“If you treat colors like the 'words' in the example above, and how many pixels of that color are in the image, human made images (artwork, photography, etc) DO NOT follow a zipfian distribution, but AI generated images (across several models I tested) DO follow a zipfian distribution.”

“The paper proves that determining the thinness of a tree is coNP-hard.”

“The paper shows that the homeomorphism problem for compact topological n-manifolds is Borel equivalent to equality on natural numbers, while the homeomorphism problem for noncompact topological 2-manifolds is of maximal complexity.”

“The gradient expansion includes an unexpected zeroth order term depending on the differences between thermo-hydrodynamic fields at the decoupling and the initial hypersurface. This term encodes a memory of the initial state...”

“Any Clifford+T circuit with T-depth D can be controlled with T-depth O(D), even without ancillas.”

“The conditional entropy or code length in many cases continues to decrease with context length at least to $N\sim 10^4$ characters, implying that there are direct dependencies or interactions across these distances.”

“The paper shows that the Ornstein-Uhlenbeck process can be transformed exactly into a stochastic process defined self-consistently in the comoving frame.”

“The paper proves that the chromatic number of $P_5$-free graphs is at most a polynomial function of the clique number.”

“The paper proves that for certain values of the circle diameter, the number of touching pairs is less than that from a specific spiral construction, which is conjectured to be extremal.”

“The paper constructs 3-fold blocking sets of conjectured size, obtained as the disjoint union of three linear blocking sets of Rédei type, and they lie on the same orbit of the projectivity (x:y:z)↦(z:x:y).”

“Late time levels are enhanced for the coated particles, implying a reduced effective interfacial diffusivity and a broadened release-time distribution.”

“The algorithm achieves linear time complexity when the number of colors is greater than 3.637 times the maximum degree plus 1.”

“The paper proves that the 'chordality condition' is also sufficient.”

“The paper proves the existence of guided electromagnetic waves at the interface of two honeycomb photonic crystals, resembling edge states in electronic systems.”

“Sub-ensemble correlations are determined by the covariance operator, inducing a natural geometry in which statistical independence corresponds to orthogonality of the measurement functionals.”

“The paper shows that fundamental limitations on the localizability of quantum states render the two scenarios, in principle, distinguishable.”

“Cube particles form a simple square assembly, overcoming lattice/topology incompatibility, and maximize entropy by distributing eight three-fold defects evenly on the sphere.”

“The paper identifies the tangent map with the dual HKR map and proves liftability along square-zero extensions to be a derived invariant.”

“The paper aims to achieve square-root cancellation in short sums of trace functions under specific conditions.”

“Responses to different perturbation types are dynamically incompatible when they occur in separate experiments... On the other hand, if both perturbation types are presented at random during the same experiment then the responses are compatible with each other and can be construed as produced by a unique underlying mechanism.”

“The paper determines the exact value of $\mathrm{ex}_r(n, ext{Berge-} kP_{\ell})$ when $n$ is large enough for $k\geq 2$, $r\ge 3$, $\ell'\geq r$ and $2\ell'\geq r+7$, where $\ell'=\left\lfloorrac{\ell+1}{2} ight floor$.”

“The generalized model preserves thermodynamic consistency by ensuring zero net energy transfer at equilibrium.”

“The emergence of a well-defined inertial response depends sensitively on cone geometry. Blunt cones exhibit quadratic scaling with impact speed over the full range of velocities studied, whereas sharper cones display a delayed transition to inertial behavior at higher speeds.”

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“Quantum errors can be modeled as deterministic physical terms rather than purely stochastic perturbations.”

“Without access to the full text, a detailed assessment is impossible.”

“The research likely focuses on the design and control of a system of 'chasers' to effectively trap a target.”

“The article's context is that it's published on ArXiv, indicating a pre-print of a scientific paper.”

“The paper develops a comprehensive semi-empirical model for the maximum droplet volume ($Ω$) and validates it against experimental measurements and reference simulations.”

“The article's core focus is on EFX allocations within triangle-free multi-graphs.”

“Nonvolatile photoswitching of a Mott state via reversible stacking rearrangement.”

“XTrace is a non-invasive dynamic tracing framework for Android applications in production.”

“The study focuses on the Fokas-Lenells equation and its solutions.”

“The analysis centers on 'first-passage times,' a core concept in the study of random walks.”

“The article's subject matter involves branching Markov additive processes.”

“The paper originates from ArXiv, indicating it is a pre-print or research publication.”

“The research focuses on the photoexcitation of moiré-trapped interlayer excitons.”

“The article focuses on critical points of degenerate metrics on algebraic varieties.”

“The article's subject is High-quality and field resilient microwave resonators on Ge/SiGe quantum well heterostructures.”

“The study focuses on the unifying spectral problem of nonnegative tensors.”

“The article is sourced from ArXiv.”

“PHOTON is a hierarchical autoregressive model.”

“The study explores fare zone assignment on tree structures.”

“On the large time behavior of the 2D inhomogeneous incompressible viscous flows.”

“Fast and Exact Least Absolute Deviations Line Fitting via Piecewise Affine Lower-Bounding”

“The paper focuses on quantifying uncertainty from the pre-training corpus for Dynamic Retrieval-Augmented Generation.”

“The research focuses on the kinetics of Bose-Einstein condensation of magnons.”

“The article is sourced from ArXiv, suggesting it's a pre-print of a research paper.”

“The research focuses on the semi-classical limit of the Dirac equation.”

“The research focuses on the scattering problem within Bose-Einstein condensates.”