arXiv subjects
Publications and source records attributed to Jinzheng Li.
Kolokolnikov conjectured that, among all simple graphs on \(n\) vertices with exactly \(2(n-2)\) edges, the complete bipartite graph maximizes algebraic connectivity. This paper proves the conjecture. The underlying Lean~4 formalization was generated with MerLean and checked by the Lean kernel.
We study supercooled first-order phase transitions in a supersymmetric hidden sector with a spontaneously broken $U(1)_X$, focusing on the frequency range of the Einstein Telescope and Cosmic Explorer. Along the D-flat direction the tree-level quartic vanishes, so the barrier is generated radiatively by soft SUSY-breaking splittings. In the $\overline{\rm DR}$ scheme the gaugino mass $M_{\tildeλ}$ sets the barrier depth, while the soft scalar mass $m_0$ stabilizes the broken vacuum. For $M_{\tildeλ}/v_X\simeq0.05$--$0.23$, the predicted signal reaches $Ω_{\rm GW}h^2\sim3\times10^{-10}$ near the percolation boundary. The observable amplitude depends sensitively on the portal coupling $δ$ through the hidden-to-visible temperature ratio at percolation: for a cold initial hidden sector the signal rises from the ET floor at $δ=10^{-6}$ to $Ω_{\rm GW}h^2\simeq7\times10^{-11}$ as the sectors approach thermal contact at $δ=10^{-4}$, while a hotter initial hidden sector gives a large signal already for weak portal coupling. We follow this evolution with an 11-variable Boltzmann system that separates the cold nucleating exterior from the reheated true-vacuum interior; reheating mainly enters through the energy budget and redshift factors. The same hidden sector can reproduce $Ω_{\rm CDM}h^2=0.12$ through relativistic dark-quark freeze-out followed by entropy dilution from hidden-Higgs decay, with $m_q\simeq30$--$800\;$keV and $N_{\rm eff}\lesssim{\rm few}\times10^{-5}$.
MerLean-Prover is an end-to-end Lean4 theorem prover that replaces sorry declarations with kernel-checkable proofs. It is built from three agent types (Planning, Check, and Lean) composed by a recursive outer loop whose unit of revision is the proof plan itself, and uses no fine-tuning, no custom RL objective, and no theorem-specific scaffolding. On FormalQualBench, a benchmark of 23 PhD-qualifying-exam theorems, MerLean-Prover solves 10/23, surpassing the strongest published open-source baseline (OpenGauss, 8/23). On Putnam2025, the same harness closes 12/12 with substantially lower total wall-clock than the next-best system that closes the full set. The harness also transfers to smaller models: Sonnet closes all four tested FormalQualBench problems, and Haiku closes the two short ones. These results suggest that harness design is a central factor in end-to-end Lean4 theorem proving, alongside raw model capability, and that a relatively simple harness can already be effective.
An analysis of baryogenesis and stochastic gravitational wave production is presented for an extension of the standard model where the dark sector consists of dark matter particles charged under a $U(1)_x$ gauge symmetry, while a subset of dark fields also carry lepton number but no $U(1)_x$ charge. We demonstrate that with CP violation induced by Yukawa couplings, equal and opposite lepton asymmetries are generated in the visible and hidden sectors. Subsequent evolution preserves lepton number separately in each sector, and sphaleron interactions partially convert the lepton asymmetry into baryon asymmetry near the temperature of the first-order phase transition. Further, we discuss stochastic gravitational wave background production for the first-order phase transition using a gauge-independent bubble nucleation dynamics which yields spectra also valid in the supercooled low-temperature regime with {$T_p/m_{A_x} \ll 1$} where $T_p$ is the percolation temperature and $m_{A_x}$ is the dark photon mass. A parameter-space scan identifies regions that simultaneously account for cogenesis of baryon asymmetry and dark matter and predict stochastic gravitational wave signals within reach of current (NANOGrav, EPTA, PPTA) and future detectors at higher frequencies, providing a unified framework for cogenesis and associated gravitational wave production.
We introduce MerLean, a fully automated agentic framework for autoformalization in quantum computation. MerLean extracts mathematical statements from \LaTeX{} source files, formalizes them into verified Lean~4 code built on Mathlib, and translates the result back into human-readable \LaTeX{} for semantic review. We evaluate MerLean on three theoretical quantum computing papers producing 2,050 Lean declarations from 114 statements in total. MerLean achieves end-to-end formalization on all three papers, reducing the verification burden to only the newly introduced definitions and axioms. Our results demonstrate that agentic autoformalization can scale to frontier research, offering both a practical tool for machine-verified peer review and a scalable engine for mining high-quality synthetic data to train future reasoning models. Our approach can also be generalized to any other rigorous research in mathematics and theoretical physics.
The recent detection of a gravitational wave background in the nano-Hertz frequency range by Pulsar Timing Array (PTA) collaborations, including NANOGrav, EPTA, and PPTA, has opened a new avenue for exploring fundamental physics in the early universe. In this work, we analyze a supercooled first-order phase transition in a hidden sector with a spontaneously broken $U(1)_X$ gauge symmetry as a source for this signal. We demonstrate that the thermal history of the hidden and visible sectors plays a crucial role in the gravitational wave power spectrum analysis. Our analysis shows that supercooled phase transitions can generate gravitational waves strong enough to explain the PTA observations while satisfying cosmological constraints from Big Bang Nucleosynthesis.
Existing large language models (LLMs) driven search agents typically rely on prompt engineering to decouple the user queries into search plans, limiting their effectiveness in complex scenarios requiring reasoning. Furthermore, they suffer from excessive token consumption due to Python-based search plan representations and inadequate integration of multimedia elements for both input processing and response generation. To address these challenges, we introduce SearchExpert, a training method for LLMs to improve their multimedia search capabilities in response to complex search queries. Firstly, we reformulate the search plan in an efficient natural language representation to reduce token consumption. Then, we propose the supervised fine-tuning for searching (SFTS) to fine-tune LLM to adapt to these representations, together with an automated dataset construction pipeline. Secondly, to improve reasoning-intensive search capabilities, we propose the reinforcement learning from search feedback (RLSF) that takes the search results planned by LLM as the reward signals. Thirdly, we propose a multimedia understanding and generation agent that enables the fine-tuned LLM to process visual input and produce visual output during inference. Finally, we establish an automated benchmark construction pipeline and a human evaluation framework. Our resulting benchmark, SearchExpertBench-25, comprises 200 multiple-choice questions spanning financial and international news scenarios that require reasoning in searching. Experiments demonstrate that SearchExpert outperforms the commercial LLM search method (Perplexity Pro) by 36.60% on the existing FinSearchBench-24 benchmark and 54.54% on our proposed SearchExpertBench-25. Human evaluations further confirm the superior readability.
The detection of a gravitational wave background in the nano-Hertz frequency range from Pulsar Timing Array (PTA) observations offers new insights into evolution of the early universe. In this work we analyze gravitational wave data from PPTA, EPTA, and NANOGrav, as arising from a supercooled first-order phase transition within a hidden sector, characterized by a broken $U(1)_X$ gauge symmetry. Several previous works have discussed challenges in producing observable {PTA signal} from supercooled phases transitions. We discuss these challenges and show how they are overcome by inclusion in part of the proper thermal history of the hidden and the visible sectors. The analysis of this work demonstrates that thermal histories of hidden and visible sectors profoundly influence the gravitational wave power spectrum, an aspect not previously explored in the literature. Further, the analysis of this work suggests that supercooled phase transitions not only align with the Pulsar Timing Array observations but also show promise for gravitational wave detection by future gravitational wave detectors. Our analysis shows that the dominant contribution to the gravitational wave power spectrum for PTA signals comes from bubble collision while the sound wave and turbulence contributions are highly suppressed. It is also found that all the PTA events are of detonation type while deflagration and hybrid events are absent. The analysis presented in this work provides a robust framework for further investigations on the origin of gravitational wave power spectrum in the early universe and for their experimental observation in the future.
The $\mathsf{SO(10)}$ model with a heavy Higgs spectrum consisting of $\mathsf{560+\overline{560}}$ and a light Higgs spectrum consisting of $2\mathsf{\times 10+320}$ plet representations of $\mathsf{SO(10)}$ is unique among $\mathsf{SO(10)}$ models.,It has the remarkable property that VEVs of $\mathsf{560}$ and $\mathsf{\overline{560}}$ can simultaneously reduce the rank of the gauge group and further reduce the remaining symmetry down to the standard model gauge group. Additionally, on mixing with the light fields all the Higgs fields become heavy except for one pair of light Higgs doublets just as in MSSM. This model has not been fully explored thus far because of the technical difficulty of computing the couplings of the heavy and the light Higgs sectors, specifically the interaction $(\mathsf{560\times 560)\cdot 320}$ involving the coupling of tensor-spinors with a third rank ~mixed tensor $\mathsf{320}$. An explicit analysis of such couplings is given in this paper. Spontaneous symmetry breaking of the $\mathsf{SO(10)}$ symmetry is carried out reducing the gauge group to $\mathsf{SU(3)}_c\times \mathsf{SU(2)}_L\times \mathsf{U(1)}_Y$ with just one just pair of light Higgs. Thus a natural deduction of MSSM arises from the $\mathsf{SO(10)}$ model with no fine tuning needed. Further, it is shown that the light Higgs doublet of the model is a linear combination of the Higgs doublet fields of the $2\mathsf{\times 10}$ and the $\mathsf{320}$ Higgs fields. It is shown that in this class of $\mathsf{SO(10)}$ models $b-t-τ$ unification can be achieved with $\tanβ$ as low as 5-10. An analysis of the sparticle spectrum within ${\tilde g}$SUGRA renormalization group evolution is given which leads to a bi-modal sparticle spectrum consisting of a compressed low mass spectrum for sleptons and weakinos and a high mass spectrum of gluino, squarks, and heavy Higgs.LHC.
Financial decision-making requires processing vast amounts of real-time information while understanding their complex temporal relationships. While traditional search engines excel at providing real-time information access, they often struggle to comprehend sophisticated user intentions and contextual nuances. Conversely, Large Language Models (LLMs) demonstrate reasoning and interaction capabilities but may generate unreliable outputs without access to current data. While recent attempts have been made to combine LLMs with search capabilities, they suffer from (1) restricted access to specialized financial data, (2) static query structures that cannot adapt to dynamic market conditions, and (3) insufficient temporal awareness in result generation. To address these challenges, we present FinSearch, a novel agent-based search framework specifically designed for financial applications that interface with diverse financial data sources including market, stock, and news data. Innovatively, FinSearch comprises four components: (1) an LLM-based multi-step search pre-planner that decomposes user queries into structured sub-queries mapped to specific data sources through a graph representation; (2) a search executor with an LLM-based adaptive query rewriter that executes the searching of each sub-query while dynamically refining the sub-queries in its subsequent node based on intermediate search results; (3) a temporal weighting mechanism that prioritizes information relevance based on the deduced time context from the user's query; (4) an LLM-based response generator that synthesizes results into coherent, contextually appropriate outputs. To evaluate FinSearch, we construct FinSearchBench-24, a benchmark of 1,500 four-choice questions across the stock market, rate changes, monetary policy, and industry developments spanning from June to October 2024.
With the development in cognitive science and Large Language Models (LLMs), increasing connections have come to light between these two distinct fields. Building upon these connections, we propose a conjecture suggesting the existence of a duality between LLMs and Tulving's theory of memory. We identify a potential correspondence between Tulving's synergistic ecphory model (SEM) of retrieval and the emergent abilities observed in LLMs, serving as supporting evidence for our conjecture. Furthermore, we speculate that consciousness may be considered a form of emergent ability based on this duality. We also discuss how other theories of consciousness intersect with our research.
Production of gravitational waves in the early universe is discussed in a cosmologically consistent analysis within a first order phase transition involving a hidden sector feebly coupled with the visible sector. Each sector resides in its own heat bath leading to a potential dependent on two temperatures, and on two fields: one a standard model Higgs and the other a scalar arising from a hidden sector $U(1)$ gauge theory. A synchronous evolution of the hidden and visible sector temperatures is carried out from the reheat temperature down to the electroweak scale.The hydrodynamics of two-field phase transitions, one for the visible and the other for the hidden is discussed, which leads to separate tunneling temperatures, and different sound speeds for the two sectors. Gravitational waves emerging from the two sectors are computed and their imprint on the measured gravitational wave power spectrum vs frequency is analyzed in terms of bubble nucleation signature, i.e., detonation, deflagration, and hybrid. It is shown that the two-field model predicts gravitational waves accessible at several proposed gravitational wave detectors: LISA, DECIGO, BBO, Taiji and their discovery would probe specific regions of the hidden sector parameter space and may also shed light on the nature of bubble nucleation in the early universe. The analysis presented here indicates that the cosmologically preferred models are those where the tunneling in the visible sector precedes the tunneling in the hidden sector and the sound speed $c_s$ lies below its maximum, i.e., $c^2_s<\frac{1}{3}$. It is of interest to investigate if these features are universal and applicable to a wider class of cosmologically consistent models.
A variety of supergravity and string models involve hidden sectors where the hidden sectors may couple feebly with the visible sectors via a variety of portals. While the coupling of the hidden sector to the visible sector is feeble its coupling to the inflaton is largely unknown. It could couple feebly or with the same strength as the visible sector which would result in either a cold or a hot hidden sector at the end of reheating. These two possibilities could lead to significantly different outcomes for observables. We investigate the thermal evolution of the two sectors in a cosmologically consistent hidden sector dark matter model where the hidden sector and the visible sector are thermally coupled. Within this framework we analyze several phenomena to illustrate their dependence on the initial conditions. These include the allowed parameter space of models, dark matter relic density, proton-dark matter cross section, effective massless neutrino species at BBN time, self-interacting dark matter cross-section, where self-interaction occurs via exchange of dark photon, and Sommerfeld enhancement. Finally fits to the velocity dependence of dark matter cross sections from galaxy scales to the scale of galaxy clusters is given. The analysis indicates significant effects of the initial conditions on the observables listed above. The analysis is carried out within the framework where dark matter is constituted of dark fermions and the mediation between the visible and the hidden sector occurs via the exchange of dark photons. The techniques discussed here may have applications for a wider class of hidden sector models using different mediations between the visible and the hidden sectors to explore the impact of Big Bang initial conditions on observable physics.
A variety of possibilities exist for dark matter aside from WIMPS, such as hidden sector dark matter. We discuss synchronous thermal evolution of visible and hidden sectors and show that the density of thermal relics can change $O(100\%)$ and $ΔN_{\rm eff}$ by a factor of up to $10^5$ depending of whether the hidden sector was hot or cold at the reheat temperature. It is also shown that the approximation of using separate entropy conservation for the visible and hidden sectors is invalid even for a very feeble coupling between the two.
Nuclear-weapon-material detection via gamma-ray sensing is routinely applied, for example, in monitoring cross-border traffic. Natural or deliberate shielding both attenuates and distorts the shape of the gamma-ray spectra of specific radionuclides, thereby making such routine applications challenging. We develop a Lagrange multiplier (LM) test for shielding. A strong advantage of the LM test is that it only requires fitting a much simpler model that assumes no shielding. We show that, under the null hypothesis and some mild regularity conditions and as the detection time increases, LM test statistic for (composite) shielding is asymptotically Chi-square with the degree of freedom equal to the presumed number of shielding materials. We also derive the local power of the LM test. Extensive simulation studies suggest that the test is robust to the number and nature of the intervening materials, which owes to the fact that common intervening materials have broadly similar attenuation functions.