We prove that Gaussian thermal input states minimize the output von Neumann entropy of the one-mode Gaussian quantum-limited attenuator for fixed input entropy. The Gaussian quantum-limited attenuator models the attenuation of an electromagnetic sign...
We prove the longstanding conjecture stating that Gaussian thermal input states minimize the output von Neumann entropy of one-mode phase-covariant quantum Gaussian channels among all the input states with a given entropy. Phase-covariant quantum Gau...
Feb 27, 2026 · Microsoft Word continues to prove why it remains the default choice for document creation across schools, businesses, and personal use. Its blend of familiar tools, powerful …
We lay down the fundations of the theory of groups of finite Morley rank in which local subgroups are solvable and we proceed to the local analysis of these groups. We prove the main Uniqueness Theorem, analogous to the Bender method in finite grou...
Let $M = Γ\backslash G$ be a nilmanifold endowed with an invariant complex structure. We prove that Kuranishi deformations of abelian complex structures are all invariant complex structures, generalizing a result of C. Maclaughlin, H. Pedersen, Y....
Under the assumption of an initial datum divergence free and in L2, we prove the existence of a weak solution to the Navier-Stokes initial boundary value problem enjoying the energy equality on (0,t), almost everywhere in t>0, in particular, for all...
We present "Gasper," a proof-of-stake-based consensus protocol, which is an idealized version of the proposed Ethereum 2.0 beacon chain. The protocol combines Casper FFG, a finality tool, with LMD GHOST, a fork-choice rule. We prove safety, plausible...
whether hearsay evidence of implied assertions should be admissible in court to prove or justify the issue within contents. Implied assertions are generally
TL;DR: The $1 Trillion Advertising Pivot No One Sees Coming **OpenAI is building the largest advertising platform in history.** With 800M users (95% free), $13.5B in losses, 2.5B daily queries, strat...
Feb 27, 2026 · Microsoft Word continues to prove why it remains the default choice for document creation across schools, businesses, and personal use. Its blend of familiar tools, powerful …
Generic sentences express generalisations about the world without explicit quantification. Although generics are central to everyday communication, building a precise semantic framework has proven difficult, in part because speakers use generics to g...
In this paper we suggest how f-bounded generics in nominally-typed OOP can be extended to the more general notion we call `doubly f-bounded generics' and we suggest how doubly f-bounded generics can be reasoned about. We also (attempt to) prove, usin...
In earlier work, Jockusch, Propp, and Shor proved a theorem describing the limiting shape of the boundary between the uniformly tiled corners of a random tiling of an Aztec diamond and the more unpredictable `temperate zone' in the interior of the...
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Continuing the first part of the paper, we consider scalar decentralized average-cost infinite-horizon LQG problems with two controllers. This paper focuses on the slow dynamics case when the eigenvalue of the system is small and prove that the singl...
Let $R$ be a commutative noetherian ring. The $n$-semidualizing modules of $R$ are generalizations of its semidualizing modules. We will prove some basic properties of $n$-semidualizing modules. Our main result and example shows that the divisor clas...
We define weight changing operators for automorphic forms on Grassmannians, i.e., on orthogonal groups, and investigate their basic properties. We then evaluate their action on theta kernels, and prove that theta lifts of modular forms, in which the...
These days, someone alleges something before presenting evidence to prove it (or perhaps without evidence at all). But the word allege comes directly from the Middle English verb alleggen, meaning …
We prove the security of the 1984 protocol of Bennett and Brassard (BB84) for quantum key distribution. We first give a key distribution protocol based on entanglement purification, which can be proven secure using methods from Lo and Chau's proof...
To probe what we can't prove, so the unprovable may become probable; testing for Scala (⭐ 55)
The "slope-number" of a graph $G$ is the minimum number of distinct edge slopes in a straight-line drawing of $G$ in the plane. We prove that for $Δ\geq5$ and all large $n$, there is a $Δ$-regular $n$-vertex graph with slope-number at least $n^{1...
We study straight-line drawings of planar graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane grap...
Since the beginning, Roquette has excelled in developing versatile and renewable ingredients from plant-based raw materials that support better and healthier lives and proven pharmaceutical …
One looks at expansive subgroups in particular examples of Roquette groups. This study is motivated by the importance of expansive subgroups in the theory of stabilizing bisets highlighted in [BouThe]. In this paper we prove the non-existence of expa...
In this note we revisit the dart graph and the squared dart digraph constructions and prove that they yield strongly connected digraphs when applied to connected graphs of minimum valence at least 3....
Life on the farm proves to be challenging for a plucky pig in this endearing family comedy.
Prior testnets have shown that while consumer-grade hardware can technically participate as a prover, it is unlikely to be effective due to high level of competition. (⭐ 18)
We prove certain type symmetric inequalities in $\textbf{R}^{2}$ and $\textbf{R}^3$, that ocur in many problems of analysis. These inequalities are generalizations of the Jensen's inequality from one variable to two and three variables...
We introduce the notion of a $[z, r; g]$-mixed cage. A $[z, r; g]$-mixed cage is a mixed graph $G$, $z$-regular by arcs, $r$-regular by edges, with girth $g$ and minimum order. In this paper we prove the existence of $[z, r ;g]$-mixed cages and exhib...
A multivariable hypergeometric-type formula for raising operators of the Macdonald polynomials is conjectured. It is proved that this agrees with Jing and Jozefiak's expression for the two-row Macdonald polynomials, and also with Lassalle and Schlo...
We prove a level raising mod $\ell=2$ theorem for elliptic curves over $\mathbb{Q}$. It generalizes theorems of Ribet and Diamond-Taylor and also explains different sign phenomena compared to odd $\ell$. We use it to study the 2-Selmer groups of modu...
In this article we prove level raising for cuspidal eigenforms modulo prime powers (for odd primes) of weight $k\geq 2$ and arbitrary character, extending the result in weight two established by the work of Tsaknias and Wiese and generalizing (partia...
May 12, 2016 · Greetings! I had hoped to do much of this alone, as a treat to you great guys of this forum, but sadly I yet again proved myself to be utterly useless! Basically what I have, are all the files …
For a graph with largest normalized Laplacian eigenvalue $λ_N$ and (vertex) coloring number $χ$, it is known that $λ_N\geq χ/(χ-1)$. Here we prove properties of graphs for which this bound is sharp, and we study the multiplicity of $χ/(χ-1)$....
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# LLMs use "Bag of Heuristics" to do approximate retrieval! The age-old question regarding LLMs: **Do large language models (LLMs) solve reasoning tasks by learning robust generalizable algorithms, ...
Crowell: >The 5-foot-11, 210-pounder brings a physical, downhill running style and a proven track record of production after reclassifying from the 2027 class. He rushed for 2,632 yards and 35 to...
Content Credentials (also known as C2PA signatures) are a digital media metadata specification. They aim to provide provenance information about a piece
Jun 9, 2025 · From listening more than you speak to framing deals around mutual gains, the most effective negotiators rely on proven techniques to build trust and drive win-win outcomes. Below, 20 …
In this paper, we analyze the Bollobás and Riordan polynomial $\mathcal{R}$ for ribbon graphs with half-ribbons introduced in [Combinatorics, Probability and Computing 31, 507-549, 2022]. We prove the universality property of a multivariate version...