“Source: ChatGPT”

“Tolan built a voice-first AI companion with GPT-5.1, combining low-latency responses, real-time context reconstruction, and memory-driven personalities for natural conversations.”

“N/A”

“The author states, "In conclusion, write it in CLAUDE.md. 100%. Seriously. After trying various methods, the most reliable approach is to write directly in CLAUDE.md." They also mention the team's initial excitement and subsequent failure to activate a TDD workflow skill.”

“The paper derives the graphicality of infinite sequences for double power-laws, uncovering a rich phase-diagram and pointing out the existence of five qualitatively distinct ways graphicality can be violated.”

“The paper develops a monotone iterative technique of lower and upper solutions to investigate the existence, uniqueness and approximability of the solution for the original classical Melan equation.”

“The paper constructs cw-expansive homeomorphisms on compact surfaces of genus greater than or equal to zero with a fixed point whose local stable set is connected but not locally connected.”

“The article focuses on the mathematical analysis of a chemotaxis-Navier-Stokes system.”

“The paper demonstrates a continuum of collisions between hydrodynamic modes at complex wavevector for dispersion relations with a branch point at the origin.”

“The paper discovers three new families of periodic orbits and proves the existence of stable periodic orbits for restitution coefficients larger than previously known.”

“The paper proves a new BD entropy inequality for a class of non-isentropic compressible fluids and shows the "viscous shallow water system with transport entropy" will admit global classical solutions for arbitrary large initial data to the spherically symmetric initial-boundary value problem in both two and three dimensions.”

“The paper describes the structure of the twisted Jacquet module π_{N,ψ} of π with respect to N and a non-degenerate character ψ of N.”

“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.”

“We prove the nonexistence of $(120, 35, 10)$-difference sets, which has been an open problem for 70 years since Bruck introduced the notion of nonabelian difference sets.”

“The paper proves that any ancient, asymptotically cylindrical flow is non-collapsed, convex, rotationally symmetric, and belongs to one of three canonical families: ancient ovals, the bowl soliton, or the flying wing translating solitons.”

“The paper establishes the existence of weak steady solutions and provides a necessary and sufficient condition for nontrivial translational or rotational motion.”

“The paper derives necessary and sufficient conditions for the existence of such residual generators and provides explicit design formulas.”

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

“The paper discovers novel sporadic dualities, some of which involve condensation of anyons with non-abelian statistics, i.e. gauging non-invertible one-form global symmetries.”

“The paper provides an example where the deterministic subcategory is the category of Stone spaces and the kernels correspond to a restricted class of Kleisli arrows for the Radon monad.”

“The observation of a stacked quantum Hall effect (QHE) and a nonlinear Hall effect (NLHE) provides supporting evidence for the anticipated valley contrasted Berry curvature, a typical signature of a spin valley locked state.”

“The paper proves the existence of an optimal closed-loop policy for the original MFTG when the state spaces are at most countable and the action spaces are general Polish spaces.”

“The paper introduces a practical notion of quasi-ergodicity: ensembles prepared in a small angular patch at fixed purity rapidly spread to cover all directions, while the purity gradually decreases toward its minimal value.”

“The paper proves that the unreduced singular instanton homology has 2-torsion for any null-homologous fibered knot (except for a specific case) and provides a formula for calculating it.”

“If a reflexive sheaf $\mathcal{E}$ on a log terminal Kähler-Einstein variety $(X,ω)$ is slope stable with respect to a singular Kähler-Einstein metric $ω$, then $\mathcal{E}$ admits an $ω$-admissible Hermitian-Yang-Mills metric.”

“The paper concludes the existence of a biregular morphism between the corresponding de Rham complex structures.”

“The article quotes: "The user's obsession with GPT is ominous. It wasn't because there was a desire in the first place. It was because only desire was left."”

“The paper highlights the creation of coexisting helical Fermi arcs with opposite chirality on the same surface, a phenomenon not found in conventional magnetic Weyl semimetals.”

“The paper establishes asymptotically tight lower and upper bounds on the over-thresholds and shows that for infinitely many instances of m the two bounds coincide.”

“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 resulting augmented excess free-energy functional quantitatively reproduces equilibrium density profiles, coexistence curves, and surface tensions across a broad temperature range, and accurately predicts contact angles and droplet shapes far beyond the training regime.”

“At the 68% confidence level, the maximum dark matter mass is estimated to be 0.150 solar masses, with an uncertainty.”

“The paper finds that as the modification parameter increases, neutron stars grow in both radius and mass, and a 'frozen state' emerges, forming a critical horizon.”

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“The paper focuses on searches for new physics particles that could be accessible by the BESIII if their masses lie in the few-GeV range.”

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“The paper establishes a correspondence between kernels in graph theory and specialized equilibria.”

“Ce$^{3+}$ substitution at Sm$^{3+}$ sites transform the weak ferromagnetic (FM) $Γ_4$ state into robust AFM $Γ_1$ configuration through a gradual crossover.”

“The resulting evolution exhibits new features absent in the fully wetted case, including the coexistence of moving and pinned facets or the emergence and long-lived metastable states.”

“The main goal is to prove the (subsequence) convergence of the proposed numerical method to a large-data global weak solution in two dimensions, without relying on cut-offs or additional regularization.”

“If there isn’t something else out there and it’s really just LLM‘s then I’m not sure how the world can improve much with a confidently incorrect faster way to Google that tells you not to worry”

“The paper completely resolves the existence problem of $\mathrm{TOC}_{q}(n,d,w)$s for the cases $d=2$ and $d=2w$.”

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“Antigravity is a tool created by Google that helps with programming using AI.”

“High-ionization lines (e.g., Civ λ1549) exhibit strong blueshifts and asymmetric profiles indicative of fast, inner winds, while low-ionization lines (e.g., Hβ, Mgii λ 2800) show more symmetric profiles consistent with predominant emission from slower, denser regions farther out.”

“Google is finally letting users change their Gmail address without losing data”

“The density of the chemical substance stays bounded for all time if its initial datum is bounded. This implies a significant distinction from the classical Keller--Segel system: diffusion driven by the chemical potential gradient can prevent the formation of concentration singularities.”

“The paper provides valuable insights into the strategic dynamics of policy competition.”

“The paper provides "necessary and sufficient conditions for $\mathcal{A}$ to admit the structure of a model category whose cofibrant objects are $\mathcal{C}$ and whose fibrant objects are $\mathcal{F}$."”

“The study likely employs tools from functional analysis to establish existence, uniqueness, and regularity results for solutions.”