arXiv subjects

Gang Yang

Publications and source records attributed to Gang Yang.

At least 19 recordsLinked to original sources

arXiv2026

Three-Loop Five-Point CK-Dual Amplitudes and UV Structure in N=4 SYM and N=8 SUGRA

We construct the complete full-color three-loop five-point integrand of N=4 super-Yang--Mills theory in a representation that manifestly satisfies color--kinematics duality. Its double copy gives the corresponding N=8 supergravity integrand. For four-dimensional external states, we evaluate the ultraviolet poles of both amplitudes in the critical dimension, Dc=6. Extending the external-state dependence to D dimensions is subtle. We consider a candidate replacement of the four-dimensional prefactors by expressions built from D-dimensional tree amplitudes. It reproduces the open-string prediction for the SYM pole with generic D-dimensional external states, whereas the corresponding gravity expression differs from the string-inspired one by an evanescent term.

hep-th↗

arXiv2026

New upper bound for multicolor Ramsey numbers

Let $R_r(k)$ denote the diagonal $r$-color graph Ramsey number. We prove that there exist absolute constants $c,K>0$ such that \[ R_r(k)\le \exp\!\left(-c\frac{k}{r^2\log^4(2r)}\right)r^{rk} \] for every $r\ge2$ and every $k\ge Kr^2\log^6(2r)$. The proof combines a positive-coefficient root filter of variable order with a retained-spine refinement of the multicolor book method.b

math.CO↗

arXiv2026

Thinking More, Harnessing Better: State Machine Guided Harness Automatic Generation with Project Digestion and Workflow Decomposition

High-quality fuzz harnesses are essential for effective gray-box fuzzing. While Large Language Models (LLMs) offer promise for automating this task, existing one-turn generation methods suffer from hallucinations and inadequate coverage due to coarse-grained function targeting and misaligned generation workflows. We present SynapseFlow, an automatic harness generator that addresses these limitations through two key innovations: dataflow-aware function aggregation and a staged, rollback-enabled generation workflow decomposition. SynapseFlow first analyzes source code to construct Structural Flow Graphs and extract coherent Function Triplets. It then synthesizes harnesses via a decomposed four-stage process governed by a staged rollback algorithm to ensure correctness. We evaluated SynapseFlow on 25 real-world open-source software projects. The experimental results indicate that SynapseFlow outperforms state-of-the-art tools (OSS-Fuzz-Gen, CKGFuzzer, PromeFuzz), achieving 3.07$\times$, 1.71$\times$, and 4.26$\times$ higher branch coverage, and 1.77$\times$, 1.51$\times$, and 1.36$\times$ higher bug detection rates, respectively. Most importantly, SynapseFlow discovered 7 previously unreported bugs (5 assigned CVEs), demonstrating its practical effectiveness in real-world bug discovery.

cs.CR↗

arXiv2026

Solution to a conjecture of Alon, D\k{e}bski, Grytczuk and Przyby\l{}o on fixed-cardinality arithmetic progressions

Fix a positive integer $n$, and put $B_d=\{d,2d,\ldots,nd\}$. Let $M_k(n)$ be the least integer $m$ for which one translate of each of $B_1,\ldots,B_k$ can be placed pairwise disjointly in $[m]$. We prove that, for every $\eps\in(0,1)$ and all sufficiently large $k$, one has $M_k(n)\le n\lceil(1+\eps)k\rceil$. Since the trivial counting bound gives $M_k(n)\ge nk$, it follows that $M_k(n)=(1+o(1))nk$ for every fixed $n$. This confirms a conjecture of Alon, D\k{e}bski, Grytczuk and Przyby\l{}o on prescribed-difference packings of fixed-cardinality arithmetic progressions.

math.CO↗

arXiv2026

Dyeing form factors as amplitudes

The double copy of form factors has revealed a striking feature: poles that are spurious from the gauge-theory perspective become physical propagators in gravity. At the same time, form factors obey hidden factorization relations on the kinematics of these poles. We explain both phenomena by introducing a dyeing procedure, which promotes the color-singlet operator, or the Higgs particle representing it, to an adjoint massive state. The original form factor is recovered by the inverse bleaching operation, realized as a $U(1)$ decoupling of the dyed leg. In the dyed theory, these apparent spurious poles turn into ordinary physical propagators of colored amplitudes, and the hidden factorization relations follow from standard BCJ relations. Applying this framework to multiple operator insertions gives a systematic double-copy construction for multi-Higgs amplitudes and, as a byproduct, reveals scalar-ordering sectors. We also discuss higher-length scalar operators and fermionic operators, including the dyed vector construction for $\bar{\psi}\gamma^{\mu}\psi$, as well as a loop-level example.

hep-th↗

arXiv2026

Double copy of form factors with multiple operator insertions

Extending the double copy of scattering amplitudes to more general physical quantities involving local gauge-invariant operators is a central open question. While progress has been made in the double copy of form factors (FFs) with a single-operator insertion, it has led to two intriguing features: poles that are spurious from the FF viewpoint become physical propagators in gravity, and FFs obey hidden factorization relations on these poles. This picture is difficult to generalize to FFs with multiple operator insertions due to even more complicated spurious pole structures. We resolve this problem by introducing a "dyeing" procedure that promotes color-singlet operators to adjoint colored states, while the original FF is recovered by the inverse "bleaching" (U(1) decoupling) operation. In this new picture, the spurious poles are propagators of the dyed state, and the hidden factorization relations follow from BCJ relations of the dyed amplitudes. For multiple operator insertions, this framework uncovers a new scalar-ordering structure that survives the double copy to gravity.

hep-th↗

arXiv2026

A complete solution to the biased Alon-Krivelevich-Spencer-Szab\'o criterion problem for the discrepancy game

Let $H=(V,\mathcal E)$ be a finite hypergraph. For positive integers $p$ and $q$, the $(p:q)$-biased discrepancy game on $H$ is played in complete rounds. In each round, Balancer first claims $p$ previously unclaimed vertices, and then Unbalancer claims $q$ previously unclaimed vertices. Let $B$ and $U$ be the final sets of vertices claimed by Balancer and Unbalancer, respectively. For an edge $e\in\mathcal E$, define $D_e = q|B\cap e|-p|U\cap e| = (p+q)|B\cap e|-p|e|$. Thus $D_e$ measures the deviation of Balancer's share of $e$ from the density $p/(p+q)$. In 2005, Alon, Krivelevich, Spencer and Szab\'o proved a Chernoff-type potential criterion for the unbiased alternating discrepancy game, corresponding to the case $p=q=1$, and asked for a biased analogue for general $p,q$. In this paper, we prove a complete biased analogue in the complete-round formulation. More precisely, for every finite hypergraph $H=(V,\mathcal E)$ and every fixed bias $(p:q)$, we give an explicit exponential condition under which Balancer has a strategy forcing $-L_e^- \le D_e \le L_e^+$ for every $e\in\mathcal E$, where $L_e^+$ and $L_e^-$ are prescribed edge-dependent target values.

math.CO↗

arXiv2026

FLASH: Fast Learning via GPU-Accelerated Simulation for High-Fidelity Deformable Manipulation in Minutes

Simulation frameworks such as Isaac Sim have enabled scalable robot learning for locomotion and rigid-body manipulation; however, contact-rich simulation remains a major bottleneck for deformable object manipulation. The continuously changing geometry of soft materials, together with large numbers of vertices and contact constraints, makes it difficult to achieve high accuracy, speed, and stability required for large-scale interactive learning. We present FLASH, a GPU-native simulation framework for contact-rich deformable manipulation, built on an accurate NCP-based solver that enforces strict contact and deformation constraints while being explicitly designed for fine-grained GPU parallelism. Rather than porting conventional single-instruction-multiple-data (SIMD) solvers to GPUs, FLASH redesigns the physics engine from the ground up to leverage modern GPU architectures, including optimized collision handling and memory layouts. As a result, FLASH scales to over 3 million degrees of freedom at 30 FPS on a single RTX 5090, while accurately simulating physical interactions. Policies trained solely on FLASH-generated synthetic data in minutes achieve robust zero-shot sim-to-real transfer, which we validate on physical robots performing challenging deformable manipulation tasks such as towel folding and garment folding, without any real-world demonstration, providing a practical alternative to labor-intensive real-world data collection.

cs.RO↗

arXiv2026

Less Approximates More: Harmonizing Performance and Confidence Faithfulness via Hybrid Post-Training for High-Stakes Tasks

Large language models are increasingly deployed in high-stakes tasks, where confident yet incorrect inferences may cause severe real-world harm, bringing the previously overlooked issue of confidence faithfulness back to the forefront. A promising solution is to jointly optimize unsupervised Reinforcement Learning from Internal Feedback (RLIF) with reasoning-trace-guided Reasoning Distillation (RD), which may face three persistent challenges: scarcity of high-quality training corpora, factually unwarranted overconfidence and indiscriminate fusion that amplifies erroneous updates. Inspired by the human confidence accumulation from uncertainty to certainty, we propose Progressive Reasoning Gain (PRG) to measure whether reasoning steps progressively strengthen support for the final answer. Furthermore, we introduce HyTuning, a hybrid post-training framework that adaptively reweights RD and RLIF via a PRG-style metric, using scarce supervised reasoning traces as a stable anchor while exploiting abundant unlabeled queries for scalability. Experiments on several domain-specific and general benchmarks demonstrate that HyTuning improves accuracy while achieving confidence faithfulness under limited supervision, supporting a practical "Less Approximates More" effect.

cs.LG↗

arXiv2026

On the minimum number of monochromatic solutions to the strict Schur inequality in 2-colored integer intervals with negative left endpoint

Kosek, Robertson, Sabo, and Schaal studied the minimum number $M_k(n)$ of monochromatic solutions to the strict Schur inequality system $x_1\le x_2\le x_3$ and $x_1+x_2<x_3$ in $2$-colorings of $[k+1,k+n]$. They proved that for every fixed $k\ge 0$, $M_k(n)= \frac{n^3}{12(1+2\sqrt2)^2}(1+o_k(1)),$ and left open the case $k\le -2$. In this paper, we resolve that remaining range.

math.CO↗

arXiv2026

Complete Resolution of the Butler-Costello-Graham Conjecture on Monochromatic Constellations

A constellation pattern is a finite increasing rational sequence $Q=[0=q_0<q_1<\cdots<q_k=1]$, and a $Q$-constellation in $[n]$ is obtained by scaling and translating a rational pattern $Q$, with key examples including arithmetic progressions. In 2010, Butler, Costello, and Graham proposed a conjecture, that is, for any constellation pattern $Q$ there is a coloring pattern of $[n]$ that has $\gamma n^2+o\left(n^2\right)$ monochromatic constellations, where $\gamma$ is smaller than the coefficient for a random coloring. In this paper, we confirm this conjecture. As applications of this conjecture, we obtain interval-uncommon translation-invariant linear systems associated with rational constellations and a ground-state bound for deterministic arithmetic hypergraph spin systems.

math.CO↗

arXiv2026

Non-Hermitian Structure and Exceptional Points in Yang-Mills Theory from Analytic Continuation of Nc

We show that analytic continuation of the number of colors, Nc, naturally endows Yang-Mills theory with a non-Hermitian structure. By examining the spectrum of the dilatation operator as a function of complex Nc, we identify a network of Exceptional Points (EPs) -- non-Hermitian degeneracies where anomalous dimensions degenerate and operator eigenstates coalesce. We demonstrate that these EPs act as topological defects in complex Nc-space, generating non-Abelian geometric phases and enforcing nontrivial monodromies among gauge-invariant operators. Moreover, we establish a correspondence between the spontaneous breaking of an emergent PT symmetry of the dilatation operator and the fundamental spacetime PT symmetry of the underlying gauge theory. In the vicinity of EPs, the resulting non-Hermitian dynamics produces logarithmic scaling behavior in correlation functions, characteristic of logarithmic conformal field theories. Our results place conventional unitary Yang-Mills theory within a broader complexified parameter space possessing rich topological structure, suggesting a new interface between non-Hermitian physics and quantum field theory.

hep-th↗

arXiv2026

Fast and Reliable Gradients for Deformables Across Frictional Contact Regimes

Differentiable simulation establishes the mathematical foundation for solving challenging inverse problems in computer graphics and robotics, such as physical system identification and inverse dynamics control. However, rigor in frictional contact remains the "elephant in the room." Current frameworks often avoid contact singularities via non-Markovian position approximations or heuristic gradients. This lack of mathematical consistency distorts gradients, causing optimization stagnation or failure in complex frictional contact and large-deformation scenarios. We introduce our unified fully GPU-accelerated differentiable simulator, which establishes a rigorous theoretical paradigm through: Long-Horizon Consistency: enforcing strict Markovian dynamics on a coupled position-velocity manifold to prevent gradient collapse; Unified Contact Stability: employing a mass-aligned preconditioner and soft Fischer--Burmeister operator for smooth frictional optimization; Robust Material Identification: resolving FEM singularities via a derived "Within-block Commutation" condition. Our experiments demonstrate our solver efficacy in bridging the Sim-to-Real gap, delivering precise, low-noise gradients in contact-rich tasks like dexterous manipulation and cloth folding. By mitigating the gradient instability issues common in conventional approaches, our framework significantly enhances the fidelity of physical system identification and control.

cs.GR↗

arXiv2026

Continuous Telemonitoring of Heart Failure using Personalised Speech Dynamics

Remote monitoring of heart failure (HF) via speech signals provides a non-invasive and cost-effective solution for long-term patient management. However, substantial inter-individual heterogeneity in vocal characteristics often limits the accuracy of traditional cross-sectional classification models. To address this, we propose a Longitudinal Intra-Patient Tracking (LIPT) scheme designed to capture the trajectory of relative symptomatic changes within individuals. Central to this framework is a Personalised Sequential Encoder (PSE), which transforms longitudinal speech recordings into context-aware latent representations. By incorporating historical data at each timestamp, the PSE facilitates a holistic assessment of the clinical trajectory rather than modelling discrete visits independently. Experimental results from a cohort of 225 patients demonstrate that the LIPT paradigm significantly outperforms the classic cross-sectional approaches, achieving a recognition accuracy of 99.7% for clinical status transitions. The model's high sensitivity was further corroborated by additional follow-up data, confirming its efficacy in predicting HF deterioration and its potential to secure patient safety in remote, home-based settings. Furthermore, this work addresses the gap in existing literature by providing a comprehensive analysis of different speech task designs and acoustic features. Taken together, the superior performance of the LIPT framework and PSE architecture validates their readiness for integration into long-term telemonitoring systems, offering a scalable solution for remote heart failure management.

cs.SD↗

arXiv2026

TrapSuffix: Proactive Defense Against Adversarial Suffixes in Jailbreaking

Suffix-based jailbreak attacks append an adversarial suffix, i.e., a short token sequence, to steer aligned LLMs into unsafe outputs. Since suffixes are free-form text, they admit endlessly many surface forms, making jailbreak mitigation difficult. Most existing defenses depend on passive detection of suspicious suffixes, without leveraging the defender's inherent asymmetric ability to inject secrets and proactively conceal gaps. Motivated by this, we take a controllability-oriented perspective and develop a proactive defense that nudges attackers into a no-win dilemma: either they fall into defender-designed optimization traps and fail to produce an effective adversarial suffix, or they can succeed only by generating adversarial suffixes that carry distinctive, traceable fingerprints. We propose TrapSuffix, a lightweight fine-tuning approach that injects trap-aligned behaviors into the base model without changing the inference pipeline. TrapSuffix channels jailbreak attempts into these two outcomes by reshaping the model's response landscape to adversarial suffixes. Across diverse suffix-based jailbreak settings, TrapSuffix reduces the average attack success rate to below 0.01 percent and achieves an average tracing success rate of 87.9 percent, providing both strong defense and reliable traceability. It introduces no inference-time overhead and incurs negligible memory cost, requiring only 15.87 MB of additional memory on average, whereas state-of-the-art LLM-based detection defenses typically incur memory overheads at the 1e4 MB level, while composing naturally with existing filtering-based defenses for complementary protection.

cs.CR↗

arXiv2026

Fully strange tetra- and penta-quarks in a chiral quark model

Motivated by the recently reported resonant structure $X(2300)$, a strong candidate for a fully strange tetraquark with positive parity, we perform a systematic study of fully strange tetra- and penta-quark systems within a chiral quark model. Low-lying $S$-wave configurations of the $ss\bar s\bar s$ and $ssss\bar s$ systems are investigated using the Gaussian Expansion Method (GEM) combined with the Complex Scaling Method (CSM), which allows for a unified treatment of bound, resonant, and scattering states. For tetraquarks, all possible configurations: meson-meson, diquark-antidiquark, and K-type structures, with complete color bases, are incorporated, while baryon-meson and diquark-diquark-antiquark configurations are considered for pentaquarks. Several weakly bound states and narrow resonances are identified in both sectors. In particular, a compact fully strange tetraquark with $J^P=1^+$ is found near $2.3\,\text{GeV}$, providing a natural interpretation of the $X(2300)$ resonance. Additional exotic states with dominant hidden-color and K-type components are predicted in the mass ranges $1.6-3.1$ GeV for tetraquarks and $2.6-3.2$ GeV for pentaquarks. The internal structure of these states is analyzed through their sizes, magnetic moments, and wave-function compositions, highlighting the essential role of channel coupling and exotic color configurations. Finally, promising two-body strong decay channels are proposed to facilitate future experimental searches.

hep-ph↗

arXiv2026

Boolean lattice without small rainbow subposets

A Boolean lattice $\mathcal{B}_n=(2^X, \leq)$ is the power set of an $n$-element ground set $X$ equipped with inclusion relation. For two posets $\mathcal{P}$ and $\mathcal{Q}$, we say that $\mathcal{Q}$ contains an \emph{induced copy} of $\mathcal{P}$ if there exists an injection $f : \mathcal{P} \to \mathcal{Q}$ such that $f(X) \le f(Y)$ if and only if $X \le Y$ in $\mathcal{P}$. A $k$-coloring is exact if all colors are used at least once. For posets $\mathcal{Q}$ and $\mathcal{P}$, the \emph{Boolean Gallai-Ramsey number} $\operatorname{GR}_{k}(\mathcal{Q}:\mathcal{P})$ is defined as the smallest $n$ such that any exact $k$-coloring of the sets in $\mathcal{B}_n$ contains either a rainbow induced copy of $\mathcal{Q}$ or a monochromatic induced copy of $\mathcal{P}$ and the \emph{Boolean rainbow Ramsey number} $\operatorname{RR}(\mathcal{Q}:\mathcal{P})$ is defined as the smallest $n$ such that any coloring of the sets in $\mathcal{B}_n$ contains either a rainbow induced copy of $\mathcal{Q}$ or a monochromatic induced copy of $\mathcal{P}$. In this paper, we first study the structural properties of exact $k$-colorings of the sets in Boolean lattice without rainbow induced copy of small posets. As the application of these results, we give exact values and some bounds of Boolean Gallai-Ramsey numbers and Boolean rainbow Ramsey numbers, which improve a result of Chen, Cheng, Li, and Liu in 2020 and give an answer of a question proposed by Chang, Gerbner, Li, Methuku, Nagy, Patk\'{o}s, and Vizer in 2022.

math.CO↗

arXiv2026

Direct and Indirect Loop Equations in Lattice Yang-Mills Theory

The dynamics of Wilson loops are governed by an infinite set of Schwinger-Dyson equations and trace relations. In the context of the lattice positivity bootstrap, a central challenge is determining a dynamically independent basis of these operators within a truncated space. We present a systematic framework to address this problem, utilizing a geometric plaquette-cut and subloop-cut strategy to efficiently generate all (local) direct equations. Furthermore, we identify and analyze "indirect equations", which arise from the elimination of higher-length intermediate loops. We elucidate the origin of these subtle relations and propose a vertex-filtering strategy to construct them. Applying the above framework to SU(2) lattice Yang-Mills theory, we provide explicit counts of independent canonical loops and equations in 2, 3, and 4 dimensions, along with a statistical analysis of their asymptotic growth.

hep-th↗