Many reasoning tasks require short partial satisfying assignments (implicants), sometimes focusing on a set of important variables. SAT-to-Ising-QUBO formulations are implicitly designed so that ground states correspond to total assignments, since the Ising/QUBO model assigns a value to every spin and has no native representation of unassigned variables. We introduce an Ising/QUBO framework that incorporates "don't-care" semantics into the quadratic model via a dual-polarity representation, enabling the retrieval of short implicants. The encoding supports implicant shrinking and projection through minor objective modifications. We provide parameter regimes under which ground states correspond to short partial satisfying assignments, achieving minimality and, when the quadratic penalty function permits, minimum-cardinality. We empirically evaluate the encoding with simulated annealing on random 3-SAT enumeration benchmarks and non-CNF formulas, showing that it leaves about one-third of variables unassigned on random 3-SAT formulas while preserving satisfiability, and that consecutive polarity-freezing rounds achieve minimality (and minimum-cardinality) with high probability.

We study the spectrum of 4-cycle row-stochastic matrices. For real eigenvalues the spectral region is [-1,1]. For nonreal eigenvalues a+ib we derive necessary conditions in terms of the real and imaginary parts, including the inequality a+|b| <= 1 and the condition (b^2+a^2+a)^2+2a^2-b^2 >= 0. We also prove conversely that every point in the corresponding interior region occurs as an eigenvalue of a 4-cycle matrix. The proof is organized through a reformulation of the characteristic equation, an argument parametrization, a convex-analytic criterion, and explicit boundary constructions. Hence, the spectral region for the 4-cycle row-stochastic matrices is exactly and explicitly determined.

Large Language Model (LLM)-based agent systems are increasingly used for scientific tasks, yet their practical capability remains constrained by the narrow scope of manually curated tools they can invoke. Much scientific computational functionality already exists in open-source code repositories, but these resources remain difficult to standardize, operationalize, and invoke reliably for agent use. Here we present ToolRosella, a framework that automatically transforms heterogeneous scientific code repositories into standardized, agent-invocable tools. ToolRosella combines repository analysis, tool interface construction, execution testing, and iterative repair to address the problem of repository-to-tool standardization. Across 122 GitHub repositories spanning 35 subdisciplines in six domains, ToolRosella reaches a 61.5\% repository conversion success rate after iterative repair, with a 4.4 speedup over human engineers. The resulting 1,580 callable tools support a downstream task success rate of 84.0\% and improve performance when integrated into other agent frameworks, particularly on tasks whose required tools are absent from fixed, curated inventories.

We explicitly describe the tropicalization of a cluster variety of finite type C, realizing it as the space of axially symmetric phylogenetic trees. We also find all occurring sign patterns of coordinates, for both the cluster variety and the cluster configuration space. We show that each of the corresponding signed tropicalizations is, combinatorially, dual to either a cyclohedron or an associahedron. As additional results, we construct Gröbner and tropical bases for the defining ideals of both varieties, and classify the arising toric degenerations.

Nonlinear energy exchange between vibrational modes underlies phenomena ranging from internal resonance and wave mixing to frequency-comb generation, yet modal interactions are typically inferred from spectra rather than directly observed in space. Here, we image nonlinear modal energy routing in a nearly mirror-symmetric microelectromechanical resonator using phase-locked multi-harmonic stroboscopic interferometry. By reconstructing the spatial eigenmode content of individual harmonics, we show that harmonics generated by a driven mode can be carried by distinct spatial eigenmodes, directly resolving spatial pathways of nonlinear energy transfer. Our measurements further reveal that this modal routing persists away from integer frequency matching: in the off-resonant regime, generated harmonic components are dominated by eigenmodes sharing the driven mode's mirror parity, whereas spectrally closer opposite-parity modes remain strongly suppressed. A nonlinear modal framework based on geometric nonlinearity shows that the relevant cubic coupling coefficients factorize into symmetry-dependent modal-overlap integrals, identifying mirror parity as the selection rule for nonlinear modal interaction. This work identifies spatial symmetry as a design parameter for nonlinear energy routing and provides a route to symmetry-engineered control of energy flow in multimode nonlinear wave systems.

Integrated circuits are a cornerstone of modern information technology, and analog wave-based architectures could enable fast and efficient processing beyond conventional charge electronics. In magnonics, spin waves provide a highly tunable, compact and energy-efficient medium for on-chip microwave signal transport and processing. However, progress has been limited to isolated elements or short devices, severely limiting the overall functional complexity and scalability. Here we realize the key elements of universal magnonic circuitry, using a single-step direct laser writing process in yttrium iron garnet, and monolithically cascade them in multi-stage programmable devices and networks. Using magneto-optical Kerr effect microscopy, we show efficient spin-wave propagation and preserved phase coherence in waveguide structures for hundreds of wavelengths. In coupled waveguides, we observe complete and periodic power transfer over several coupling lengths, and in phase shifters we achieve arbitrary, tunable phase delays. By cascading these elements, we realize programmable splitters, frequency demultiplexers, and phase-controlled 2x2 routers, where output power and relative phase can be programmed on demand via external fields. Finally, we realize programmable magnonic interferometric meshes for on-chip radio-frequency signal routing, with up to six magnonic inputs and outputs and seven cascaded stages, without the need for intermediate amplification. These direct-write cascaded networks bridge a long-standing gap in magnonic scalability, offering a viable pathway toward integrated, large-scale architectures for both classical and quantum processing.

We present multi-epoch optical spectroscopy of the interstellar comet 3I/ATLAS obtained between December 2025 and January 2026 (heliocentric distances 1.8-3.3 au), yielding post-perihelion production rates and mixing ratios for CN, C$_3$, C$_2$, CH, and gaseous metals (Fe I and Ni I). Our results show that the coma is less depleted in C$_2$ after perihelion than before, indicative of subsurface activation or compositional heterogeneity. The outgassing profiles reveal a pronounced perihelion asymmetry: CN and metal production rates decline more gradually outbound than inbound, consistent with the reported behavior of H$_2$O and implying a change in the comet's activity pattern across perihelion. Despite being metal-rich relative to its H$_2$O content, 3I follows the metal-CO correlation observed in comets of diverse origins, suggesting that gaseous metal release is more closely linked to a CO-bearing volatile reservoir than to H$_2$O, potentially in the form of metal carbonyls. In addition, the [O I] $\lambda6300$ emission shows a significant residual after subtracting the expected contributions from H$_2$O, CO$_2$, and CO, which may reflect systematic uncertainties in the photodissociation yields of those molecules or a contribution from additional oxygen-bearing parents.

For a wide class of bipartite systems with localized couplings, we establish existence of an effective light-cone for propagation of entanglement. This result yields a hard lower bound on the time it takes, under ideal conditions (no loss, no decoherence), to transport entanglement to a distant location (say, a node of a graph-structured quantum network), or to maintain it there.

Compared with the results of Planck-only analyses, recent measurements from the Atacama Cosmology Telescope (ACT) indicate a preference for a slightly bluer scalar spectral index, placing canonical inflationary models in General Relativity (GR) under mild pressure. We demonstrate that $f(T)$ gravity systematically accommodates these dataset-dependent preferences by suppressing the tensor-to-scalar ratio in monomial and hilltop potentials, and by shifting the spectral index of E-models toward the ACT-favored region. Incorporating Big Bang Nucleosynthesis bounds, we break the degeneracy between the inflationary $e$-folding number and the post-inflationary thermal history. A direct side-by-side comparison reveals that reconciling models such as the Starobinsky potential with ACT data in GR strictly necessitates a non-standard, stiff (kinetic-dominated) reheating phase. In contrast, torsional corrections in $f(T)$ gravity significantly enlarge the viable parameter space, relaxing these stringent phenomenological requirements and establishing a coherent framework that jointly constrains CMB observables and reheating dynamics.

Using characterizations in terms of various differential operators, including partial, normal, and tangential derivatives, we extend the family of Bergman spaces of $\mathcal H$-harmonic functions on the real hyperbolic ball from the range $α>-1$ to all $α\in\mathbb R$. We then generalize several properties of Bergman spaces; projection, duality, atomic decomposition, and inclusion relations, to this extended family.

We explore the ground-state properties of a single impurity immersed in a one-dimensional quantum droplet medium formed by a two-component Bose mixture. Relying on ab-initio simulations, we demonstrate that tuning the impurity-droplet interactions allows to controllably reshape the droplets density profiles and associated correlation patterns. For attractive impurity-medium couplings, the impurity becomes localized within the droplet which exhibits a density hump at the vicinity of the impurity, while repulsive interactions facilitate their phase-separation. Comparing our many-body results to the appropriate extended Gross-Pitaevskii description, we find adequate agreement for the droplet density profiles, with the effective field approach systematically overestimating impurity localization. Following a release of the external trap, we unveil that the sign and magnitude of the interactions between the impurity and the droplet hosts dictate the response of the three-component setting which experiences expansion unless strongly attractive intercomponent couplings are present. These results corroborate the role and presence of correlations in impurity-droplet mixtures and inspire future investigations on impurity physics for probing droplet configurations.

We demonstrate the applicability of large-angle convergent-beam electron diffraction (LACBED) for Burgers vector determination in monoclinic $β$-Ga$_2$O$_3$. The inner product $g \cdot b$ in this non-orthogonal system can be evaluated without a metric tensor by using the dual relationship between real and reciprocal lattice bases. Based on this framework, Burgers vectors of dislocations introduced by nanoindentation were unambiguously determined from LACBED node counts. The results are consistent with weak-beam dark-field imaging, confirming the effectiveness of LACBED for $β$-Ga$_2$O$_3$.

We provide a pedagogical introduction to eigenstate thermalization. This phenomenon, which occurs in generic quantum systems, allows one to understand why thermalization takes place in isolated systems under unitary dynamics. We motivate eigenstate thermalization using random matrix theory and discuss recent complementary results for the volume-law entanglement entropy of Haar-random states. We discuss numerical results that highlight the corresponding behaviors in quantum many-body systems.

Let $k$ be a field, $f \colon X \to Y$ a birational morphism of integral connected schemes proper over $k$ with $Y$ normal, $x \in X(k)$ lying over $y \in Y(k)$. For Tannakian categories $\mathcal{C}_X \subset \mathfrak{Vect}(X)$ and $\mathcal{C}_Y \subset \mathfrak{Vect}(Y)$, denote by $π(\mathcal{C}_X,x)$ and $π(\mathcal{C}_Y,y)$ the corresponding Tannaka group schemes. We establish a unified Tannakian criteria for the natural homomorphism $π(\mathcal{C}_X,x)\to π(\mathcal{C}_Y,y)$ to be an isomorphism. As applications, for a birational map $X \dashrightarrow Y$ between smooth projective varieties over a perfect field $k$, we prove that there exists a natural isomorphism $π^{*}(X,x)\cong π^{*}(Y,y)$ for any $* \in \{S,N,EN,F,EF,Loc,ELoc,\acute{e}t, E\acute{e}t,uni\}$. In particular, we prove that the induced homomorphism $π^{str}(X,x)\to π^{str}(Y,y)$ is an isomorphism for any birational morphism $ X \rightarrow Y$.

Let $k$ be a field, $X$ a connected scheme proper over $k$, $D\subsetneq X$ an ample effective connected divisor, $x\in D(k)$. For Tannakian categories $\mathcal{C}_X$ and $\mathcal{C}_D$ whose objects consist of vector bundles on $X$ and $D$ respectively, we establish general Tannakian criteria for the natural homomorphism \(π(\mathcal{C}_D,x)\to π(\mathcal{C}_X,x)\) to be faithfully flat, a closed immersion, or an isomorphism. As applications, under Langer type positivity assumptions, we prove that \(π^{\ast}(D,x)\longrightarrow π^{\ast}(X,x)\) is an isomorphism for $\ast\in\{S,N,EN,F, EF,Loc,ELoc,\acute{e}t,E\acute{e}t,uni\}$ over perfect fields.

Two applications of gates from the B gate equivalence class can generate all two-qubit gates. This local equivalence class is invariant under the mirror (multiplication with the SWAP gate) operation, inverse (Hermitian conjugate) operation, and the combined inverse and mirror operations. The last two symmetries are associated with the ability of a two-qubit gate to generate the two-qubit local gates and the SWAP gate in two applications. No single local equivalence class of two-qubit gates, except the B gate equivalence class, has these two symmetries. Only the planar regions of the Weyl chamber, describing the mirror operation, contain the local equivalence classes with either one of the two symmetries. We show that there exist one-parameter families of local equivalence classes on these planes, with and without the B gate equivalence class, such that each of them can be used to construct a parameterized universal two-qubit quantum circuit that involves only two nonlocal two-qubit gates. We also discuss the implementation of the gates from a few families of local equivalence classes on superconducting quantum computers for optimal generation of all two-qubit gates. We provide upper bounds on the number of two-qubit gates required to generate an arbitrary $n$-qubit gate for two families, each of which is conjectured to generate all two-qubit gates in two applications. We show that there exists a positive correlation between the area of the convex hull of the squared eigenvalues of the nonlocal part of a parameterized two-qubit gate and the fractional volume of the Weyl chamber covered in two applications of the parameterized two-qubit gate for two families of local equivalence classes.

We propose a new framework to systematically incorporate data uncertainty in Gaussian Splatting. Being the new paradigm of neural rendering, Gaussian Splatting has been investigated in many applications, with the main effort in extending its representation, improving its optimization process, and accelerating its speed. However, one orthogonal, much needed, but under-explored area is data uncertainty. In standard 4D Gaussian Splatting, data uncertainty can manifest as view sparsity, missing frames, camera asynchronization, etc. So far, there has been little research to holistically incorporating various types of data uncertainty under a single framework. To this end, we propose Graphical X Splatting, or GraphiXS, a new probabilistic framework that considers multiple types of data uncertainty, aiming for a fundamental augmentation of the current 4D Gaussian Splatting paradigm into a probabilistic setting. GraphiXS is general and can be instantiated with a range of primitives, e.g. Gaussians, Student's-t. Furthermore, GraphiXS can be used to `upgrade' existing methods to accommodate data uncertainty. Through exhaustive evaluation and comparison, we demonstrate that GraphiXS can systematically model various uncertainties in data, outperform existing methods in many settings where data are missing or polluted in space and time, and therefore is a major generalization of the current 4D Gaussian Splatting research.

We study free Carrollian quantum field theories from an algebraic perspective and explore their implications for flat space holography. As explicit examples, we construct the electric and magnetic Carrollian Weyl algebras obtained from Carroll limits of the relativistic scalar field and analyze their states, including vacuum and thermal configurations. For the massive electric theory, we find a regular Carroll-invariant vacuum state and a regular KMS state, yielding a consistent Carrollian thermodynamic system. By contrast, the massless electric and magnetic theories are more subtle: depending on the quantization, they admit either no regular distinguished vacuum or only nonregular Carroll-invariant ground states, while still supporting nonregular thermal states. We further analyze alternative classes of states in the massless electric theory, including spatially homogeneous quasifree pure states and Sorkin--Johnston states. Motivated by these results, we discuss consequences for flat space holography. We construct a well-defined state relevant for Carrollian holography whose Hilbert-space representation factorizes into a standard Fock sector and a nonseparable zero-mode sector, thereby highlighting the role of infrared degrees of freedom in the boundary theory.

We generalize the formalism of open quantum systems to introduce anyon baths. In particular, we work out a dissipative anyon bath composed of independent pairs of one-dimensional Grundberg-Hansson harmonically bound anyons, which are characterized by one statistical parameter. Using a mapping of these anyons to a bosonic bath with rescaled oscillator frequencies, we show that the original bilinear system-bath coupling assumes a particular non-polynomial form. To determine the relaxation properties, we use the imaginary-time path integral formalism together with a generalization of Wick's theorem in the form of a smearing formula. The latter allows to approximately calculate the anyon bath spectral density, which acquires a nontrivial temperature dependence. The corresponding relaxation dynamics of the dissipative harmonic oscillator in an anyon bath is found. Well defined limits are revealed for both low and high temperatures. Anyonic features turn out to be most pronounced in the regime of intermediate temperatures.

X-rays are emitted from the corona above the orbiting matter of the accretion disk and travel either directly to us or illuminate the disk. This illumination of the inner disk is enhanced by gravitational light bending, which focuses the rays towards the black hole and therefore towards the inner radii of the disk. These rays that hit the inner radii are reflected back to us, and we observe them in the X-ray reflection spectrum. In this work, we create novel general-relativistic ray-tracing simulations to investigate the effects of altering the geometry of the accretion disks of black holes on the most dominant part of the reflection spectrum, the iron K$α$ line. Work demonstrating the effect of disk geometry on the iron line has been performed, though many previous analyses have assumed a simplistic system, consisting of a point-source corona with a flat and infinitesimally thin accretion disk. We extend these models to more realistic accretion disk approximations. These include a constant-aspect-ratio disk, a radiation-pressure-dominated Shakura-Sunyaev disk, an expanded inner disk that has a nonnegligible scale height in its inner regions due to radiation pressure, as well as various warped-disk configurations. Using measurement uncertainties from XRISM, we find that nonnegligible thickness in accretion disks underestimates the black hole spin, coronal height, and inclination angle if fitted with a flat-disk model. The warped-disk model could not be fit with the flat-disk approximation.

The Chebyshev bounds for the prime-counting function, i.e., $π(x) \asymp x/\ln x$, is established in a new way. This new approach follows the outline $π(x) \asymp \bigl(\sum_{p \le x} \sqrt{\ln p / p}\bigr)^{2} \asymp x/\ln x$. Here, the second $\asymp$ is derived from the classical estimate by Mertens, i.e., $\sum_{p \le x} (\ln p)/p = \ln x + O(1)$; while the first $\asymp$ is proved by considering the difference $\bigl(\sum_{p \le x} \sqrt{\ln p/p}\bigr)^{2} - \sum_{p \le x} (\ln p)/p$, which is shown as having the same order as $π(x)$.

We present a modified gravity framework based on a principle of vacuum displacement, where the vacuum is modeled as a Higgs-type scalar field $χ$ undergoing spontaneous symmetry breaking. The macroscopic manifestation of such vacuum displacement principle is phenomenologically introduced via a low-energy effective scalar tensor coupling so that baryonic matter acts as an impurity in the vacuum substrate. This interaction leads to a restorative buoyancy force that modifies the geodesic equation and violates the Weak Equivalence Principle. We show that this mechanism naturally recovers the Schwarzschild metric in the vacuum limit while providing a Yukawa-corrected Newtonian potential in the presence of matter. This correction offers a dynamical explanation for flat galactic rotation curves and a tracking mechanism for the cosmological constant, potentially resolving the coincidence and fine-tuning problems without the need of dark sectors.

RG flows and IR phases of QFTs can be constrained by generalized symmetries and their anomalies. Broken symmetries act on the space of coupling constants of families of theories, and can also have IR-constraining family anomalies. We generalize family anomaly considerations to cases of broken generalized/categorical symmetries, including higher-group and non-invertible symmetries. We consider the anomaly inflow and SymTFTs of such generalized families of QFTs, and their implications for RG flows and constraints on the IR phases. As examples, we apply family anomalies to study the IR phases of $4d$ QCD-like theories deformed by irrelevant, multi-fermion interactions.

Autocatalytic processes underlie diverse systems in which replication is triggered at interfaces, including heterogeneous catalysis on solid substrates, enzyme activity at membranes, viral infections, biofilm growth, and spatially structured ecosystems. In a typical scenario, particles move in a bulk medium and interact with surface regions, where they may either disappear or reproduce through branching, splitting or fission. Here, we develop a general theoretical framework to understand such surface-mediated autocatalytic processes. We show that the interplay between loss and replication at surfaces gives rise to rich population dynamics. For this purpose, we derive a renewal-type nonlinear integral equation for the generating function of the population size, providing access to its full probability distribution and statistical moments. We further establish an equivalent description in terms of a Fokker-Planck equation with nonlinear Robin-type boundary conditions that encode surface reactions. Our results identify distinct dynamical regimes and universal scaling laws, and provide a unified framework to predict when surface activity promotes extinction or explosive growth. These findings offer quantitative insight into catalytic efficiency, metabolic regulation, and population persistence in spatially heterogeneous environments.

Continuous Integration and Continuous Deployment (CI/CD) have become fundamental to modern software development, with GitHub Actions (GHA) emerging as a dominant automation platform. In this study, we analyze real-world execution records of GHA, examining how developers react to workflow failures, how these workflows are utilized by projects, and how these aspects relate to project characteristics. We quantitatively analyze 258,300 workflow run records from 952 repositories and perform an in-depth qualitative analysis of 21 selected, diverse GitHub repositories to understand how maintainers and contributors interact with workflow results. We identify three distinct failure response patterns, observe that higher usage intensity of GHA workflows correlates with lower failure rates, and uncover a configuration-usage gap where the presence of configuration files masks disabled or unused workflows. Moreover, our qualitative analysis of relationships between project characteristics and utilization patterns yields five hypotheses for future validation.

A primary goal of the Habitable Worlds Observatory (HWO) is to detect and measure the abundance of biosignature molecules, such as water (H2O) and oxygen (O2), in the atmosphere of Earth analogs. This is expected to require deep spectroscopic observations lasting hundreds of hours per planet. In this context, it is essential to optimize the spectral resolution of the spectrograph to both maximize the number of planets that can be studied over the lifetime of the mission, and also to reduce the risks of false detections. The purpose of this work is to provide a framework to explore the spectral resolution design trade-space for HWO. This framework must be valid and comparable across all spectral resolutions from low (R<100) to high resolutions (R>10,000), and account for the spectral correlation of the residual starlight (i.e., speckle noise chromaticity). Leveraging the concept of "template matching", we develop a simulation toolkit based on the Python package EXOSIMS to compute the detection significance of planets and molecules. We then simulate observations of Earth analogs around 164 stars using representative mission parameters to explore the effects of the detector noise and the correlated speckle noise floor. Our findings suggest that a moderate or high resolution spectrograph (R>1,000) will provide higher sensitivity to critical molecules compared to a low resolution spectroscopy mode (e.g., R~140). The correlated speckle noise may also entirely suppress our ability to detect bio-signatures at low spectral resolutions. We conclude that a more comprehensive study combined with detailed models of its stability, and other sources of correlated noise, is necessary to fully explore the trade space of spectral resolution and detectability of key species.

X-ray microscopy has become an important tool for non-destructive testing, e.g., in battery research. However, imaging a cm-scale battery cell at the desired (sub-)micrometer resolution has been challenging. State-of-the-art X-ray microscopy techniques with a suited field-of-view provide (sub-) $10\,μm$ resolution, typically limited by the detector point-spread function and the (effective) detector pixel size. This work presents a super-resolution X-ray microscopy approach overcoming both limitations. It requires a structured X-ray illumination to encode high-frequency sample information that is natively unresolved within the resolved region of support. A mathematical framework is developed that decodes this information and generates a super-resolved image from multiple acquisitions with different phase shifts of the structured X-ray illumination. The presence of this encoded high-frequency information is first experimentally demonstrated, followed by quantification and validation using a resolution test chart. A resolution improvement by a factor of 2.2 is shown. Finally, we extend the proposed super-resolution technique to X-ray microtomography. Since the image acquisition scheme is inherently multimodal, phase-contrast and dark-field X-ray images can be computed additionally. These results showcase the direct impact of the proposed technique across both non-destructive testing and biomedical imaging, alleviating pixel-size limitations in detectors and sample-size restrictions.

We consider on an arbitrary Riemannian manifold $M$ the \textit{Leibenson equation} $\partial _{t}u=Δ_{p}u^{q}$, that is also known as a \textit{doubly nonlinear evolution equation}. We prove that if $p>1$ and $q>0$ then the Cauchy-problem \begin{equation*} \left\{ \begin{array}{ll} \partial _{t}u=Δ_{p}u^{q} &\text{in}~M\times (0, \infty), \\u(x, 0)=u_{0}(x)& \text{in}~M, \end{array}% \right. \end{equation*} has a unique weak solution for any $u_{0}\in L^{1}(M)\cap L^{\infty}(M)$.

A new framework is introduced for examining and evaluating the fundamental limits of lossless data compression, that emphasizes genuinely non-asymptotic results. The {\em sample complexity} of compressing a given source is defined as the smallest blocklength at which it is possible to compress that source at a specifically constrained rate and to within a specified excess-rate probability. This formulation parallels corresponding developments in statistics and computer science, and it facilitates the use of existing results on the sample complexity of various hypothesis testing problems. For arbitrary sources, the sample complexity of general variable-length compressors is shown to be tightly coupled with the sample complexity of prefix-free codes and fixed-length codes. For memoryless sources, it is shown that the sample complexity is characterized not by the source entropy, but by its Rényi entropy of order~$1/2$. Nonasymptotic bounds on the sample complexity are obtained, with explicit constants. Generalizations to Markov sources are established, showing that the sample complexity is determined by the source's Rényi entropy rate of order~$1/2$. Finally, bounds on the sample complexity of universal data compression are developed for families of memoryless sources. There, the sample complexity is characterized by the minimum Rényi divergence of order~$1/2$ between elements of the family and the uniform distribution. The connection of this problem with identity testing and with the associated separation rates is explored and discussed.

We study graviton production from an oscillating inflaton condensate during reheating by systematically comparing Boltzmann and Bogoliubov descriptions for inflaton potentials of the form $V(ϕ)\proptoϕ^n$ around the minimum. The Bogoliubov framework provides a unified description of graviton production, capturing both perturbative and non-perturbative effects across short and long wavelengths, whereas the Boltzmann approach is restricted to perturbative production at short wavelengths. For the quadratic case ($n=2$), we find that the two approaches yield identical graviton spectra at short wavelengths, indicating that the Boltzmann treatments fully captures perturbative gravitational production in this regime. For steeper potentials ($n>2$), however, we identify a sizable contribution arising from the non-adiabatic transition between inflation and reheating. This component is naturally incorporated in the Bogoliubov formalism but absent in the Boltzmann description, and we show that it is important over a broad range of momenta. We derive analytic approximations within both frameworks that clarify the physical origin and scaling behavior of the spectrum. Our results delineate the regime of validity of Boltzmann approaches and show that, for steeper inflaton potentials, graviton production is governed by non-adiabatic transition dynamics for which the Bogoliubov formalism provides the most appropriate description.