arXiv subjects

Teng Liu

Publications and source records attributed to Teng Liu.

At least 19 recordsLinked to original sources

arXiv2026

Spectral condensation in a finite nonequilibrium atmospheric transition

Order parameters are difficult to define in high-dimensional nonequilibrium systems that lack a Hamiltonian, a thermodynamic limit or an observed control coordinate. Here we show that such transitions can be diagnosed from the spectrum of occupations over data-derived eigen-microstates. We combine Eigen Microstate Theory with a Marchenko--Pastur random-matrix baseline to isolate an emergent sector, whose entropy quantifies competition among statistically significant collective states. As a finite atmospheric realization, we analyse 51 sudden stratospheric warmings in ERA5. The event-aligned ensemble undergoes spectral condensation, decondensation and recondensation: a polar-vortex state dominated by a few eigen-microstates gives way to a high-entropy regime of competing emergent states before selecting a reorganized weak-vortex state. A stochastic wave--mean-flow model, in which upward wave-activity flux provides a reduced control coordinate, reproduces the same entropy maximum, collapse and top-down timing. These results identify emergent-sector entropy as an order-parameter-like, state-based spectral diagnostic for non-Hamiltonian transitions and place polar-vortex breakdown within a broader class of finite nonequilibrium phase reorganizations.

physics.ao-ph↗

arXiv2026

NeighborDiv: Training-free Zero-shot Generalist Graph Anomaly Detection via Neighbor Diversity

Graph Anomaly Detection (GAD) is increasingly shifting to Generalist GAD (GGAD) for cross-domain "one-for-all" detection, but existing GGAD methods predominantly rely on the neighbor consistency principle, falling into the \textbf{Node-to-Neighbor Consistency Paradigm} for anomaly quantification. These methods suffer from complex training pipelines, heavy training data dependency, high computational costs, and unstable cross-domain generalization. To address these limitations, we propose NeighborDiv, a training-free generalist graph anomaly detection framework based on neighbor diversity. Departing from the dominant Node-to-Neighbor Consistency Paradigm, we shift the focus to the \textbf{Neighbor-to-Neighbor Diversity Paradigm}, and uncover that the internal structural dispersion of a node's neighbor set is a powerful, independently discriminative anomaly signal. We quantify neighbor diversity via the variance of inter-neighbor feature similarities, which captures how a node organizes its local graph environment, and operates independently of conventional node-to-neighbor consistency frameworks. Extensive experiments under two standard GGAD evaluation paradigms show NeighborDiv achieves state-of-the-art performance, with relative gains of 10.25% in average AUC and 17.78% in average AP over the second-best baseline under Single-Domain Independent Training (SDIT), and 6.89%/9.58% in AUC/AP under Unified Multi-Domain Training (UMDT), respectively. Notably, NeighborDiv yields zero performance volatility across all datasets, eliminating training-set dependency and establishing a lightweight and highly practical GGAD framework.

cs.LG↗

arXiv2026

Symmetry-Enforced Non-Hermitian Jarzynski Equality in an SU(2)-Rotated Family of Hybrid $\mathcal{PT}$--$\mathcal{APT}$ Systems

The Jarzynski equality is a cornerstone of nonequilibrium thermodynamics, linking work statistics to equilibrium free-energy differences. Although it has been extensively verified in classical and quantum Hermitian settings, its status in non-Hermitian dynamics remains under debate. Here we show that, in a postselected no-quantum-jump framework, a conditional non-Hermitian Jarzynski equality holds when the transition probabilities obey a parity-exchange symmetry. We study a constructed family of two-level hybrid Hamiltonians formed as linear combinations of parity-time ($\mathcal{PT}$) and anti-parity-time ($\mathcal{APT}$) symmetric terms, and demonstrate using complementary geometric and algebraic arguments that the parity-exchange symmetry persists throughout the corresponding $\mathrm{SU}(2)$-rotated orbit. Relative to previous $\mathcal{PT}$-focused conditional Jarzynski equality results, the advance here is an extension of the symmetry criterion from the isolated $\mathcal{PT}$ endpoint to a broader $\mathcal{PT}$--$\mathcal{APT}$ hybrid family. Experimentally, we implement three representative points, $\theta_k = 0, \pi/4, \pi/2$, in a single trapped $^{171}\mathrm{Yb}^+$ ion and measure the resulting work distributions under cyclic protocols with $\Delta F = 0$, confirming the predicted symmetry criterion at those points. Our results establish a symmetry-based extension of the conditional non-Hermitian Jarzynski relation within this restricted two-level setting.

quant-ph↗

arXiv2026

The SRG/eROSITA diffuse soft X-ray background II. spectra and morphology of the eROSITA bubbles in the western Galactic hemisphere

The eROSITA bubbles (eRObub) were discovered in 2020 in the first SRG/eROSITA All-Sky Survey, and are among the most extended structures in the X-ray sky. Using eROSITA all-sky maps and spatially resolved spectra, we aim to infer the three-dimensional structure and measure the hot gas properties of the eRObub. We fit spectra binned to a constant S/N and high-S/N spectra from custom regions to examine gas properties in more detail. We fit the morphology of eRObub with a parametrised geometrical model that describes a blast wave propagating into an idealised Galactic halo from the centre. We found the interior of the western eRObub is best characterised by two emission components with relatively uniform temperatures: a hotter component at $kT=0.60\pm0.02$ keV, and a colder one at $kT=0.21^{+0.03}_{-0.01}$ keV, where the latter's emission measure is about five times higher on average. Our spectra suggest sub-solar abundances ($Z=0.2\pm0.1 Z_\odot$), consistent with expectations for the Galactic halo, while we find no conclusive evidence for $\alpha$-element enhancement. In contrast, the North Polar Spur exhibits higher abundances ($Z>0.5 Z_\odot$), which, at face value, disfavours a common origin. We spectrally confirm an apparent cool shell at $kT\sim0.18$-$0.2$ keV surrounding the northern eRObub, assuming collisional ionisation equilibrium. We found no noticeable difference in X-ray emission in regions overlapping with the Fermi Bubbles. Our geometrical model suggests that the horizontal size of both eRObub is well-constrained (semi-minor axis $\sim 6$ kpc), but their vertical extent is uncertain, as the observed X-ray emission is almost insensitive to the existence and location of a bubble cap. Additionally, a tilt ($\sim 30^{\circ}$) towards $l\sim 220^{\circ}$ is needed to reproduce the projected image of the northern eRObub, whereas the southern bubble requires little tilt.

astro-ph.HE↗

arXiv2026

Planetary climate interactions of the Qinghai-Tibetan Plateau

The Qinghai-Tibetan Plateau (QTP), Earth's "Third Pole", profoundly shapes the Asian monsoon and regional climate and exerts far-reaching influence on the global climate system. Yet its role in organizing planetary-scale climate interactions remains poorly quantified. Here we develop a climate network framework to explicitly resolve the planetary teleconnection architecture associated with the QTP across historical observations and future climate projections, with physical consistency assessed using Lagrangian trajectory diagnostics and targeted numerical experiments. We uncover a persistent and directional interaction structure linking the QTP with multiple major climate tipping elements. In particular, we identify a robust tripolar interaction mode coupling the QTP with both the Arctic and Antarctica through coherent atmospheric-oceanic pathways. Our findings establish the QTP as a critical planetary climate integrator, revealing a significant blind spot in current climate models and risk frameworks regarding cascading tipping dynamics in a warming world.

physics.ao-ph↗

arXiv2026

A Regime Shift in Atlantic Surface Currents Reveals a Step-like Decline of the Meridional Overturning Circulation

The Atlantic surface currents associated with the Atlantic Meridional Overturning Circulation (AMOC) play a central role in regulating Earth's climate, yet their large scale dynamical response to climate variability remains poorly understood. Here we identify a previously unrecognized basin scale phase of Atlantic surface circulation, termed the Atlantic Convergence Divergence Mode (ACDM), characterized by a convergence divergence pattern in the North Atlantic and coherent meridional flows in the South Atlantic. We show that the ACDM experienced a pronounced regime shift in 2009, marked by weakened vertical water exchange and reduced meridional transport. This transition closely coincides with direct RAPID MOCHA AMOC observations and is driven by AMOC modulated multicale forcing: a low frequency oceanic thermal reorganization that preconditions the system, and episodic atmospheric shocks that trigger the shift. By identifying the ACDM variability as a sensitive and physically grounded proxy for interannual AMOC fluctuations, we reveal that the observed 2009 shift signifies a nonlinear, step like weakening of AMOC that triggered a fundamental basin scale reorganization of Atlantic surface currents. Our results offer a dynamical explanation for the AMOC's recent decline and demonstrate its inherently nonlinear nature, highlighting the need to account for step like transitions in assessing its stability and future evolution.

physics.ao-ph↗

arXiv2026

Reliability-Aware Geometric Fusion for Robust Audio-Visual Navigation

Audio-Visual Navigation (AVN) requires an embodied agent to navigate toward a sound source by utilizing both vision and binaural audio. A core challenge arises in complex acoustic environments, where binaural cues become intermittently unreliable, particularly when generalizing to previously unheard sound categories. To address this, we propose RAVN (Reliability-Aware Audio-Visual Navigation), a framework that conditions cross-modal fusion on audio-derived reliability cues, dynamically calibrating the integration of audio and visual inputs. RAVN introduces an Acoustic Geometry Reasoner (AGR) that is trained with geometric proxy supervision. Using a heteroscedastic Gaussian NLL objective, AGR learns observation-dependent dispersion as a practical reliability cue, eliminating the need for geometric labels during inference. Additionally, we introduce Reliability-Aware Geometric Modulation (RAGM), which converts the learned cue into a soft gate to modulate visual features, thereby mitigating cross-modal conflicts. We evaluate RAVN on SoundSpaces using both Replica and Matterport3D environments, and the results show consistent improvements in navigation performance, with notable robustness in the challenging unheard sound setting.

cs.SD↗

arXiv2026

The average X-ray spectrum of the volume-complete M-, F-, G-, and K-type star sample within 10 pc of the Sun

F, G, K and M type stars are the most abundant stellar population in the Milky Way and are expected to contribute to its diffuse X-ray emission. Yet their intrinsic average X-ray spectrum remains poorly constrained due to their faint X-ray luminosities, leaving their collective role in the X-ray background of the Milky Way uncertain. We analysed the volume-complete sample of M- (M0--M6) and FGK-type stars within 10 pc of the Sun using data from eROSITA all-sky survey aboard the Spectrum-Roentgen-Gamma (SRG) mission (eRASS:4). Individual spectra were normalized by exposure and distance and stacked to produce representative averages. The distance-normalized emission measures yield an average X-ray luminosity of $(2.6 \pm0.1)\times 10^{27}$ erg/s for M-type stars, and $(15\pm3)\times 10^{27}$ erg/s for F, G and K-type stars in 0.2--2.0 keV. The average spectra could be well described by a sum of three and two thermal models. Fitted temperatures and abundances remain consistent across M-star subgroups, while early-M stars are surprisingly on average less luminous than mid/late-M types. These results offer new insights into the collective X-ray properties of nearby stars, and provide motivation to explore the link with the unresolved soft X-ray background of the Galaxy.

astro-ph.HE↗

arXiv2026

CIV wind properties of the SDSS-V X-ray selected quasars: strong optical-to-UV emission is key regardless of X-ray strength

We present an investigation of the rest-frame optical/UV and X-ray properties for a sample of 3027 X-ray selected quasars between $1.5 \leq z \leq 3.5$ detected in the deepest Spectrum Roentgen Gamma/eROSITA data available and observed by the fifth iteration of the Sloan Digital Sky Survey (SDSS-V). We parametrize the CIV$\lambda1549$ emission line to infer the strength of accretion disc winds and perform X-ray spectral fitting. The X-ray spectral properties -- namely, the 2keV monochromatic luminosity (L$_\text{2keV}$) and spectral slope -- are not strongly correlated with wind strength. Despite this result, the X-ray selected sample is shifted towards lower CIV blueshifts and higher equivalent widths than the optically selected sample observed in previous SDSS surveys, and matching in optical luminosity, redshift, and Eddington ratio does not reduce these differences. We estimate the far-UV luminosity using the HeII$\lambda1640$ line luminosity and define the slopes between this and the 2500A monochromatic luminosity ($L_{2500}$) and L$_\text{2keV}$ ($\alpha_\text{ouv}$ and $\alpha_\text{uvx}$, respectively) in a similar manner to the familiar $\alpha_\text{ox}$ parameter, which tracks the spectral slope between $L_{2500}$ and L$_\text{2keV}$. The quantity $\alpha_\text{ouv}$ is more strongly correlated with wind strength in our sample than $\alpha_\text{ox}$. We show that the correlation between $\alpha_\text{ox}$ and wind strength is driven by the relationship between the optical luminosity and wind strength. Our results are consistent with a radiation line-driven wind, whereby the ionising far-UV photons must not over-ionise the gas. The hard X-ray photons are few enough in number to have a negligible effect on the ionisation state of the material.

astro-ph.GA↗

arXiv2026

Generative deep learning improves reconstruction of global historical climate records

Accurate assessment of anthropogenic climate change relies on historical instrumental data, yet observations from the early 20th century are sparse, fragmented, and uncertain. Conventional reconstructions rely on disparate statistical interpolation, which tends to smooth local features and create unphysical artifacts, often leading to an underestimation of intrinsic variability and extremes. While recent machine learning approaches have improved reconstruction accuracy, they remain confined to purely spatial inpainting of coarse-resolution fields. Here, we present a unified, probabilistic generative deep learning framework that overcomes these limitations and reveals previously unresolved historical climate variability back to 1850. Leveraging a learned generative prior of Earth system dynamics, our model performs probabilistic inference to estimate spatiotemporally consistent historical temperature and precipitation fields from sparse observations. Our approach preserves the higher-order statistics of climate dynamics, transforming reconstruction into a robust uncertainty-aware assessment. We demonstrate that our reconstruction mitigates the smoothing effects inherent in widely used historical reference products, including those underlying IPCC assessments, especially regarding extreme weather events. Notably, we uncover higher early 20th-century global warming levels compared to existing reconstructions, primarily driven by more pronounced polar warming, with mean Arctic warming trends exceeding established benchmarks by 0.15--0.29C per decade for 1900--1980. Conversely, for the modern era, our reconstruction indicates that the broad Arctic warming trend is likely overestimated in recent assessments, yet explicitly resolves previously unrecognized intense, localized hotspots in the Barents Sea and Northeastern Greenland.

physics.geo-ph↗

arXiv2026

Warming-driven rise in soil moisture entropy signals destabilization of the Asian Water Tower

The Tibetan Plateau (TP), known as the "Asian Water Tower," is currently undergoing a rapid wetting trend. While this moisture increase is often viewed as beneficial for water availability, it remains unclear whether the hydrological system itself is becoming more resilient or drifting toward instability. Here, we apply an entropy-based framework to quantify the changing structural organization of the TP's soil moisture system. We show that from 2000 to 2024, regional wetting has driven a long-term decline in entropy, reflecting an increase in system order and stability due to enhanced hydrological buffering capacity. This stability is modulated by the El Ni\~no-Southern Oscillation (ENSO), which regulates regional heterogeneity via a distinct spatial dipole. Crucially, however, CMIP6 climate projections reveal an alarming reversal: future warming triggers a rise in entropy. This transition signals a loss of systemic resilience, characterized by intensified spatial disorder and potential abrupt regime shifts by the mid-century. Our findings suggest that while current wetting provides a stabilizing buffer, continued warming is projected to amplify spatial heterogeneity, thereby destabilizing the Asian Water Tower, with significant risks for downstream water security.

physics.ao-ph↗

arXiv2025

Phase transition revealed by eigen microstate entropy

We introduce the eigen microstate entropy ($S_{\text{EM}}$), a novel metric of complexity derived from the probabilities of statistically independent eigen microstates. After establishing its scaling behavior in equilibrium systems and demonstrating its utility in critical phenomena (mean spherical, Ising, and Potts models), we apply $S_{\text{EM}}$ to non-equilibrium complex systems. Our analysis reveals a consistent precursor signal: a significant increase in $S_{\text{EM}}$ precedes major phase transitions. Specifically, we observe this entropy rise before biomolecular condensate formation in liquid-liquid phase separation in living cells and months ahead of El Ni\~no events. These findings position $S_{\text{EM}}$ as a general framework for detecting and interpreting phase transitions in non-equilibrium systems.

cond-mat.stat-mech↗

arXiv2025

Inferix: A Block-Diffusion based Next-Generation Inference Engine for World Simulation

World models serve as core simulators for fields such as agentic AI, embodied AI, and gaming, capable of generating long, physically realistic, and interactive high-quality videos. Moreover, scaling these models could unlock emergent capabilities in visual perception, understanding, and reasoning, paving the way for a new paradigm that moves beyond current LLM-centric vision foundation models. A key breakthrough empowering them is the semi-autoregressive (block-diffusion) decoding paradigm, which merges the strengths of diffusion and autoregressive methods by generating video tokens in block-applying diffusion within each block while conditioning on previous ones, resulting in more coherent and stable video sequences. Crucially, it overcomes limitations of standard video diffusion by reintroducing LLM-style KV Cache management, enabling efficient, variable-length, and high-quality generation. Therefore, Inferix is specifically designed as a next-generation inference engine to enable immersive world synthesis through optimized semi-autoregressive decoding processes. This dedicated focus on world simulation distinctly sets it apart from systems engineered for high-concurrency scenarios (like vLLM or SGLang) and from classic video diffusion models (such as xDiTs). Inferix further enhances its offering with interactive video streaming and profiling, enabling real-time interaction and realistic simulation to accurately model world dynamics. Additionally, it supports efficient benchmarking through seamless integration of LV-Bench, a new fine-grained evaluation benchmark tailored for minute-long video generation scenarios. We hope the community will work together to advance Inferix and foster world model exploration.

cs.CV↗

arXiv2025

Unveiling the Sources of X-ray Luminosity in DESI Galaxy Groups: Insights from the SRG/eROSITA All-Sky Survey

We use the first eROSITA all-sky survey (eRASS1) to investigate the contributions of AGN and extended gas to the total X-ray luminosity ($L_X$) of galaxy groups with different halo masses ($M_h$) at different redshifts. The presence of AGN in their central galaxies is identified using multi-wavelength catalogs, including the X-ray counterparts, the ASKAP radio catalog, and the DESI spectroscopic measurements. We apply the stacking method to obtain sufficient statistics for the X-ray surface brightness profile and the $L_X$ for groups with different central AGN properties. We find that the X-ray groups exhibit the highest $L_X$, followed by groups with QSO, radio, BPT-AGN, and non-AGN centrals. Moreover, the $L_X$ of the $M_h \lesssim 10^{13}h^{-1}M_\odot$ groups is dominated by the central AGN, while the X-ray emission from extended gas tends to be more prominent in the $M_h \gtrsim 10^{13}h^{-1}M_\odot$ groups. In groups where the AGN play a major role in X-ray emission, the contribution from extended gas is minor, resulting in significant uncertainties concerning the extended X-ray emission. When the subset containing the X-ray detected counterparts is excluded, the extended gas component becomes easier to obtain. A correlation has been identified between the X-ray luminosity of the central AGN and extended gas. However, once we account for the positional offset, their correlation becomes less prominent. Currently, the results are not conclusive enough to confirm whether there is a connection between the AGN feedback and extended gas. However, they provide a new perspective on the feedback processes in the history of group assembly.

astro-ph.GA↗

arXiv2025

UpBench: A Dynamically Evolving Real-World Labor-Market Agentic Benchmark Framework Built for Human-Centric AI

As large language model (LLM) agents increasingly undertake digital work, reliable frameworks are needed to evaluate their real-world competence, adaptability, and capacity for human collaboration. Existing benchmarks remain largely static, synthetic, or domain-limited, providing limited insight into how agents perform in dynamic, economically meaningful environments. We introduce UpBench, a dynamically evolving benchmark grounded in real jobs drawn from the global Upwork labor marketplace. Each task corresponds to a verified client transaction, anchoring evaluation in genuine work activity and financial outcomes. UpBench employs a rubric-based evaluation framework, in which expert freelancers decompose each job into detailed, verifiable acceptance criteria and assess AI submissions with per-criterion feedback. This structure enables fine-grained analysis of model strengths, weaknesses, and instruction-following fidelity beyond binary pass/fail metrics. Human expertise is integrated throughout the data pipeline (from job curation and rubric construction to evaluation) ensuring fidelity to real professional standards and supporting research on human-AI collaboration. By regularly refreshing tasks to reflect the evolving nature of online work, UpBench provides a scalable, human-centered foundation for evaluating agentic systems in authentic labor-market contexts, offering a path toward a collaborative framework, where AI amplifies human capability through partnership rather than replacement.

cs.AI↗

arXiv2025

Discovery of an X-ray Luminous Radio-Loud Quasar at $z=3.4$: A Possible Transitional Super-Eddington Phase

We report the multiwavelength properties of eFEDS J084222.9+001000 (hereafter ID830), a quasar at $z=3.4351$, identified as the most X-ray luminous radio-loud quasar in the eROSITA Final Equatorial Depth Survey (eFEDS) field. ID830 shows a rest-frame 0.5-2 keV luminosity of $\log (L_\mathrm{0.5-2\,keV}/\mathrm{erg}~\mathrm{s}^{-1}) = 46.20 \pm 0.12$, with a steep X-ray photon index ($\Gamma =2.43 \pm 0.21$), and a significant radio counterpart detected with VLA/FIRST 1.4 GHz and VLASS 3 GHz bands. The rest-frame UV to optical spectra from SDSS and Subaru/MOIRCS $J$-band show a dust reddened quasar feature with $A_\mathrm{V} = 0.39 \pm 0.08$ mag and the expected bolometric AGN luminosity from the dust-extinction-corrected UV luminosity reaches $L_\mathrm{bol,3000}= (7.62 \pm 0.31) \times 10^{46}$ erg s$^{-1}$. We estimate the black hole mass of $M_\mathrm{BH} = (4.40 \pm 0.72) \times 10^{8} M_{\odot}$ based on the MgII$\lambda$2800 emission line width, and an Eddington ratio from the dust-extinction-corrected UV continuum luminosity reaches $\lambda_\mathrm{Edd,UV}=1.44 \pm 0.24$ and $\lambda_{\mathrm{Edd,X}} = 12.8 \pm 3.9$ from the X-ray luminosity, both indicating the super-Eddington accretion. ID830 shows a high ratio of UV-to-X-ray luminosities, $\alpha_\mathrm{OX}=-1.20 \pm 0.07$ (or $\alpha_\mathrm{OX}=-1.42 \pm 0.07$ after correcting for jet-linked X-ray excess), higher than quasars and little red dots in super-Eddington phase with similar UV luminosities, with $\alpha_\mathrm{OX}<-1.8$. Such a high $\alpha_\mathrm{OX}$ suggests the coexistence of a prominent radio jet and X-ray corona, in this high Eddington accretion phase. We propose that ID830 may be in a transitional phase after an accretion burst, evolving from a super-Eddington to a sub-Eddington state, which could naturally describe the high $\alpha_\mathrm{OX}$.

astro-ph.GA↗

arXiv2025

ADP-VRSGP: Decentralized Learning with Adaptive Differential Privacy via Variance-Reduced Stochastic Gradient Push

Differential privacy is widely employed in decentralized learning to safeguard sensitive data by introducing noise into model updates. However, existing approaches that use fixed-variance noise often degrade model performance and reduce training efficiency. To address these limitations, we propose a novel approach called decentralized learning with adaptive differential privacy via variance-reduced stochastic gradient push (ADP-VRSGP). This method dynamically adjusts both the noise variance and the learning rate using a stepwise-decaying schedule, which accelerates training and enhances final model performance while providing node-level personalized privacy guarantees. To counteract the slowed convergence caused by large-variance noise in early iterations, we introduce a progressive gradient fusion strategy that leverages historical gradients. Furthermore, ADP-VRSGP incorporates decentralized push-sum and aggregation techniques, making it particularly suitable for time-varying communication topologies. Through rigorous theoretical analysis, we demonstrate that ADP-VRSGP achieves robust convergence with an appropriate learning rate, significantly improving training stability and speed. Experimental results validate that our method outperforms existing baselines across multiple scenarios, highlighting its efficacy in addressing the challenges of privacy-preserving decentralized learning.

cs.LG↗

arXiv2025

A UV to X-Ray View of Soft Excess in Type 1 Active Galactic Nuclei. II. Broadband Correlations

The physical origin of soft X-ray excess (SE) is a long lasting question, with two prevailing theories -- ``warm corona'' and ``ionized reflection'' -- dominating the discussion. In the warm corona scenario, SE originates from upscattered disk photons and should therefore correlate strongly with UV emission. Conversely, in the ionized reflection scenario, SE arises from the illumination of the accretion disk by the hot corona and should primarily correlate with the hard X-ray primary continuum (PC). In this second paper of the series, we investigate the correlations among SE, UV and PC, leveraging a sample of 59 unobscured type 1 AGNs compiled in \citet{Chen+2025a}. Our extensive analysis reveals a strong intrinsic correlation between SE and UV that remains robust after controlling for PC ($p_\mathrm{null}\lesssim 10^{-7}$). In contrast, the correlation between SE and PC is weaker but still statistically significant ($p_\mathrm{null}\lesssim 5\times 10^{-2}$). These findings suggest that, in addition to ionized reflection -- a natural outcome of the hot corona illuminating the disk -- a warm corona component is essential, and may even dominate, in producing the soft excess. Additionally, we report a mild anti-correlation between SE strength ($q$) and PC photon index ($\Gamma_\mathrm{PC}$) ($p_\mathrm{null}=10^{-2}$), suggesting a potential competition between the warm and hot coronae. Finally, we find that the $\Gamma_\mathrm{PC}$ values we derived with SE properly incorporated exhibit a much weaker correlation with $\lambda_\mathrm{Edd}$ ($p_\mathrm{null}=2\times 10^{-2}$) than previously reported in the literature. This highlights the critical role of accurately modeling SE in studies of the $\Gamma_\mathrm{PC}$--$\lambda_\mathrm{Edd}$ relation.

astro-ph.HE↗