“The American Mathematical Society president said it was 'rigorous, correct, and elegant.'”

“N/A - Lacking a specific quote from the content (Tweet and Paper).”

“Unfortunately I cannot directly pull the quote from the linked content due to access limitations.”

“The paper identifies physical theories as least fixed points of admissibility constraints derived from Galois connections.”

“The paper proves an orbifold type decomposition theorem and shows that the total Hochschild homology is isomorphic to a symmetric algebra.”

“If a finitely generated VI^m-module is generated in degree ≤ d and related in degree ≤ r, then its regularity is bounded above by a function of m, d, and r.”

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

“The best model solves 8.25% of tasks at pass@1 (32.50%/4.17%/0.00% by Easy/Medium/High) and 12.00% at pass@4 (50.00%/4.76%/0.00%).”

“The paper develops a solid geometric framework for the theory by creating isochrons, which are the level sets of the asymptotic phase, using the Graph Transform theorem.”

“The paper finds a partial extension of Poincaré duality theorem to hypersurfaces obtained by non-primitive Viro's combinatorial patchworking.”

“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 provides a complete characterization of the family of tubal products that yield an Eckart-Young type result.”

“The paper proves a central limit theorem for the Euclidean distance between two independent random vectors uniformly distributed on $l_p^n$-balls.”

“The paper initiates the study of these processes, state some theorems and several intriguing conjectures found by computations of the finite Markov chain.”

“The article's subject is the Yaglom theorem applied to critical branching random walk on Z^d.”

“MATP surpasses prompting-based baselines by over 42 percentage points in reasoning step verification.”

“Propositional logics are usually polynomial-time reducible to their fragments with at most two variables (often to the one-variable or even variable-free fragments).”

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“The minimal throat area of a traversable wormhole sets the upper bound on information transfer.”

“The article's focus is on the application of a mathematical theorem (Atiyah-Singer index theorem) to a specific area of physics (non-SUSY physics).”

“The article is likely a scientific paper, so direct quotes are not applicable in this context. The core concept revolves around quantum mechanics and particle physics.”

“KANO provides a transparent and structured representation of the latent degradation fitting process.”

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

“The paper constructs a covariant formulation for self-dual Yang-Mills and self-dual gravity, and subsequently extends this construction to the full Chiral Higher Spin Gravity.”

“The Hinge Theorem establishes that controlling the Likelihood-Ratio Distortion metric is necessary and sufficient for preserving inference.”

“The embedding of classical first-order logic into SOL is precisely what makes the symbolic method possible.”

“The article is found on ArXiv.”

“The paper generalizes the linear-sized spectral sparsification theorem and provides bounds on the sparsification function for various convex cones.”

“The paper introduces a Biorthogonal Graph Fourier Transform (BGFT) adapted to directed diffusion.”

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“"There is no clear primary source (original text) or official namer confirmed for the term 'Double Pythagorean Theorem.'"”

“The article's subject focuses on a new rigidity theorem of Einstein manifolds and the curvature operator of the second kind.”

“The research focuses on Gaussian Optimal Transport.”

“When stability holds, the ordinary least-squares estimator satisfies a central limit theorem, and classical Wald-type confidence intervals -- designed for i.i.d. data -- become asymptotically valid even under adaptation, \emph{without} incurring the $\\sqrt{d \\log T}$ price of adaptivity.”

“A new converse theorem for Borcherds products.”

“The article is sourced from ArXiv, indicating a pre-print research paper.”

“The article likely provides a clear and concise explanation of Herbrand's Theorem and its proof.”

“The article is likely to contain mathematical formulas, theorems, and proofs related to the specified topics.”

“The research focuses on Hölder-Lipschitz functions on fundamental domains of lattices in $\mathbb{R}^{d}$.”

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“The paper focuses on regret analysis of optimism bandit algorithms.”

“MSC-180 is a benchmark for automated formal theorem proving from Mathematical Subject Classification.”

“The article's content is not available, so a specific quote cannot be provided. However, the title itself provides a concise summary of the research's focus.”

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