arXiv subjects

Jin Sun

Publications and source records attributed to Jin Sun.

At least 19 recordsLinked to original sources

arXiv2026

Majoron-driven spontaneous leptogenesis in type-II seesaw model

We investigate a minimal realization of spontaneous leptogenesis in the type-II seesaw model, where the lepton and Higgs asymmetries are generated as decay and inverse-decay processes drive the plasma toward the displaced equilibrium dictated by a rotating Majoron background. We derive the complete set of Boltzmann equations governing the evolution of asymmetric particle densities and analytically and numerically identify the freeze-out and freeze-in regimes. The resulting asymmetries depend primarily on the triplet branching fractions and are nearly independent of the triplet mass. The asymmetry scales as the square root of the smaller branching fraction when either decay mode into leptons or Higgs fields is suppressed, reflecting the symmetry structure; the lepton number is conserved once either coupling is turned off. We also show that the Majoron background does not induce CP-asymmetric decay of the scalar triplet in the massless final state limit, and thus its impact is negligible. Our results establish spontaneous leptogenesis as a simple and robust alternative to thermal type-II leptogenesis that requires neither additional scalar triplets nor explicit CP-violating interactions.

hep-ph↗

arXiv2026

Counterexamples to Escobar's conjecture

Escobar (J Funct Anal 165(1):101-116, 1999) conjectured that for every $n\ge 3$, an $n$-dimensional compact Riemannian manifold with nonnegative Ricci curvature and all boundary principal curvatures bounded below by $\kappa>0$ must satisfy $\sigma_1\geq \kappa$. We disprove this conjecture for every $n\geq 3$ by constructing conformal deformations of the Euclidean unit ball. We first establish a perturbative criterion, then construct explicit polynomial conformal factors satisfying this criterion. For every sufficiently small $t>0$, the resulting metrics $g_t=e^{2t\Phi}g_{\mathbb{R}^n}$ have positive Ricci curvature, every boundary principal curvature is strictly larger than $1$, and $\sigma_1(\mathbb{B}^n,g_t)<1$. The proof requires several computations, some of which were carried out in Mathematica. The Mathematica code is attached to this submission.

math.SP↗

arXiv2026

Dear Algo: A Precision-First Agentic Intent Layer for Unified Search and Recommendation

Search and recommendation serve a shared discovery objective but encode intent differently. We study this boundary through Dear Algo on Threads, a deployed product where open-ended requests such as \emph{more NBA news} or \emph{less politics} steer subsequent feed recommendations rather than return a one-shot result list. Its agentic intent layer compiles explicit, inferred, negative, and compound intent into a grounded executable plan, then invokes conventional retrieval and optional semantic or multimodal reranking. The layer shares an intent-to-retrieval contract without requiring one model or serving path across search-like and recommendation-like modes. We evaluate Dear Algo under a precision-first objective. In a blinded audit of 300 public request-item pairs (296 evaluable), a strict categorical LLM-as-a-judge gate achieved 94.4\% exact-Relevant precision [88.8\%, 98.9\%]. Across 72 normalized request clusters, the full configuration produced 7.73 judge-qualified candidates per 20 slots versus 6.61 for an LLM-derived-query baseline, a gain of 1.11 [0.12, 2.12]. In a candidate-randomized serving-path study restricted to the reranker path's first 72 eligible hours, the user-weighted judge-Irrelevant share among judged admissions was 2.80\% versus 4.78\% off (-1.97 points [-3.02, -0.94]), while Exact-Relevant share was 2.24 points higher [0.08, 4.41]. Together, these studies show how explicit natural-language intent can be carried into feed recommendation under a precision-first evaluation framework

cs.AI↗

arXiv2026

The Weinstock inequality for convex domains in hyperbolic space

We prove the Weinstock inequality for the first Steklov eigenvalue of convex domains in hyperbolic space $\mathbb{H}^{n}$, resolving Open Question 4.27 of Colbois-Girouard-Gordon-Sher(2024) for the remaining case $n=3$. Our argument replaces the global monotonicity required in earlier work Gu-Li-Wan(2025) with a one-crossing property, which is established via an explicit slope comparison. The proof works uniformly for all $n\geq 3$.

math.SP↗

arXiv2026

Self-Evolving Code-with-Image Reasoning

Multimodal models increasingly reach for tools when solving visual tasks (crop, zoom, rotate, brighten), a paradigm known as thinking-with-images. The central challenge is one of perception: tools mostly serve to expose visual evidence, reasoning over that evidence stays in language, and most targets are ones a human could in principle determine by inspection. Some visual questions, however, are not bottlenecked by perception: recovering their answers requires executing a multi-step visual algorithm over the pixels. On such questions a model often names the correct algorithm at once yet still answers wrong, because language can describe an algorithm without being able to run one. Code-with-Image crosses that line: given nothing but a Python interpreter, the model must implement a genuine visual algorithm in code to solve the task; the program itself becomes the reasoning. The bottleneck then shifts from executing code to deciding which algorithm to implement. So we let the model teach itself: a training-free reflection loop studies its own failed programs, tests repairs against constructive ground truth, and keeps what survives as portable skills. On our Code-with-Image Bench (CwI-Bench), thirty task families induced by hidden visual computations with disjoint learning and evaluation splits, even GPT-5.6-luna stays below 30% with tool-free chain of thought; given a bare interpreter it reaches 43%, and with skills evolved through its own executable reflection, 67%. The open 27B model climbs the same ladder (9% $\rightarrow$ 33% $\rightarrow$ 56%), and the skills are plain text, transferable across scales and families. When code carries the reasoning, debugging code becomes debugging reasoning.

cs.CV↗

arXiv2026

Unraveling weak radiative hyperon decays with broken flavor symmetry

We present a broken $SU(3)$ flavor analysis of weak radiative decays of spin-1/2 hyperons, incorporating current-current and electromagnetic-penguin contributions as well as charge- and mass-insertion effects. Six independent reduced amplitudes describe all decay channels, while a minimal relation between the parity-conserving and parity-violating form factors reduces to eight free parameters. A global fit to the ten available observables yields $\chi^2/\mathrm{d.o.f.}=0.98$ and accommodates the large negative asymmetry in $\Sigma^+\to p\gamma$. The resulting nonzero effective form factor $g_{b_8}$ provides a possible flavor-symmetry realization of the parity-violating amplitude while remaining compatible with Hara's theorem, which constrains the current-current contribution in the exact symmetry limit. Our analysis favors a sizable negative value of $\alpha_\gamma(\Xi^- \to \Sigma^- \gamma)$, which differs from the current experimental result by approximately $1.3\sigma$. Future precision measurements of this observable will provide a decisive test of this prediction.

hep-ph↗

arXiv2026

To $1/2$-logconcavity and beyond: Geometric properties of Dirichlet eigenfunctions

We prove that, on a bounded open convex domain $\Omega\subset\mathbb{R}^n$, the first Dirichlet eigenfunction of the Laplacian or the Ornstein--Uhlenbeck operator is $\alpha$-logconcave for every $\alpha\in(0,1/2]$. This extends the recent $1/2$-logconcavity theorem of Crasta--Fragal\`{a} for the Laplacian to the weighted Gaussian setting and, simultaneously, to a broader range of exponents. More precisely, if $u$ denotes the first eigenfunction normalized by $\|u\|_\infty=1$, then for every $\alpha\in(0,1/2]$, the function $-\bigl(-\log(\kappa u(x))\bigr)^{\alpha}$ is concave in $\Omega$ provided the scaling parameter $\kappa$ lies below an explicit threshold $\kappa_\alpha(\Omega)\in(0,1)$, which depends on the first Dirichlet eigenvalue and on the diameter of~$\Omega$. For the Ornstein--Uhlenbeck operator, $\kappa_\alpha(\Omega)$ also depends on the distance between $\Omega$ and the origin. Moreover, we establish a local counterpart: for every $\kappa\in(0,1)$, the function $\bigl(-\log(\kappa u)\bigr)^{\alpha}$ is convex on a convex neighborhood $\Omega_\kappa$ of the unique maximum point of~$u$. We also provide counterexamples showing that unscaled $1/2$-logconcavity may fail for the first Dirichlet eigenfunction of a Schr\"odinger operator with a smooth convex potential, and for the first Dirichlet eigenfunction of a weighted Laplacian associated with an affine log-concave weight.

math.AP↗

arXiv2026

TRON: Targeted Rule-Verifiable Online Environments for Visual Reasoning RL

Reinforcement learning (RL) for visual reasoning needs scalable, verifiable, and controllable training signals. Existing visual RL post-training trains on static curated datasets, with fixed image-question-answer samples bounded by their collection budget. In this work, we introduce TRON (Targeted, Rule-verifiable Online eNvironments), an online environment substrate: a training rollout is generated on demand by a controllable generator-verifier program that samples a fresh latent visual state, renders an image, asks a question, and exactly verifies the answer. A single run can therefore draw an unbounded stream of fresh instances at the difficulty level required by the current curriculum. The current TRON suite contains 520 environments organized into five ability buckets (spatial, mathematical, diagram, pattern/logic, and counting); the same substrate supports both a single full model trained on all buckets and per-bucket ability-specialist models, with no additional data collection. We also introduce a substrate analysis covering generation reliability, instance and level diversity, cross-environment near-duplicates, and base-model pass rate by difficulty level. RL post-training with METHOD consistently improves performance on ten external multimodal reasoning benchmarks across Qwen3-VL-4B, Qwen2.5-VL-7B, and MiMo-VL-7B-SFT.

cs.AI↗

arXiv2026

Self-Improving Small Object Grounding in LVLMs

Can internal attention patterns in Large Vision Language Models (LVLMs) identify reliable small-object boxes without fine-tuning? In this work, we provide an affirmative answer. Attention structure in LVLMs encodes grounding quality-a lightweight IoU regressor trained solely on attention maps achieves strong IoU prediction (Pearson r > 0.67). This regressor powers the regressor-based variant of our Attention-based Candidate Selection (ACS) framework, called ACS-Learned, which selects the best box from multiple sampled candidates to improve object grounding. By analyzing what the regressor learns, we reveal which transformer layers and heads are most critical and derive ACS-Free: a training-free selector that ranks candidates by attention entropy on these discriminative heads, with no learned component at inference. Experiments on COCO and Objects365 demonstrate up to 19% self-improvement on small object localization, with ACS-Free ranking best among all training-free methods, demonstrating that useful attention structure improves both localization reliability and interpretability in LVLMs.

cs.CV↗

arXiv2026

Sharp long distance upper bounds for solutions of Leibenson's equation on Riemannian manifolds

We consider on Riemannian manifolds the Leibenson equation $\partial _{t}u=\Delta _{p}u^{q}$ that is also known as a doubly nonlinear evolution equation. We prove sharp upper estimates of weak subsolutions to this equation on Riemannian manifolds with non-negative Ricci curvature in the whole range of $p>1$ and $q>0$ satisfying $q(p-1)<1$. In this way, we improve the result of \cite{Grigoryan2024a} and prove Conjecture 1.2 from \cite{Grigoryan2024a}.

math.AP↗

arXiv2026

Parabolic Frequency for Doubly Nonlinear Equations on Manifolds

We establish monotonicity formulas for a parabolic frequency function associated with sign-changing solutions to a class of doubly nonlinear parabolic equations of the form $\partial_t u = \mathcal{L}_{p,\varphi} u^q$ on weighted complete Riemannian manifolds without any curvature assumption, where $\mathcal{L}_{p,\varphi}$ denotes the weighted $p$-Laplacian and $p>1$, $q>0$. As a consequence, we obtain results on backward uniqueness for $q(p-1)\geq 1$ and unique continuation at infinity for $q(p-1) > 1$. We further consider equations with a controlled nonlinear perturbation term and derive an almost-monotonicity formula for the parabolic frequency. By employing the parabolic frequency, we also establish some Liouville-type results for ancient solutions in the case $q(p-1)\geq 1$.

math.AP↗

arXiv2026

Revealing Neutrino Mass Ordering at CEPC and FCC-ee

The neutrino masses ordering remains one of the most important open questions in neutrino physics. While upcoming oscillation experiments aim to resolve this problem at low energies, complementary approaches are highly desirable. In this Letter, we show that the neutrino mass ordering can be probed at high-energy colliders through the lepton-flavor structure of heavy neutral lepton (HNL) interactions. In the minimal Type-I seesaw scenario with two nearly degenerate HNLs, the heavy--light neutrino mixings are strongly correlated with the light-neutrino mass spectrum, leading to distinct flavor patterns for the normal and inverted hierarchies. We demonstrate that future $Z$ factories, such as CEPC and FCC-ee, can probe the neutrino mass ordering for total HNL mixings as small as $U_{\rm tot}^2 \gtrsim 4 \times 10^{-9}$, and discriminate between the two hierarchies for $U_{\rm tot}^2 \gtrsim 10^{-6}$. Our results establish collider searches for HNLs as a powerful and complementary probe of the neutrino mass ordering.

hep-ph↗

arXiv2026

Decoding the Amplitude Pair with Distinct CPV Phases in Charmed Baryon Decays

In this Letter, we propose a strategy to extract information on the hierarchical amplitude pair in singly Cabibbo-suppressed (SCS) charmed baryon two-body decays, with a dominant amplitude proportional to $\lambda_s = V_{cs}^* V_{us}$ from tree operators and sub-leading one proportional to $\lambda_b = V_{cb}^* V_{ub}$ from both penguin and tree contributions. The coexistence of these two amplitudes is essential for generating nonzero CP violation (CPV) effects. Since the $\lambda_b$ amplitude is strongly suppressed, its experimental determination is highly challenging. However, by exploiting SU(3) flavor symmetry, which relates the well-measured Cabibbo-favored (CF) amplitudes to the SCS tree amplitudes, information on the $\lambda_b$ amplitude can be extracted. Using current experimental data, a conservative analysis yields $\lambda_b$ amplitudes can be as large as about $10\%$ of the corresponding tree amplitudes with a significance of $2.1\sigma$. In addition, the Lee-Yang parameters of these decays provide an independent probe of this elusive term. We further identify two golden decay channels, $\Xi_c^0 \to p K^-$ and $\Xi_c^0 \to \Sigma^+ \pi^-$, which are particularly well suited for experimental studies of CPV.

hep-ph↗

arXiv2025

RSTR: Reducing SpatioTemporal Redundancy in Diffusion Transformers

Diffusion Transformers (DiTs) have achieved remarkable success in image generation, yet their deployment is hindered by high computational costs. We identify two sources of redundancy. First, temporal redundancy: Classifier-Free Guidance (CFG) applies costly dual forward passes at every timestep, yet guidance matters only at specific steps, and variable scales at critical steps can compensate for skipping others. Second, spatial redundancy: under variable guidance, different transformer blocks exhibit heterogeneous sensitivity, yet uniform calibration across all blocks wastes computation while failing to address their varying requirements. We present RSTR, the first framework to jointly reduce spatiotemporal redundancy in diffusion transformers. Stage-1 addresses temporal redundancy through evolutionary search, discovering sparse guidance schedules with variable scales. Stage-2 addresses spatial redundancy through adaptive rank allocation, assigning calibration capacities to transformer regions based on their sensitivity. Experiments on DiT-XL/2, PixArt-$\alpha$, FLUX, and state-of-the-art Qwen-Image demonstrate 50%-70% compute savings while maintaining or improving quality. On DiT-XL/2, RSTR achieves 57% savings with 15% FID improvement; on Qwen-Image, 3.43$\times$ speedup with preserved quality.

cs.CV↗

arXiv2025

Parabolic Frequency on Gaussian Spaces and Unique Continuation

We establish an almost-monotonicity formula for a parabolic frequency on Gaussian spaces for solutions of the Ornstein-Uhlenbeck heat equation with lower-order terms: $$\partial_t u = L_\gamma u + b(x,t) \cdot \nabla u + c(x,t)u, $$ where $L_\gamma = \Delta - x \cdot \nabla$ is the Ornstein-Uhlenbeck operator. In contrast to classical results that require $b$ and $c$ to be bounded, we only assume that $b$ is bounded and $c$ satisfies a linear growth condition, while the solution $u$ is allowed to have at most exponential quadratic growth. The key innovation is a weighted $L^2$ framework that uses the backward Mehler kernel as a weight, which naturally encodes the underlying measure and compensates for the unbounded coefficients. From the frequency monotonicity, we derive the strong unique continuation principle. This extends Poon's seminal results and complements recent geometric generalizations by Colding and Minicozzi in the context of Gaussian measure spaces. We further apply our framework to establish unique continuation for equations with potentials exhibiting quadratic growth or certain singularities.

math.AP↗

arXiv2025

Collider Probes of Four-Lepton Final States in Maximally Flavor-Violating $U(1)_{L_{\mu}-L_{\tau}}$ Model

We investigate the collider signatures of the maximally flavor-violating $U(1)_{L_\mu-L_\tau}$ model, where a new gauge boson $Z^\prime$ and scalar triplets induce lepton flavor-changing interactions in the $\mu$-$\tau$ sector. Focusing on four-lepton final states at multi-TeV lepton colliders, we conduct a detailed analysis of cross sections, asymmetries, and polarization effects. We show that the signal cross section is highly sensitive to $m_{Z^\prime}$ and the effective parameters $\tilde{g}/m_{Z^\prime}$, while remaining largely insensitive to the triplet Yukawa couplings within the phenomenologically allowed region. The forward-backward asymmetry exhibits a characteristic monotonic dependence on $m_{Z^\prime}$, and beam polarization can significantly suppress Standard Model backgrounds while enhancing new physics contributions. We find that over the phenomenologically allowed parameter space, the predicted observables remain highly sensitive to the underlying model parameters. These results demonstrate that multi-lepton final states are powerful probes of the $U(1)_{L\mu - L_\tau}$ framework and offer valuable guidance for future searches at muon and electron-positron colliders.

hep-ph↗

arXiv2025

Probing flavor-diagonal couplings of doubly-charged scalar at low and high energies

We investigate the phenomenology of a TeV-scale doubly-charged scalar from the right-handed sector within the framework of left-right symmetric models. Focusing on its flavor-diagonal couplings to right-handed electrons and muons, we assess probes from both high-energy colliders and low-energy precision experiments. High-energy processes include Bhabha scattering at LEP and future circular electron-positron colliders (CEPC/FCC-ee), direct production at the LHC, and dedicated searches and precision measurements at proposed muon colliders and $\mu$TRISTAN. Low-energy observables encompass parity-violating M{\o}ller scattering, muon anomalous magnetic moment, and muonium-antimuonium oscillations. Our combined analysis indicates that for a doubly-charged scalar in the $1$-$3$ TeV range, the flavor-diagonal Yukawa couplings to electrons and muons as small as $10^{-2}$ are accessible. Observations of such a doubly-charged scalar would potentially point toward the type-I seesaw mechanism of neutrino masses in the left-right symmetric model with $D$-parity breaking.

hep-ph↗

arXiv2025

Unavoidable induced subgraphs forced by graphs with many vertices of prescribed properties

Given a function $p : V(G)\to \mathbb N$ and an integer $k\ge 0$, define $p_k(G)$ as the number of vertices with $p(v)\ge k$. We say that $p_k(G)$ is bounded for all $\HH$-free graphs if there exists a constant $c=c(\HH)$ such that $p_k(G)<c$ for all such graphs $G$. Here, a graph $G$ is said to be $\HH$-free if it contains no member of $\HH$ as an induced subgraph. When $p$ represents the degree of a vertex, Ramsey's theorem implies that $p_0(G)$ is bounded for every $\{K_n, E_n\}$-free graphs, where $K_n$ and $E_n$ denote the complete graph and the edgeless graph on $n$ vertices, respectively. The connected version of Ramsey's theorem says that $p_0(G)$ is bounded for all $\{K_n, P_n, K_{1,n}\}$-free connected graphs, where $P_n$ and $K_{1,n}$ are the $n$-vertex path and the star with $n$ leaves. In this paper, we extend the Ramsey's theorem to $p_2(G)$ where $p$ denotes the degree, the local independent number, the local component number, and sharp degree, that is, we characterize the forbidden family of graphs $\HH$ such that $p_2(G)$ is bounded for all (connected) $\HH$-free graphs. Moreover, we also characterize the forbidden family of graphs $\HH$ for which there is a constant $c=c(\HH)$ such that $p_c(G)$ is bounded for all $\HH$-free graphs.

math.CO↗