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

“Our approach relies on a unified formulation of the distance from a point to a hyperplane on the considered spaces.”

“今回、私は最新論文「Geometry of Reason: Spectral Signatures of Valid Mathematical Reasoning」に出会い、Spectral Attention解析という新しい手法を試してみました。”

“Geometry of Reason: Spectral Signatures of Valid Mathematical Reasoning”

“GaMO expands the field of view from existing camera poses, which inherently preserves geometric consistency while providing broader scene coverage.”

“Both uniform attention and trainable attention architectures implement the same algorithm via topologically and geometrically equivalent representations.”

“The paper classifies the irreducible components of V(d,n), gives criteria for the ideal I(d,n) to be prime or a complete intersection, and for the variety V(d,n) to be normal. It also gives near-equivalent conditions for V(d,n) to be factorial.”

“The paper formulates the covariant hydrodynamics equations as an intersection problem on an infinite dimensional symplectic manifold associated with spacetime.”

“The PDE-ODI principle converts a broad class of parabolic differential equations into systems of ordinary differential inequalities.”

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

“The paper shows that almost proper varieties, as well as p-adic (weakly admissible) period domains in the sense of Rappoport-Zink belong to this class.”

“The discrete period matrix admits the same canonical decomposition $Π= rac{1}{2} H + i T$ as in the smooth setting, where $H$ encodes the topological type and $T$ is purely imaginary.”

“The paper revisits the process of eigenvalue approximation from the perspective of computational spectral geometry.”

“The paper determines the splitting field and a set of 68 linearly independent generators for the Mordell--Weil lattice of the elliptic surface.”

“The paper shows that non-planar diagrams, specifically MHV diagrams, can be represented by pseudo-positive geometries in the Grassmannian G(2,n).”

“The paper derives fundamental estimation limits for a wide-band near-field sensing systems employing orthogonal frequency-division multiplexing signaling over a coherent processing interval.”

“Near the lasing threshold, we achieve a 475-fold enhancement in optical contrast and a 180-fold improvement in magnetic sensitivity compared with a conventional single-pass geometry.”

“The paper establishes a correspondence between solutions of the Liouville equation and the Weierstrass representations of spacelike and timelike minimal surfaces.”

“The holographic duals are ''bubbling wormhole'' geometries: multi-covers of AdS$_5$ $ imes S^5$ whose conformal boundary consists of multiple four-spheres intersecting on a common circle.”

“Each such variety is irreducible and admits a rational parametrization. The assignment is functorial: algebra quotients correspond to monomial maps among the varieties.”

“The study employs cross-spectral analysis techniques to characterize the coherent dynamics of the flow, providing insight into the influence of geometry on unsteady swirl dynamics.”

“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 computes operator entanglement in closed form and shows that, for Haar-uniform product inputs, their entangling power is fully determined by the latter.”

“The introduction of the 'Darboux family' as a tool for studying r-matrices in four-dimensional indecomposable coboundary Lie bialgebras.”

“The paper shows that changing the gluing edge isomorphisms does not affect the quasi-isometry type of these groups.”

“The paper parametrizes composition algebras, Freudenthal algebras, and involutions of the second kind.”

“For any objective with log-sum-exp structure over distances or energies, the gradient with respect to each distance is exactly the negative posterior responsibility of the corresponding component: $\partial L / \partial d_j = -r_j$.”

“An acyclic mcp graph is amenable if and only if a.e. component has at most two nonvanishing ends, while it is nowhere amenable exactly when a.e. component has a nonempty perfect (closed) set of nonvanishing ends.”

“The paper explains that the situation where the T-dual of a toric Kähler geometry is a generalized Kähler geometry involving semi-chiral fields is generic for polycylinders, tori and related geometries.”

“The paper shows a relation to Hurwitz numbers which count ramified coverings of certain type.”

“On $\mathscr{M}$-arrangements of conics and lines with ordinary singularities.”

“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).”

“The paper provides direct experimental evidence of a pseudo-electric field that results in an unusual dynamic strain-induced Hall response.”

“The method achieves improved performance over state-of-the-art reconstruction methods, without task-specific supervised training or fine-tuning.”

“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 discovered accelerator, featuring second differences and cross-product terms, achieved over 75 percent success rate in improving convergence compared to raw sequences.”

“The paper discusses two approaches for extracting the QGT: quasi-QGT and pseudospin tomography.”

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

“DeepSeek-V3 has the best performance in all three categories... All three LLMs exhibited notably weak performance in Geometry.”

“The paper presents the main ideas and techniques involved in the linear versions of several conjectures, including the Shafarevich conjecture and Kollár's conjecture.”

“The paper introduces two complementary high-order strategies for triangular elements: a reduced quadrilateralization approach and a triangle based spectral element method based on Dubiner polynomials.”

“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 identifies an additional contribution originating from a relative rotation in the polarization vectors, formulating this effect as a gravitational holonomy associated to the internal Lorentz group.”

“The resulting equations take the form of Regge-Wheeler equations modified by expectation values of the quantum black hole geometry, providing a clear characterization of quantum corrections to the classical description of the black hole interior.”

“TRL achieves excellent calibration, matching or exceeding the reliability of Deep Ensembles (in terms of ECE) while requiring only a fraction (1/5) of the training cost.”

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

“Backpropagation arises as the differential of a KL projection map on a delta-lifted factorization.”

“Rectangular samples with $L_x eq L_y$ host a finite spin polarization, which vanishes in the symmetric limit $L_x=L_y$ and in the thermodynamic limit.”

“The paper builds examples of real space sextics with 64 and 120 totally real tritangents.”