Galaxies at z=1.5-4.4. I. A Diversity of Nebular Attenuation Curves and Evidence for Non-Unity Dust Covering Fractions
We present the nebular attenuation curves and dust covering fractions for 24 redshift z=1.5-4.4 star-forming galaxies using multiple Balmer and Paschen lines from the JWST/AURORA survey. Nebular reddening derived from Paschen lines exceeds that from Balmer lines for at least half the galaxies in the sample when assuming the commonly-adopted Galactic extinction curve, implying the presence of optically-thick star formation. The nebular attenuation curves exhibit a broad range of normalizations (…

Conditions Implying Annular Chaos: Quantitative results and Computer Assisted Proofs
M. J. Capi\'nski, M. Gr\"oger, A. Passeggi, F. A. Tal
https://arxiv.org/abs/2506.06608

Conditions Implying Annular Chaos: Quantitative results and Computer Assisted Proofs
We derive quantitative sufficient conditions for rotational chaos and diffusion in annular homeomorphisms, building on the topological criteria established in [31]. These conditions depend only on basic properties of the maps, making their implementation straightforward. To demonstrate the effectiveness of the method, we provide computer-assisted proofs of rotational chaos and diffusion for classical families of annular maps and their variations, in both conservative (twist and non-twist) and d…

On the parametrised Whitehead torsion of families of nearby Lagrangian submanifolds
Sylvain Courte, Noah Porcelli
https://arxiv.org/abs/2506.06110 https://…

On the parametrised Whitehead torsion of families of nearby Lagrangian submanifolds
Motivated by the strong nearby Lagrangian conjecture, we constrain the parametrised Whitehead torsion of a family of closed exact Lagrangian submanifolds in a cotangent bundle. We prove the parametrised Whitehead torsion admits a factorisation through simpler maps, in particular implying it is trivial on $π_0$, $π_1$, and that its image is divisible by the Euler characteristic. We provide concrete implications for the Lagrangian monodromy question in the case of a high dimensional torus. Th…

I read "Then I Am Myself the World: What Consciousness Is and How to Expand It" by Christof Koch.
Interesting book which spends like 8 or 9 chapters detailing all the experiments which prove beyond much doubt that consciousness, and self awareness, is a thing done by a brain.
It describes how perception is a construction of a description, has a chapter called "computational mind"
And then spends the last two chapters describing why he thinks the mind can't be computed, because drugs have made him think experience is some kind of magic associated with highly interconnected causal structures.
Apparently, he thinks, once things become interconnected enough they become able to cause things independently of the physics running those connections.
Which is crazy, obviously. There's nothing causal in direct connections between neurons that isn't equally causal in modeled connections between virtual neurons.
All his evidence in the book from neural MRI scans to the effects of psychedelic drugs and symptoms of strokes and disease point to the brain simulating a virtual reality which is the basis of perception.
That simulated world in which we live is full of colour and shape and sounds and emotions and millions of mental constructs that are built to be correlated by the senses with the outside world, but are not equal to the world itself. We live in a dream constructed to correlate with reality.
But then instead of taking the next step: That consciousness itself is a property of a simulated being inside that mental model of the universe, a property which the brain simulates and applies to the virtual self that's doing the experiencing inside that model, he jumps towards some magic implying pan-psychism or that sufficiently interconnected networks become causally self-complete for some reason nobody can fathom.
Sure, colour and shape and emotions are all made up by the brain but experience can't be! For some reason.
You see in truth dualism is false, in that there is no spirit realm in which ghosts animate the matter of the body somehow.
Yet also, dualism is true, in that there is a simulated mental reality which we live in, computed by the brain in which all perception and experience are created, which is related-to but separate-from the unfolding complicated dance of energy that is the universe our bodies interact with.
People take some DMT trip, and the model of the universe emulated by their brain collapses and breaks. Their virtual simulated self inside their mind has these experiences of being one with the universe or the experience of feeling dead yet conscious or whatever, and these hippies think that the broken down simulated experience is real and reflects how consciousness is more fundamental than the atoms that make up the neurons in their brain.
Instead of realizing it shows them that their experienced universe is a simulacrum, they think they get a more direct experience of reality somehow. A consciousness more pure than any mere base atom.
"Then I am myself the world" is a great title. Everything you ever experience is created and simulated in your brain like a dream, the whole universe is inside your head. Even the fact of experience itself.
But that isn't the conclusion Koch reaches somehow, he just jumps from describing the evidence that this is so straight into ascribing super-causal magic consciousness to particular arrangements of atoms that integrated information theory suggest have high correlation, and thinks therefore conciousness is itself the entire universe.
Ah well, fun book. I like arguing in my head with authors that are wrong.
#reading #books #consciousness #thenIAmMyselfTheWorld

Planets similar in size are often dissimilar in interior
E. Mamonova, Y. Shan, P. Hatalova, S. C. Werner
https://arxiv.org/abs/2506.05089 https://

Planets similar in size are often dissimilar in interior
Recent works have found evidence of significant intrasystem uniformity in planet properties such as radius, mass, and orbital spacing, collectively termed 'peas in a pod' trends. In particular, correlations in radius and mass have been interpreted as implying uniformity in planet bulk density and composition within a system. However, the samples used to assess trends in mass tend to be small and biased. In this paper, we re-evaluate correlations in planet properties in a large sample of systems…