arXiv subjects

Qihang Wang

Publications and source records attributed to Qihang Wang.

At least 19 recordsLinked to original sources

arXiv2026

Strong Borel-Cantelli laws and clusters of visits for random intermittent maps

Near the neutral fixed point of an intermittent map, a single entrance into a small target can be followed by a long run of consecutive visits, so the number of visits need not follow its mean. We study targets $[0,u_n]$ for iid random compositions of Liverani-Saussol-Vaienti maps with a bounded parameter law that is regularly varying at its minimum $α\in(0,1)$; this includes a single map. For $u_n=cn^{-g}L(n)$, where $c>0$, $0<g\leq1$ and $L$ is slowly varying, the visit count is almost surely asymptotic to its mean if and only if $\sum_n n^{-1}(nu_n)^{-(1-α)/α}<\infty$. Under the stationary law, the count divided by its mean converges to one in $L^1$ exactly when $nu_n\to\infty$. Thus clusters of visits separate these two modes of convergence.

math.DS↗

arXiv2026

Uniform large-genus asymptotics of Weil-Petersson volumes

Let $V_{g,n}$ be the Weil--Petersson volume of the moduli space of hyperbolic surfaces of genus $g$ with $n$ cusps. The fixed-$n$ large-genus expansion of Mirzakhani and Zograf has correction terms polynomial in $n$ of degree $2i$ at order $g^{-i}$, and ceases to be uniform when $n$ is of order $\sqrt g$. We prove an asymptotic expansion in powers of $1/g$ that holds uniformly in all $n\ge0$, with coefficients analytic in a density parameter that ranges over a compact interval, including the limits $n/g\to0$ and $n/g\to\infty$. Its leading term is explicit, contains no undetermined constant and has relative error $O(1/g)$; truncation at an order proportional to $\sqrt g$ gives relative error $O(\exp(-a\sqrt g))$ for some $a>0$. For fixed $n$ this confirms Zograf's conjecture that the constant in the Mirzakhani--Zograf asymptotics is $1/\sqrtπ$. We also determine, at every cusp density, the limits of the volume ratios $V_{g,n}/V_{g-1,n+2}$ and $V_{g,n+1}/(2gV_{g,n})$ and, in all degrees, the asymptotics of the ratios of adjacent coefficients of the one-boundary volume polynomial; this answers two questions of Mirzakhani. The proof deforms mixed $κ_1$--$ψ$ intersection numbers into pure $ψ$ intersection numbers along a family whose recursion has nonnegative coefficients, fixes the overall constant through Painlevé I without assuming resurgence, and recovers individual volumes by a local limit theorem in the number of cusps. As an application, the spectral gap of a Weil--Petersson random surface with $n\gg\sqrt g$ cusps tends to zero in probability; this removes the restriction $n/g\to0$ from a theorem of Shen and Wu.

math.DG↗

arXiv2026

Beyond Shor's Conjecture: Optimal Quantum Measurements at Fixed Error

We prove Shor's conjecture: an orthogonal measurement maximizes the information obtainable from any two quantum states in finite dimension. We then show that an error constraint can require three outcomes. For a class of full-rank qubit pairs, the best orthogonal basis switches abruptly as the error penalty increases. Near the switch, three outcomes yield more information at the same error than any orthogonal measurement or random mixture of them. The extra outcome distinguishes confidence levels in one guess; every outcome is used.

quant-ph↗

arXiv2026

Four Special Directions over Prime Fields: Structure and Complete Classification

A direction of the affine plane $\mathbb{F}_p^2$ is special for a set if the lines in that direction do not all meet the set in the same number of points. We classify, for every prime $p\ge5$, the subsets of $\mathbb{F}_p^2$ with exactly four special directions. There are $54$ affine-equivalence classes, occurring only for $p=5,7,11,13,17$, and we give explicit representatives. In particular, $17$ is the largest prime admitting such a set, which answers a question of Ghidelli, Kiss and Somlai, and over $\mathbb{F}_{13}$ the minimum size is $65$, attained by exactly two classes. The key structural fact is that the projection polynomials of such a set share a vertex: the set is either centrally symmetric about this point or differs from its reflection by exchanging one full line with one empty line. We also show that, over an odd prime field, a Boolean function on $\mathbb{F}_p^d$ with exactly four active projective Fourier lines is pulled back from a plane, so the classification extends to every dimension. The classification and the exclusion of the primes $19\le p<2048$ are computer-assisted; the structural results and the exclusion of larger primes are proved directly.

math.CO↗

arXiv2026

Cotangent cohomology and higher-order obstructions of matroids

Matroid Stanley-Reisner rings admit essential deformation obstructions of arbitrarily high order over every field, already at corank three. For each $m\ge3$, we construct a connected cosimple matroid and $m$ fine-homogeneous first-order classes whose proper subcollections integrate jointly and whose pairwise primary cup products vanish. A specified joint $(m-1)$-jet nevertheless has no lift to order $m$, even without preserving the grading. The construction rests on formulas for every multigraded component of the second cotangent cohomology $T^2$ and of its primary cup image, expressed through flats and parallel classes of the dual matroid. These formulas show that $T^2$ vanishes exactly when every connected component has corank at most two, or equivalently when there is no $U_{1,4}$-minor. This proves a conjecture of Constantinescu, Klein, Nguyen, Singh, and Venturello (2025) and characterizes formal smoothness of the affine deformation functor. For the duals of rank-three truncations of $U_{2,m}\oplus U_{2,n}$, $m,n\ge3$, each nonzero homogeneous class modulo the primary cup image is realized as a higher-order obstruction, and the quotient has an explicit presentation with $m+n-2$ minimal homogeneous generators.

math.CO↗

arXiv2026

$q$-Zeta positivity for root and Ferrers-cell posets

We prove that Chapoton's $q$-Zeta numerator has nonnegative coefficients for the positive-root poset of every finite reduced irreducible crystallographic root system, graded by root height minus one and normalized by Chapoton's prescribed denominator. The same holds for every interval of the root poset with zero adjoined. The key observation is that adjoining a minimum changes the numerator only by the substitution $t\mapsto qt$. The numerator thereby becomes a nonnegative combination of flag $h$-numbers of a lower-semimodular lattice, and a classical labelling of the dual lattice gives a positive descent expansion. To make the coefficients explicit, we construct signed edge-lexicographic (EL) labellings of Ferrers-cell posets with nonincreasing boundaries. They give ballot-word formulas in types $A$, $B$, and $C$, which prove an observation of Chapoton in type $B$, and a coloured path formula in type $D$. For trapezoidal boundaries, one-boundary major-index enumerators evaluate the path sums in Gaussian-binomial form.

math.CO↗

arXiv2026

Exact Chained-Word Threshold and Monotone-Path Structure in the Even Root-of-Unity Kaleidoscope Yang-Baxter Algebra

Qiu, Guan, and Yu conjectured that in the even-order Kaleidoscope Yang--Baxter equation every word $ΛT^{k_1}Λ\cdots T^{k_M}Λ$, built from a square-zero matrix $Λ$ and integer powers of a shift $T$ of order $N$, vanishes once $M\geq N/2$. We prove this for every even $N\geq4$ and every complex parameter $u$ with $u\neq0$ and $u^N\neq1$, and show that the bound is sharp. For $M=N/2-1$ we determine exactly which words are nonzero; each of them has rank two. After block reduction, the factors associated with the intervening powers of $T$ lower a common flag of length $N/2$ by at least one step. The spectral idempotents of $T$ then give a presentation of the algebra generated by $T$ and $Λ$ by paths between levels, in which two paths compose only when the level changes monotonically. This algebra is independent of $u$, has dimension $N^2-N+2$, and is a pullback of two incidence algebras. Its radical is generated by $Λ$ and has nilpotency index $N/2+1$, and the algebra has infinite global dimension and infinite representation type. Replacing powers of $T$ by arbitrary functions of $T$ gives exact rank formulas and, for $N\geq6$, rank-one elements in the top radical power. Finally, four conditions on a filtered pair of operators over an arbitrary field recover the threshold and the radical; none of them can be omitted.

math-ph↗

arXiv2026

Counterexamples to $R$-superlinear convergence of cyclic steepest descent

The cyclic steepest descent method computes the exact steepest descent stepsize at the start of each cycle and reuses it for a fixed number $m$ of iterations. For strictly convex quadratics in $n$ variables, it has been suggested that the method converges $R$-superlinearly whenever $m\ge(n+1)/2$. We show that this cannot hold for every initial point, already at the threshold cycle length. For $n=m=2$ we exhibit an initial point from which the method follows the classical zigzag trajectory of steepest descent: the stepsize never changes and the error is halved at every iteration. The same mechanism yields linearly convergent trajectories for every Hessian with at least two distinct eigenvalues and every cycle length. For $n=3$ and $m=2$ we construct a second, genuinely three-dimensional counterexample: all components of the gradient remain nonzero, consecutive cycles use two different stepsizes, and every four iterations reduce the gradient exactly by the factor $1/49$. Both trajectories are given in closed form. Consequently, any $R$-superlinear convergence result for this method at the threshold must exclude a set of initial points, as recent almost-everywhere results do.

math.OC↗

arXiv2026

Convergence of cyclic steepest descent for quadratics with two distinct eigenvalues

The cyclic steepest descent method computes the exact steepest descent stepsize at the start of each cycle and reuses it for a fixed number $m\ge2$ of iterations. We study this method for strictly convex quadratics whose Hessian has exactly two distinct eigenvalues, of arbitrary multiplicities, and determine its behavior from every initial point. At the minimizer no update is needed. For nonoptimal initializations, a gradient in one eigenspace gives one-step termination. If both eigenspace components are nonzero and have equal norm, the stepsize never changes and the error contracts by the same constant factor at every iteration. In the remaining case, both components are nonzero and unequal in norm, and the method converges doubly exponentially and hence $R$-superlinearly. Thus $R$-superlinear convergence fails exactly on an explicit cone of initial points of measure zero. The proof reduces the method to an exact scalar recurrence for the ratio of the two eigenspace components at the start of each cycle. We also determine the leading term of the logarithm of the error at every iteration within a cycle, which identifies the exact exponent of the doubly exponential decay and shows that this convergence is not $Q$-superlinear.

math.OC↗

arXiv2026

Integral homology lattices of matching and circulant complexes

Bouc's hook cycles span the rational top homology of the matching complex of $K_{2k+1}$. We prove that their integral saturation quotient has exponent exactly $2^{\lfloor k/2\rfloor}$ for every $k\geq1$, and construct divided-power cycles attaining this bound. For $k\geq2$, the homology lattice is not isomorphic to the standard integral hook lattice as an $\mathfrak S_{2k+1}$-module. For circulant complexes, we determine the integral dihedral homology modules of $\operatorname{Ind}(C_{3s}^{s-1})$, $\operatorname{Ind}(C_{3s+1}^{s-1})$ and $\operatorname{Ind}(C_{3s+2}^{s-1})$, for $s\geq3$, $s\geq2$ and $s\geq3$, respectively, and classify the least scalar lifts of all primitive equivariant quotients to the rank-one module with trivial rotation and negative reflection. Tate localization relates prime-order gluing to fixed-point homology under a free, single-degree homology hypothesis. Explicit cycle subgroups separate saturation defects from obstructions to equivariant sections. For circulant independence complexes with jumps two and three, we prove an eight-periodic ordinary homotopy classification and a fixed-space obstruction to uniform representation suspensions. For every fixed nonempty bounded positive jump set, a finite-state construction gives a rational critical-face series.

math.CO↗

arXiv2026

When Complementary Measurements Count the Same Classical Bit Twice: Counterexamples to CQC, ECQC, and Complementarity-Based Certification

Mutually unbiased measurements are commonly expected to expose independent facets of a quantum state: a correlation that is classical in one basis should disappear in a complementary basis. In higher dimensions, however, this intuition becomes particularly subtle because correlations recovered in different settings need not represent different information. To expose this loophole, we propose a two-branch classical null test: before the setting is chosen, a shared bit selects one of two orthogonal product preparations, producing a rank-two classical--classical state, and the candidate protocol then runs unchanged. Different settings can read the same bit through different outcome patterns. This two-branch classical architecture disproves the complementary-quantum correlation (CQC) conjecture in every dimension $d\geq3$. A distinct rank-two classical--classical state disproves its complete-basis extension (ECQC) at $d=7$, with an overrun that grows without bound along prime dimensions. Its qutrit CQC instance also gives classical false positives for a proposed quantum-correlation measure and a proposed one-sided semi-device-independent steering criterion, and refutes a conditional-probability conjecture. The failures identify the missing requirement: information read in different settings must be nonredundant. In experiments and applications, the same low-overhead architecture can serve as a calibration test before a multibasis score is assigned quantum meaning.

quant-ph↗

arXiv2026

Single-Token Expected-Value Scoring for Cold-Start Candidate Ranking

AI-assisted sourcing streamlines candidate review, reducing the administrative burden of manual screening for recruiters. However, deploying language models as production rankers remains challenging. Zero-shot Large Language Models (LLMs) may produce unstable, non-deterministic scores and rank less accurately, while conventional deep neural rankers require millions of logged interactions that a low-traffic, niche sourcing platform does not produce. What is available instead is a few hundred thousand ordinal relevance labels -- small by ranker-training standards, but sufficient when a pretrained language model already encodes the general world knowledge the task depends on. We present single-token expected-value scoring, a ranking primitive that casts candidate-job relevance as an ordinal classification over the grade tokens {1, ..., 5} and reads the relevance score as the expectation of the first-token probability distribution. Because the score comes from a single decoding step rather than open-ended generation, it is a deterministic function of the model's logits, requires no output parsing, and serves at low latency. To learn the non-linear interdependencies of heterogeneous hiring criteria from this supervision alone, we fine-tune a Small Language Model (SLM) with a hybrid ordinal regression loss combining a Mean Squared Error term, which preserves ordinal distance, with a categorical Cross-Entropy term, which sharpens class boundaries. We evaluate along two dimensions -- Jobseeker Relevance and Employer Relevance -- using NDCG@10 and low relevance rate. Offline, our fine-tuned model outperforms a heuristic baseline and zero-shot LLMs. An end-to-end simulation shows the same direction at larger magnitude (+54.2% Jobseeker NDCG@10, -46.7% low relevance rate), and a live online experiment reduces employer low-relevance by 27.3% and raises employer keep rate by 7.07%.

cs.IR↗

arXiv2026

Fröberg's Conjecture for Quintics and Septics in Four Variables

Let $k$ be a field of characteristic zero and let $S=k[x_1,x_2,x_3,x_4]$. We prove Fröberg's predicted Hilbert series for ideals generated by $r$ general forms of equal degree $d$ for every $r\geq1$ in each of the two cases $d=5$ and $d=7$. Relative to the classical cases $r\leq5$ and the equal-degree theorem through degree $d+2$ of Boij--Dannetun--Lundqvist, the generator-count ranges requiring new input are $6\leq r\leq11$ for quintics and $6\leq r\leq21$ for septics. The proof reduces each slice to finitely many endpoint ranks of Macaulay multiplication matrices. For quintics, ten exact endpoint computations based on twenty-one sparse forms suffice. For septics, a nested family of 120 integral forms supplies fifteen endpoint computations. In every endpoint certificate for these new ranges, an explicitly recorded maximal minor is nonzero modulo $2$, hence is a nonzero integer. The case $r=5$ is the classical strong Lefschetz instance; for quintics we also record a matching modular rank and Koszul bound. Zariski openness then gives the result over every characteristic-zero field. The unrestricted Fröberg conjecture remains outside the scope of the paper. The main results of this paper were obtained through a generative-AI workflow using OpenAI GPT-5.6 Sol, Anthropic Claude Fable 5, and Grok 4.6. Further details appear in the disclosure at the end of the paper.

math.AC↗

arXiv2026

Residual bounds for Schur-stable polynomials

Let $r_n$ be the infimum of \[ \frac{\lVert P'-P'(0)P\rVert_{H^2}}{\lVert P\rVert_{H^2}} \] over all degree-$n$ polynomials $P$ satisfying $P(0)=1$ whose zeros lie in the closed unit disk. We prove the quantitative residual bound \[ r_n\geq \exp\!\bigl(-(1+o(1))\sqrt n\log n\bigr) \qquad(n\to\infty). \] As an application, we answer Erdős Problem 973 on exterior power sums in the negative, in a form quantitatively stronger than the answer first obtained by Luo, Yang, and Zhu.

math.CV↗

arXiv2026

Complementary Quantum Correlations Are Universal for Qubits

Extracting total correlations from a quantum system usually requires reconstructing its state, whereas many experiments access only a few measurement settings. A possible shortcut is to add the mutual informations obtained from complementary measurements; in dimensions above two, however, this procedure can count the same classical correlation twice. We establish that qubits are protected from such overcounting. For every two-qubit state, the correlations observed in two complementary local bases are bounded by the premeasurement quantum mutual information. The proof traces this protection to binary-entropy curvature on the Bloch ball and combines a qubit information-exclusion tradeoff with data processing under local dephasing. Consequently, two correlation tables give a tomography-free lower bound on total correlation. A score above one bit also certifies a quantitative one-way entanglement-distillation rate; when applied to the Choi state of a qubit channel, the same data lower bound its quantum capacity. The theorem therefore identifies both an operational use of complementarity and the trusted two-dimensional setting in which its correlation accounting is valid.

quant-ph↗

arXiv2026

Automated SVA Generation with LLMs

Functional verification remains a dominant cost in modern IC development, and SystemVerilog Assertions (SVAs) are critical for simulation-based monitoring and formal property checking. However, writing SVAs by hand is time-consuming and error-prone. Directly prompting general-purpose large language models (LLMs) is also unreliable: the generated properties are often syntactically invalid or semantically incorrect, and the problem is exacerbated by scarce, high-quality domain training data. We present SVA Generator, a data-centric framework that translates natural-language SVA Descriptions (SVADs) into executable SVAs. It uses AST-grounded constraint injection and an automated supervision pipeline that enforces structural consistency and reduces hallucinations via de-duplication and constraint checks. To enable rigorous evaluation, we introduce a benchmark suite stratified by AST depth and use formal property equivalence checking to quantify semantic correctness separately from syntax validity, by checking mutual implication between the generated and reference properties under the same clocking and environment assumptions. Across all difficulty tiers, SVA Generator achieves comparable Syntax Pass Rate (SPR) to strong general LLM baselines, while delivering substantially higher Semantic Equivalence Rate (SER) on deeper tiers: +24.5 pp on D2, +26.0 pp on D3, and +17.5 pp on D4 relative to the best-performing general LLM, corresponding to a +22.7 pp SER improvement on average over D2--D4. These results highlight that high-fidelity data construction and depth-stratified benchmarking are key to reliable, semantics-preserving SVA generation.

cs.AR↗

arXiv2025

Image2Net: Datasets, Benchmark and Hybrid Framework to Convert Analog Circuit Diagrams into Netlists

Large Language Model (LLM) exhibits great potential in designing of analog integrated circuits (IC) because of its excellence in abstraction and generalization for knowledge. However, further development of LLM-based analog ICs heavily relies on textual description of analog ICs, while existing analog ICs are mostly illustrated in image-based circuit diagrams rather than text-based netlists. Converting circuit diagrams to netlists help LLMs to enrich the knowledge of analog IC. Nevertheless, previously proposed conversion frameworks face challenges in further application because of limited support of image styles and circuit elements. Up to now, it still remains a challenging task to effectively convert complex circuit diagrams into netlists. To this end, this paper constructs and opensources a new dataset with rich styles of circuit diagrams as well as balanced distribution of simple and complex analog ICs. And a hybrid framework, named Image2Net, is proposed for practical conversion from circuit diagrams to netlists. The netlist edit distance (NED) is also introduced to precisely assess the difference between the converted netlists and ground truth. Based on our benchmark, Image2Net achieves 80.77% successful rate, which is 34.62%-45.19% higher than previous works. Specifically, the proposed work shows 0.116 averaged NED, which is 62.1%-69.6% lower than state-of-the-arts. Our datasets and benchmark are available at https://github.com/LAD021/ci2n_datasets.

cs.AR↗

arXiv2025

TDEdit: A Unified Diffusion Framework for Text-Drag Guided Image Manipulation

This paper explores image editing under the joint control of text and drag interactions. While recent advances in text-driven and drag-driven editing have achieved remarkable progress, they suffer from complementary limitations: text-driven methods excel in texture manipulation but lack precise spatial control, whereas drag-driven approaches primarily modify shape and structure without fine-grained texture guidance. To address these limitations, we propose a unified diffusion-based framework for joint drag-text image editing, integrating the strengths of both paradigms. Our framework introduces two key innovations: (1) Point-Cloud Deterministic Drag, which enhances latent-space layout control through 3D feature mapping, and (2) Drag-Text Guided Denoising, dynamically balancing the influence of drag and text conditions during denoising. Notably, our model supports flexible editing modes - operating with text-only, drag-only, or combined conditions - while maintaining strong performance in each setting. Extensive quantitative and qualitative experiments demonstrate that our method not only achieves high-fidelity joint editing but also matches or surpasses the performance of specialized text-only or drag-only approaches, establishing a versatile and generalizable solution for controllable image manipulation. Code will be made publicly available to reproduce all results presented in this work.

cs.CV↗