Subject
Proofs, structures, equations, geometry, topology, and applied mathematics.
An arXiv preprint proves coefficient-by-coefficient blowup identities for local Hirzebruch geometries, then extends the framework conditionally to local P2.
Scientific publication3 min read
A mathematical preprint reports exactly 28 quasi-Galois points on the Fermat quartic, including four Galois points and 24 points that are not Galois. It also gives an algebraic test and a K3-surface correspondence for studying such points on smooth quartic surfaces.
Scientific publication3 min read
A mathematical preprint derives conditional lower bounds for quantum ground-state decay, while finding that a direct full-model approach cannot stay uniform as time grows.
Scientific publication4 min read
A mathematical preprint proves that a disjoint-clique construction gives the exact maximum number of large cliques in broad families of graphs that avoid a fixed tree. The result moves the reported general threshold to logarithmic order but leaves small clique sizes, especially triangles, open.
Scientific publication5 min read
An arXiv preprint derives exact local Fourier-Jacobi formulas for Sp4 and proposes a global norm identity whose consequences depend on the refined GGP conjecture and, for bounds, GRH.
Scientific publication4 min read
A mathematical preprint proposes a Fourier-based proof for real-frequency mode stability in subextremal Kerr, using dual solutions and a boundary calculation to show that the specified quasinormal modes are the zero solution.
Scientific publication4 min read
A mathematical preprint reports that every actual reduced polar hyperplane of a plane-curve topological zeta function lies in the multivariable Bernstein-Sato zero locus. It also finds matching non-equivariant motivic and topological pole data in that setting, while higher-dimensional examples show the pattern has limits.
Scientific publication3 min read
A formal study reports exact agreement among three canonical-basis partitions, then connects Richardson subsets to Demazure modules and weights to Bruhat interval polytopes.
Scientific publication3 min read
The work gives an infinite-matrix system a geometric reading and extends it into a two-component KP framework, with formal links to AKNS and ASDYM.
Scientific publication3 min read
A theoretical mathematics preprint proves that Ramond boundary points occur in even numbers and develops finite measures and recursive volume functions for spin moduli spaces.
Scientific publication4 min read
A mathematical preprint constructs special small initial data for a quasilinear Schrödinger equation whose high-regularity Sobolev norm later becomes arbitrarily large. The result is an existence proof for selected data, not a claim about typical solutions.
Scientific publication4 min read
A mathematical preprint adapts a refined Schreyer workflow to exterior-algebra resolutions, states that its lifting procedures terminate and that the resulting algorithm returns the required syzygy basis, and illustrates a BGG cohomology route. A proposed parallel formulation remains untested for speed and scale.
Scientific publication3 min read
A new arXiv preprint reports that the rescaled D4 root lattice uniquely minimizes the theta and Epstein zeta functions across the full class of normalized four-dimensional lattices, with equality only for orthogonal copies of D4.
Scientific publication3 min read
A theoretical preprint maps the spectral conditions behind β0(H), identifies the largest class that survives every compact perturbation, and proves that β(H) is dense in the full bounded-operator algebra.
Scientific publication4 min read
A theoretical study of neutral renormalization finds that, in its defined family of cascades and towers, combinatorial data can determine geometric structure.
Scientific publication4 min read
A mathematical analysis finds that prey can spread at one model threshold, while predator expansion varies by direction and is limited by the smaller of two modeled speeds.
Scientific publication4 min read
A theoretical preprint establishes a sharp universal lower bound for the magnetic-field norm when a non-trivial Dirac zero mode exists on a sphere, while leaving a related Sobolev constant unresolved.
Scientific publication3 min read
A theoretical preprint gives exact descriptions of several spectra linked to planar fractal measures, while identifying special systems where the usual multifractal relationship fails.
Scientific publication4 min read
A computational preprint reports 84 improved upper- and lower-bound cases for q-ary covering codes across 83 parameter cells, with exact checks on codes and certificates but several unresolved gaps.
Scientific publication4 min read
An arXiv preprint identifies the order conditions behind derived window convolutions, shows how branching can disrupt their composition, and finds rooted forests where the construction supports an interleaving distance.
Scientific publication4 min read
The paper builds an exact-category model for derived tensor kernels and shows, through constructed examples, why higher-term cases can escape ordinary-ring descriptions.
Scientific publication4 min read
A mathematical preprint reports that the cone's frequency separates two regimes: global solutions are ruled out at or above it and form an ordered family below it.
Scientific publication3 min read
A theoretical number theory study finds that integers meeting several inequalities built from Euler's totient, Dedekind's and sum-of-divisors functions form a vanishing share of all integers.
Scientific publication4 min read
A theoretical study builds regular graph families that satisfy expansion conditions yet have no cycle covering more than a small fraction of all vertices. The constructions do not settle the same question for robust expanders.
Scientific publication4 min read
A mathematics preprint maps a repetition-based exponent for infinite words, finding every value from 1 to infinity over three symbols and a probability-one value of 1 under Bernoulli measure.
Scientific publication3 min read
The paper builds arithmetic de Rham and Hyodo-Kato stacks, then proves categorical links to rigid cohomology, isocrystals, D-modules and related arithmetic operations under stated assumptions.
Scientific publication4 min read
The paper classifies a diagonal operator, separates two geometric tests, and extends its stochastic-convolution analysis to the Laplacian.
Scientific publication4 min read
A proof-based analysis of stratified Lie groups finds uniform control for the full horizontal Riesz transform through p = 2, but no universal high-p bound.
Scientific publication4 min read
A new counting construction improves the rigorous lower bound for the growth rate of permutations avoiding the pattern 1324, while leaving the exact growth rate unknown.
Scientific publication3 min read
A theorem-proving paper reports an affirmative answer to Tarski's general finite-coefficient sum problem and classifies the commutative semigroups that can be represented through ordered sums of linear orders.
Scientific publication4 min read
Every qualifying pair of tournaments has an intersection discrepancy on the n to the three-halves scale, with related density-dependent bounds for oriented graphs and fixed families.
Scientific publication4 min read
A mathematical analysis controls a non-closing operator flow and bounds the error in approximate diagonalization for generalized spin-boson systems.
Scientific publication4 min read
A mathematical framework reduces symmetric time-dependent Hamiltonian systems while preserving their principal-bundle structure, with results illustrated by two mechanical examples.
Scientific publication3 min read
A mathematical preprint sets a vertex limit for minimal forbidden graphs, identifies the complete forbidden set at a threshold of 3, and narrows the shapes allowed by forests and short cycles.
Scientific publication4 min read
A finite-field proof establishes the product-size bound in a large dimension-gap regime and shows that equality requires one shared line across every family.
Scientific publication4 min read
A theoretical preprint uses a metric on prelattices to complete higher-rank spaces with lower-rank strata, then compares its boundary-vanishing cusp forms with two existing formulations.
Scientific publication4 min read
A mathematical methods preprint describes how to classify indecomposable objects in equal-rank rank-two Lusztig-Vogan categories, recover their W-graphs and test a computational procedure on reported examples.
Scientific publication3 min read
A mathematical construction gives three-dimensional normal Q-Gorenstein varieties with minimal log discrepancy one and Cartier index equal to any chosen positive integer, challenging Shokurov's index conjecture in the non-klt setting.
Scientific publication4 min read
A theorem for a planar Neumann reaction-diffusion model finds that sufficiently large diffusion recovers the scalar pattern of decay, threshold behavior and blow-up across bounded H1 data, while the worst-case stabilization cost grows on an exponential scale set by the square of the H1 radius.
Scientific publication4 min read
A mathematical preprint connects the diagonal F-threshold of a graph's binomial edge ideal to features such as matchings, independent sets and clique matchings.
Scientific publication4 min read