“AI is not a "code writing entity" but a "design assistance layer".”

“The trilinear equivalence only requires an averaging over grids, which converts a difficult exponential sum into an oscillatory integral with periodic amplitude.”

“The core challenge lies in the multiscale nature of LyC escape: ionizing photons are generated on scales of 1--100 pc in super star clusters but must traverse the circumgalactic medium which can extend beyond 100 kpc.”

“The paper provides a necessary and sufficient condition for the incenter of a given n-simplex with k-rational vertices to be k-rational.”

“The paper identifies the obstruction to the existence of the Prequantum Groupoid as the non-additivity of the integration of the prequantum form on the space of loops.”

“BF-APNN substantially reduces training time compared to RT-APNN while preserving high solution accuracy.”

“All models are exactly-solvable, admit algebraic forms for the Hamiltonian and integrals, have polynomial eigenfunctions, hidden algebraic structure, and possess a polynomial algebra of integrals.”

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“The paper checks equivalence with instanton partition function of a 5d circular quiver gauge theory...and with partition function of a defect in the same theory, also known as the Shiraishi function.”

“Our approach relies on nonlinear analysis, topological methods, and the theory of strongly continuous semigroups, yielding results applicable to a wide range of models.”

“The consistent orderings are in one-to-one correspondence with the Jacobians associated with all field redefinitions of a set of canonical degrees of freedom. For each admissible operator ordering--or equivalently, each path-integral measure--we identify a definite, positive Hilbert-space inner product. All such prescriptions define the same quantum theory, in the sense that they lead to identical physical observables.”

“The paper classifies the centrality and commutativity of skew-polynomial algebras depending on the Lie type and the order of the root of unity.”

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“treating structured schemas as non-negotiable governance contracts rather than optional output formats”

“Embedding a simple proportional integral (PI) frequency controller can significantly improves transient behavior.”

“The VIE approach is a valuable methodological scaffold: It addresses SC-HDM and simpler models, but can also be adapted to more advanced ones.”

“EPD-Solver leverages the Mean Value Theorem for vector-valued functions to approximate the integral solution more accurately.”

“The IRL-based approach achieves approximately the same performance as the conventional SDRE method, demonstrating its capability as a reliable alternative for nonlinear system control that does not require an explicit environmental model.”

“Every single line was written by Claude Code + Opus 4.5.”

“The paper likely provides a detailed mathematical treatment of the intersection of cylinders.”

“The research likely explores the properties and behavior of these operators under specific conditions.”

“The paper suggests that the ligand shift can give contribution in the constant of the symmetric Heisenberg interaction in antiferromagnetic or ferrimagnetic materials.”

“The operator reconstructs f accurately in the tested domains.”

“The paper establishes a new Heisenberg-type uncertainty principle for the quadratic-phase Dunkl transform, which extends the classical uncertainty principle for a large class of integral type transforms.”

“2025 was a year where the quality of AI-generated code improved, and I really didn't write code anymore.”

“An application to a system of $(k,ρ)$-fractional Hilfer integral equations via a measure of noncompactness.”

“The article's context is an ArXiv paper.”

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“Financial AI is evolving from an auxiliary tool that "can see and speak" to a digital employee that "can make decisions, execute, and take responsibility."”

“Integral modelling of weakly evaporating 3D liquid film with variable substrate heating”

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“The article's source is ArXiv.”

“The article's source is ArXiv.”

“The article's context indicates it explores inverse problems under integral conditions for the generalized Korteweg-de Vries equation.”

“AI is no longer an “innovation lab” side project but embedded in briefs, production pipelines, approvals, and media optimisation.”

“Stäckel problem for non-diagonal Killing tensors.”

“The paper focuses on the absorption time of the Beta-coalescent.”

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“The paper investigates the cohomology of compactified Jacobians for locally planar integral curves.”

“An inequality discovered and proved in collaboration with AI.”

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“In our discussion with Prashanth, we explore the impact the pandemic has had on Stack Overflow...”

“Cited 139,000 times, he has been integral to some of the biggest breakthroughs in AI over the past 3 decades.”