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Abstract We present a new public-domain Molecular Fitting Analysis Tool (MOFAT) designed to probe molecule-forming regions in supernovae through analysis of molecular features in the near- and mid-infrared. MOFAT employs a novel data-driven approach to explore the physical properties of these regions using time-independent radiative transfer simulations that include multidimensional, clump-like structures, constrained by high-precision observations. Such structures are required to reproduce the flux ratio between fundamental and overtone bands, overcoming limitations of traditional one-zone forward modeling, such as optical depth effects and initial configurations. Our approach enables spectral fits that can reconstruct overall abundances and temperatures and determine parameterized small-scale structures associated with physical instabilities. We systematically study the relationship between physical parameters and the profiles of CO and SiO, showing that free parameters are constrained, while detection of small-scale structure requires optically thick bands. As a demonstration, MOFAT is applied to SN 2024ggi at +285 and +385 days postexplosion. We find that CO formation triggers SiO formation in the inner layers of the CO-rich region previously studied. The inner edge of the SiO-emitting region recedes with velocities ofv₁ ≈ 1500–1000 km s⁻¹, indicating continued SiO formation. The SiO mass decreases from ∼(2–6) × 10⁻³M_⊙by roughly an order of magnitude, suggesting ongoing evaporation. SiO features indicate clumping, but most of the flux originates from optically thin regions. SiO contributes negligibly to cooling, and we find no evidence for dust formation. Finally, we discuss observational strategies to trace the evolution of molecule formation and its connection to dust formation. 

Graph neural networks (GNNs) are the dominant approach to solving machine learning problems defined over graphs. Despite much theoretical and empirical work in recent years, our understanding of finer-grained aspects of architectural design for GNNs remains impoverished. In this paper, we consider the benefits of architectures that maintain and update edge embeddings. On the theoretical front, under a suitable computational abstraction for a layer in the model, as well as memory constraints on the embeddings, we show that there are natural tasks on graphical models for which architectures leveraging edge embeddings can be much shallower. Our techniques are inspired by results on time-space tradeoffs in theoretical computer science. Empirically, we show architectures that maintain edge embeddings almost always improve on their node-based counterparts—frequently significantly so in topologies that have “hub” nodes. 

Abstract In this paper, the suitability of fast-declining Type Ia supernovae (SNe Ia) as cosmological standard candles is examined utilizing a “Hubble Flow” sample of 43 of these objects observed by the Carnegie Supernova Project (CSP). We confirm previous suggestions that fast-declining SNe Ia offer a viable method for estimating distances to early-type galaxies when the color-stretch parameter,s_BV, is used as a measure of the light-curve shape. As a test, we employ the Tripp method, which models the absolute magnitude at maximum as a function of light-curve shape and color. We calibrate the sample using 12 distance moduli based on published infrared surface-brightness fluctuations to derive a value of the Hubble constant that is in close agreement with the value obtained for the full sample of CSP SNe Ia using the same methodology. We also develop a new and simple method of estimating the distances of fast decliners based only on their colors at maximum (and not light-curve shape) and find that it leads to similar results as with using the Tripp method. This “color” technique is a powerful tool that is unique to fast-declining SNe Ia. We show that the colors of the fast decliners at maximum light are strongly affected by photospheric temperature differences and not solely due to dust extinction, and provide a physical rationale for this effect. 

Abstract We present James Webb Space Telescope (JWST) Near-Infrared Spectrograph observations of SN 2024ggi, spanning wavelengths of 1.7–5.5μm at +285.51 and +385.27 days postexplosion. These nebular spectra are dominated by asymmetric emission lines from atomic species including H, Ca, Ar, C, Mg, Ni, Co, and Fe, indicative of an aspherical explosion. The other strong features are molecular CO vibrational bands from the fundamental and first overtone. We introduce a novel, data-driven approach using non–local thermodynamic equilibrium three-dimensional (3D) radiative transfer simulations to model the CO emission with high fidelity. This method enables us to constrain the 3D CO distribution and its radial temperature structure. CO formation is found to occur prior to day +285, with subsequent evolution characterized by progressive evaporation. The CO mass decreases from approximately 8.7 to 1.3 ×10⁻³M_⊙, while the average temperature drops from ≈2900 to ≈2500 K. Concurrently, the CO distribution transitions from nearly homogeneous to highly clumped (density contrast increasing fromfc≈ 1.2 to 2). The minimum velocity of the CO-emitting region remains nearly constant (v₁≈ 1200 to 1100 km s⁻¹), significantly above the receding photosphere velocity (v_ph≈ 500 km s⁻¹), suggesting the photosphere resides within Si-rich layers. However, the temperature profile indicates that only a narrow zone reaches the conditions necessary for SiO formation. Due to a lack of observational constraints, SiO clumping is not modeled, and thus, synthetic SiO profiles for mass estimates are not highlighted. We discuss the implications of these findings for dust formation processes in SN 2024ggi.