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Cheng Cheng

Publications and source records attributed to Cheng Cheng.

At least 37 records · Page 2Linked to original sources

Ly$α$ Escape in JWST/NIRCam F430M-Selected H$α$ Emitters at $z\simeq5.5$

We study the Ly$α$ escape fraction ($f_{\rm esc}$) in an H$α$-selected sample of star-forming galaxies at $z\simeq5.5$, identified via JWST/NIRCam F430M excess and covered by archival VLT/MUSE data. By anchoring the intrinsic Ly$α$ production to H$α$ emission, our approach provides a direct and Ly$α$-unbiased probe of the escape of Ly$α$ photons in galaxies with SFR $\gtrsim 0.1\,M_\odot\,{\rm yr^{-1}}$ at this epoch. Ly$α$ emission is detected in 3 out of 12 galaxies covered by VLT/MUSE. Combining detections and upper limits, we place a conservative upper bound of $\langle f_{\rm esc}^{\rm Lyα} \rangle < 0.32$ on the population-averaged Ly$α$ escape fraction. We find that Ly$α$ detections are preferentially associated with nearly dust-free systems, while no clear correlation between SFR and $f_{\rm esc}$, suggesting a stochastic picture of Ly$α$ escape. Interestingly, three of the four Ly$α$-detected galaxies reside within a known overdense structure, suggesting that local environment may further facilitate Ly$α$ photons escape. Our H$α$-selected approach establishes a general and scalable framework for probing Ly$α$ escape by combining JWST medium- or narrow-band imaging with ground-based spectroscopic data, enabling systematic and less biased studies of Ly$α$ visibility in typical star-forming galaxies during the post-reionization era.

astro-ph.GA↗

A RELHIC twin candidate near the galaxy M51

We report the discovery of a pair of H I clouds near M51 (NGC 5194) using the Five-hundred-meter Aperture Spherical radio Telescope (FAST). These clouds have no optical counterparts and are potential candidates for Reionization-Limited H I Clouds (RELHICs). We search for compact H I sources in deep FEASTS observations using SoFiA and remove objects with optical counterparts through cross-matching with the DESI Legacy Imaging Surveys. The remaining candidates are modelled as hydrostatic H I structures embedded in Navarro-Frenk-White dark matter haloes and compared with RELHIC predictions and TNG50 simulations. We identify two H I clouds, Cloud S and Cloud N, at projected distances of 70--90 kpc from M51. Each cloud has an H I mass of approximately 10^6.5 solar masses, a velocity dispersion of about 20 km/s, and no detectable optical counterpart down to a g-band surface brightness limit of approximately 27.5 mag arcsec^-2. Their stellar luminosities are constrained to be below 10^5 solar luminosities. Their H I properties are consistent with RELHIC predictions, corresponding to host halo masses of 3.7 +- 0.4 * 10^9 solar masses. Cloud S and Cloud N are promising but not definitive RELHIC candidates. A tidal origin remains possible in the interacting M51 system, especially because the clouds are unresolved by FAST and Cloud N may show a velocity gradient. Future high-resolution interferometric observations will be crucial for distinguishing between starless dark matter haloes and tidal debris.

astro-ph.GA↗

Megaparsec-Scale Neutral Hydrogen Flows in the Neighborhood of Hickson Compact Group 100

The evolution of galaxies is strongly influenced by their ability to exchange gas with their surroundings, yet direct observational constraints on these processes remain scarce. Using ultra-deep neutral hydrogen (HI) observations with the Five-hundred-meter Aperture Spherical Telescope (FAST), we detect a diffuse HI structure extending over $\sim$1 Mpc around the compact galaxy group HCG 100, with integrated column densities down to $\sim$$8.6\times10^{17}$ cm$^{-2}$. This structure is among the most extended and lowest-density neutral gas systems ever observed in emission. The HI gas forms a coherent envelope connecting the compact group to neighboring galaxies and shows a large-scale coherent velocity gradient around HCG 100 extending across $\sim$0.6 Mpc. The extended structure contains $\sim$$1.4\times10^{10}$ $M_\odot$ of diffuse neutral gas, implying that up to $\sim$40$-$50\% of the HI gas resides outside galaxies. Such a large diffuse HI structure may arise either from large-scale tidal debris or gas accretion from the surrounding cosmic web. Our results demonstrate that massive reservoirs of diffuse neutral gas can persist on megaparsec scales around galaxy groups for extended periods, providing a previously unseen component of baryon cycling in dense environments.

astro-ph.GA↗

The FAST All Sky HI Survey DR2: the FASHI Catalog and the HI Mass Function

The FAST All Sky HI Survey (FASHI) conducted with the Five-hundred-meter Aperture Spherical radio Telescope (FAST) has mapped $\sim 19500\,\mathrm{deg}^2$ of the sky north of DEC $= -14^{\circ}$, detecting $156411$ extragalactic HI sources at $z< 0.09$ with a median sensitivity of $0.57\,\mathrm{mJy}\,\mathrm{beam}^{-1}$ at a velocity resolution of $6.4\,\mathrm{km}\,\mathrm{s}^{-1}$. The survey achieves unprecedented depth and area coverage, significantly improving upon previous single-dish surveys. Through a detailed completeness analysis that accounts for the survey's non-uniform sensitivity and line-width dependence, we construct a robust HI mass function (HIMF) using a completeness-corrected sample of over $109000$ sources. The HIMF is robustly constrained down to $M_{\mathrm{HI}}\sim 10^{6.2}\,M_{\odot}$. When systematic uncertainties are included, the HIMF is well described by a single-Schechter function with a characteristic mass $\log (M_{*} / h_{70}^{-2}M_{\odot}) = 9.89\pm 0.02$, low-mass end slope $α= -1.31\pm 0.02$, and amplitude $ϕ_{*} = (6.38\pm 0.49)\times 10^{-3}\,h_{70}^{3}\,\mathrm{Mpc}^{-3}\,\mathrm{dex}^{-1}$. The derived cosmic HI density is $Ω_{\mathrm{HI}} = (4.71\pm 0.03_{\mathrm{stat}}\pm 0.40_{\mathrm{sys}})\times 10^{-4}\,h_{70}^{-1}$. FASHI provides the most extensive and sensitive HI catalog to date, establishing an important benchmark for studies of gas accretion, galaxy evolution, and large-scale structure in the local universe.

astro-ph.GA↗

Model-Agnostic Population Inference for Gravitational-Wave Astronomy: From LVK to LISA

Inferring the intrinsic population of compact binary mergers is complicated by detector selection biases and measurement uncertainties. Traditional parametric methods are limited by the need to presuppose functional forms, introducing model-dependent biases. To overcome these limitations, we introduce an inference framework powered by deep generative modeling. We develop a flexible, data-driven population model using a Correlated Compound-Mixture Density Network. This architecture integrates mixture models to handle multimodality, Gaussian copulas for parameter dependencies, and a library of flexible marginal distributions. The network is trained to approximate the posterior distribution of the population's hyperparameters using amortized variational inference with Normalizing Flows on catalogs of gravitational-wave events. We demonstrate the framework's capabilities in two distinct regimes. First, using simulated catalogs of supermassive black hole binary mergers for the Laser Interferometer Space Antenna (LISA), we show that the method accurately recovers complex three-dimensional distributions and absolute merger rates from sparse datasets, effectively correcting for selection effects and measurement uncertainties. Second, we validate the framework on real observational data from the LIGO-Virgo-KAGRA GWTC-3 catalog, successfully inferring the population of stellar-mass binary black holes using an injection-based selection effect correction. Our results confirm that the method is robust, scalable, and applicable across different detector sensitivities and source populations.

astro-ph.IM↗

What is the True HI Gas Content in Massive Quiescent Galaxies in the Local Universe?

While massive quiescent galaxies are known to be poor in atomic hydrogen (HI), their true HI content remains poorly constrained due to the limited sensitivity and morphological biases of existing surveys. We present deep HI observations using the Five-hundred-meter Aperture Spherical radio Telescope (FAST) for a representative sample of 78 low-redshift massive quiescent galaxies, selected by stellar mass ($M_\ast > 10^{10} M_\odot$), color (NUV$-r > 5$), and specific star formation rate ($\rm \log sSFR < -11\ yr^{-1}$). Our observations reach a remarkable sensitivity of $\log(M_{HI}/M_\ast) = -2.6$ for 55 targets and $\log(M_{HI}/M_\ast) = -3.2$ for 23 targets. We find that one-third of the sample follows the HI scaling relation derived from previous surveys, while the remaining two-thirds exhibit significantly lower HI content. The HI mass fraction shows no clear correlation with specific star formation rate, NUV$-r$ color index, stellar surface mass density, and concentration. Our FAST sample shows remarkable similarity to the $ATLAS^{3D}$ sample which only includes early-type galaxies, both in its high fraction of HI-poor galaxies and its high satellite fraction among HI-poor galaxies. These results suggest that while both early-type morphology and environment may contribute to the extreme HI deficiency, neither factor alone fully explains the observed gas depletion, indicating that additional physical mechanisms must be responsible for the extreme HI deficiency prevalent in massive quiescent galaxies.

astro-ph.GA↗

A massive barred spiral galaxy at z = 5.102 discovered by JWST

We report M1149-BSG-z5, a barred spiral galaxy at $z = 5.102$, identified in the parallel field of MACS J1149+2223 with JWST and HST. M1149-BSG-z5 is the highest redshift barred galaxy candidate to date. Both isophote ellipse fitting and structural modeling support a stellar bar of length $a_\mathrm{bar} \approx 4.5$ kpc, and extended spiral arms peaking at $r \approx 5.5$ kpc. M1149-BSG-z5 is a massive main sequence star-forming galaxy, with a stellar mass of $10^{10.45}\rm M_\odot$ and a star-formation rate of $144\,\rm M_\odot/yr$. A concentrated bulge is embedded in an extended disk with a global Sérsic index $n = 2.37$. With an effective radius of $R_{e} = 2.61\rm \ kpc$, M1149-BSG-z5 is larger than typical galaxies at $z \sim 5$ and comparable to barred galaxies at $2 < z < 4$. M1149-BSG-z5 also hosts a broad-line AGN, with a relatively low black-hole-to-stellar mass ratio of $\rm M_{\rm BH}/M_\ast\sim10^{-3}$. Its metal-enriched emission-line properties indicate that it is already chemically evolved. These properties imply M1149-BSG-z5 as an early-assembled and structurally evolved galaxy. We also find that M1149-BSG-z5 resides in an overdense region with a nearby companion galaxy, suggesting an interaction-driven bar formation mechanism. Its concentrated light, early assembly and main-sequence star formation also suggest baryon-dominated, gas-rich conditions, where gravitational instability can further accelerate the bar formation.

astro-ph.GA↗

ULTIMATE-deblending I. A 50-band Ultraviolet to Mid-infrared Photometric Catalog Combining Space- and Ground-based Data in the JWST/PRIMER survey

Our understanding of the early Universe has long been limited by biased galaxy samples selected through various color criteria. With deep JWST infrared imaging, mass-complete galaxy samples can now be studied up to $z \sim 8$ for the first time. However, recent work has revealed systematic uncertainties in measuring physical properties of galaxies based solely on JWST/NIRCam and HST photometry, due to their limited wavelength coverage. This highlights the need for supplementary data, particularly in the rest-frame UV and near-infrared. Here we present the ULTIMATE-deblending project, which will eventually deliver self-consistent UV to radio photometry for galaxies detected in deep JWST surveys, including both NIRCam and MIRI data. In this first paper, we release a 50-band photometric catalog spanning CFHT/U to JWST/MIRI F1800W, covering a total of 627.1 arcmin$^2$ across two JWST/PRIMER fields. We detail the reduction of the JWST imaging data, the photometric procedures, and the spectral-energy-distribution-fitting methodology used to derive the galaxy properties. Compared with photometry including only HST and JWST bands, the inclusion of deblended low-resolution photometry from ground-based telescopes improves the accuracy of photometric redshifts by $\sim$40%, while reducing the outlier fraction by $\sim$60%. This galaxy sample can serve as a key reference for statistical studies of galaxy formation and evolution in the early Universe. The UV-to-MIR catalogs and JWST mosaics from the ULTIMATE-deblending project have been made publicly available.

astro-ph.GA↗

Nemotron 3 Ultra: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning

We introduce Nemotron 3 Ultra, a 550 billion total and 55 billion active parameter Mixture-of-Experts Hybrid Mamba-Attention language model. We pre-trained Nemotron 3 Ultra on 20 trillion text tokens, then extended the context length to 1M tokens, and post-trained using Supervised Fine Tuning (SFT), Reinforcement Learning (RL), and Multi-teacher On-Policy Distillation (MOPD). Nemotron 3 Ultra is our most capable model yet, employing multiple key technologies - LatentMoE, Multi Token Prediction (MTP), NVFP4 pre-training, multi-environment RLVR, MOPD, and reasoning budget control. Nemotron 3 Ultra achieves up to ~6x higher inference throughput as compared to state-of-the-art publicly available LLMs while attaining on-par accuracy. The state-of-the-art accuracy, high inference throughput, and 1M token context length make Nemotron 3 Ultra ideal for long-running autonomous agentic tasks. We open-source the base, post-trained, and quantized checkpoints, along with the training data and recipe on HuggingFace.

cs.CL↗

Testing Cosmic Distance Duality Relation and Transparency with DESI DR2

The Cosmic Distance Duality Relation (CDDR) is a fundamental principle of standard cosmology, linking luminosity (LD) and angular diameter distances (ADD). This work investigates the validity of the CDDR and cosmic transparency by combining the latest Baryon Acoustic Oscillations (BAO) data from DESI DR2, Type Ia Supernovae from Pantheon+, and cosmic chronometers. To address the redshift mismatch between datasets, two distinct reconstruction techniques are employed: Gaussian Process Regression (GPR) and the Free-Knots Method (FKM). The analysis performs null tests on the CDDR under different cosmological priors, finding that the null hypothesis holds and the CDDR is valid within statistical uncertainties. Although mild deviations are observed from the local distance ladder prior, internal consistency calibration indicates that these discrepancies and the Hubble tension may share a common origin, possibly related to systematic effects or new physics. Using multiple phenomenological parameterizations, the deviation parameter is also found to be statistically consistent with zero (e.g., $η_1 = 0.023 \pm 0.027$ for the linear model under Planck priors). Furthermore, the study finds no statistically significant evidence for cosmic opacity. The average of the opacity derivative is compatible with zero ($\langle dτ/dz \rangle = 0.0409 \pm 0.1024$ for GPR and $0.0730 \pm 0.1607$ for FKM). Based on these null results, stringent constraints are placed on the parameter space of Axion-Like Particles (ALPs) and Mini-Charged Particles (MCPs).

astro-ph.CO↗

Reconstructing Barrow Holographic Dark Energy in $f(Q,T)$ Gravity and Cosmic Constraint

In this work, we reconstruct the cosmological evolution of Barrow Holographic Dark Energy (BHDE) within the framework of modified gravity $f(Q,T)$. Working in the coincident gauge, we incorporate the holographic principle into non-metric gravity with non-minimal matter coupling. To address the dynamical complexity, we adopt a reconstruction approach, deriving the matter density evolution from the modified field equations rather than imposing a conserved fluid a priori. We perform parameter estimation using the latest observational data, including Type Ia supernovae, BAO, and direct Hubble parameter measurements. Our results show that the model provides a theoretical framework to describe late-time cosmic evolution and the universe's accelerated expansion. Despite the additional complexity introduced, the model offers an alternative approach for investigating dark energy within modified gravity theories.

astro-ph.CO↗

Holographic dark energy in a coasting cosmology

Coasting cosmology offers an intriguing and straightforward framework for understanding the universe. In this work, we employ the Trans-Planckian Censorship Criterion (TCC) conjecture to test the viability of the coasting cosmology and propose an entropic dark energy (EDE) model within this framework. By applying the holographic principle to constrain the dark energy density and adopting the Bekenstein entropy and Tsallis entropy as the constraining entropies of the system, we find that, in a holographic coasting cosmological framework where dark energy and dark matter evolve independently, the Tsallis entropy satisfies certain general assumptions better than the Bekenstein entropy. Thus, there may be a fundamental relationship between Tsallis entropy and dark energy. We utilize observational data from Type Ia Supernovae (SNIa), Baryon Acoustic Oscillations (BAO), and Cosmic Chronometers (CC) to constrain EDE model. The optimal Tsallis parameter obtained aligns well with theoretical expectations. To evaluate the model's fit to the observed data, we calculate the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Kullback Information Criterion (KIC), and compare these metrics with those derived from $Λ$CDM, under which the model shows some improvement. Overall, this model provides a novel and simple on the evolution of the universe.

astro-ph.CO↗

Testing the cosmological principle with quasars

The inferred velocity is consistent at the 1.56 σ level with the value of 370 km/s from a purely kinematic interpretation of the CMB dipole. Based on the motion direction component analysis, we have not found any significant deviation from cosmological principle in current released quasars data. The cosmological principle posits that the universe is homogeneous and isotropic on the large scales. In history, the cosmological principle was confirmed by various cosmological observations from CMB to large scale structure. However, several new challenges to the cosmological principle were reported in recent years, particularly in radio observations from overdispersed radio source counts to quasars. Here, we firstly present studies on the peculiar velocity of large-scale anisotropy by measuring the dipole signal from the DESI DR1 catalogue with a sample of 1,176,570 quasars (0.8 < z < 3.0). Our analysis reveals the peculiar velocity of $|v| = 443.8 \pm 204.1$ km/s towards $(l, b) = (107.4^\circ \pm 86.8^\circ, 28.4^\circ \pm 45.2^\circ)$ in Galactic coordinates.The motion direction deviates from the CMB dipole (264.02$^\circ$, 48.253$^\circ$). The inferred velocity is consistent at the 1.56 $σ$ level with the value of 370 km/s from a purely kinematic interpretation of the CMB dipole. Based on the motion direction component analysis, we have not found any significant deviation from cosmological principle in current released quasars data.

astro-ph.CO↗

The Structure and Evolution of LRDs: Insights from JWST NIRSpec Medium and High Resolution Spectroscopy at $z\sim4$

We present an analysis of medium/high-resolution JWST/NIRSpec spectra for 11 LRDs at $z \sim 4$. By decomposing the broad and narrow components of the Balmer emission lines, we investigate the connection between line emission and UV/optical continua for the LRD population. We find that the broad H$α$ luminosity strongly correlates with the optical continuum (but not with the UV), indicating a common AGN origin for both. In contrast, the [O III] line strength is correlated with the UV continuum rather than the optical. Using the width and luminosity of the broad H$α$ line, we estimate central black hole masses of $10^6-10^8 M_{\odot}$ accreting at high Eddington ratios, consistent with an early ($λ_{\rm Edd} \sim 0.6$), rapid-growth phase of AGN evolution. Assuming a constant mass accretion rate in the framework of slim-disk models, we infer growth timescales of $\sim 10^5-10^7\rm yr$, and suggest LRDs may evolve into narrow-line Seyfert 1 galaxies. Upper limits from our spectra indicate that LRDs exhibit intrinsically weak optical Fe II emission compared to typical AGN. To simultaneously account for the inferred broad-line region size and observed luminosity, we propose a "Clumpy Envelope" model in which the optical emission arises from an extended, clumpy gas with a characteristic radius of tens of light-days. The diversity in observed optical continuum shapes can be explained by radial temperature gradients and self-absorption effects within this structure. Our results demonstrate the power of JWST high-resolution spectroscopy in probing the central engines and physical nature of the LRD population.

astro-ph.GA↗

OPT-Engine: Benchmarking the Limits of LLMs in Optimization Modeling via Complexity Scaling

We investigate the capabilities and scalability of Large Language Models (LLMs) in optimization modeling, a domain requiring structured reasoning and precise formulation. To this end, we introduce OPT-ENGINE, an extensible benchmark framework with quantifiable and controllable complexity. OPT-ENGINE spans ten canonical Operations Research problems, systematically scaling from Linear Programming to Mixed-Integer Programming, providing a structured environment to probe the limits of automated problem formulation and solving. Utilizing OPT-Engine, we address three pivotal research questions. First, we examine whether Pure-Text Reasoning (PTR) via classical Chain-of-Thought can efficiently tackle optimization tasks, finding that PTR suffers from a critical robustness gap as task complexity increases. Second, we examine whether integrating external computational tools can mitigate PTR's arithmetic weaknesses and improve performance. Our results indicate that while such tools help with local calculations, they still fail to adhere to global optimization constraints. Finally, we pinpoint that for the current SOTA paradigm, Solver-integrated Reasoning (SIR), the automated formulation of constraints represents the primary bottleneck. These findings clarify the limitations of current paradigms and provide a structured roadmap for developing next-generation LLMs for optimization modeling. We release our code and data to facilitate future research (https://github.com/Cardinal-Operations/OPTEngine).

cs.CL↗

JWST's PEARLS: A clumpy ring galaxy at $z = 4.0148$

Ring galaxies are an uncommon class of galaxies whose morphology is closely related to dynamical processes that govern galaxy evolution. Some ring galaxies, known as "collisional ring galaxies", are thought to form as a consequence of head-on collisions between galaxies, and a number of high-redshift collisional ring galaxies have been discovered and/or studied in the era of the James Webb Space Telescope (JWST). In this paper, we present HST/ACS, JWST/NIRCam, and JWST/NIRSpec observations of a candidate ring galaxy at $z_{\rm spec} = 4.0148$, previously identified as a potential gravitational lens. The galaxy exhibits a complex morphology, including three bright clumps along an apparent ring with radius $\approx 0.25$" $\simeq 1.8$ kpc. It has a total SFR $= 140^{+20}_{-30}$ ${\rm M}_{\rm \odot}$ yr$^{-1}$ and $\log(M_\ast/{\rm M}_\odot) = 10.41^{+0.11}_{-0.13}$, making it similar to other high-redshift collisional ring galaxies. Although we argue strongly in favor of the collisional ring explanation, we cannot entirely rule out a galaxy-galaxy strong lensing explanation for the system's morphology, in which a foreground galaxy at $z \simeq 1.7$ lenses a galaxy at $z \simeq 4.0$ into an Einstein ring-like configuration; to confirm the nature of this source, we require kinematic information via high spectral resolution observations. We suggest that current and future gravitational lens surveys should consider high-redshift ring galaxies as possible but significant contaminants.

astro-ph.GA↗

Stable phase retrieval from short-time linear canonical transforms of signals in Gaussian shift-invariant spaces

Gabor phase retrieval for signals has attracted considerable attention in recent years. For the more general short-time linear canonical transform (STLCT), which arises naturally in optical systems and canonical time--frequency analysis, existing work has so far focused mainly on uniqueness and sampling conditions. Explicit reconstruction formulas, quantitative stability estimates, and robust reconstruction algorithms, however, are still missing. In this paper, we study uniqueness, stability, and robust reconstruction for phase retrieval from phaseless STLCT measurements in the complex Gaussian shift-invariant space $V_β^\infty(φ)$. We first prove that every signal in $V_β^\infty(φ)$ is uniquely determined, up to a global unimodular constant, by its phaseless STLCT measurements on the semi-discrete set $\fracβ{2}\mathbb Z\times\mathbb R$, and we derive an explicit reconstruction formula. We then establish stability on intervals under an anchor-point condition, showing that the stability constant is governed by the maximal spacing between adjacent anchor points rather than by the radius of the whole interval. This prevents exponential deterioration with respect to the interval size. Motivated by the practical setting in which only finitely many discrete noisy magnitude samples are available, we further develop an explicit reconstruction algorithm with quantitative robustness guarantees, where the reconstruction error is controlled by the discretization parameters, the noise level, and the conditioning induced by the anchor points. In the Fourier case, our results recover the corresponding Gabor phase retrieval results of Grohs and Liehr and provide improved stability constants.

math.FA↗

Hyperbolicity analysis of the linearised 3+1 formulation in the Teleparallel Equivalent of General Relativity

We study the properties of the principal symbol of the 3+1 equations of motion in Teleparallel Equivalent of General Relativity (TEGR) and assess the conditions for hyperbolicity. We use the Hamiltonian formulation based on the vectorial, antisymmetric, symmetric trace-free, and trace (VAST) decomposition of the canonical variables in the Hamiltonian formalism, and the Hamilton's equations previously presented in the literature. We study the system of differential equations at the linear level in one dimension, and show that the principal symbol has a sector with imaginary eigenvalues, which renders the system not hyperbolic. This situation is circumvented by identifying the problematic sectors, which are an isolated system and can be removed by a gauge fixing. We prove that the remaining system of equations is strongly hyperbolic. We also present the system in three dimensions. This is the first practical use of Hamilton's equations in TEGR, and our work can be extended for proving well-posedness in spherical symmetry, and establish numerical relativity setups in TEGR.

gr-qc↗