Determining the nature of the optical excited state (excitons or free carriers) in nanostructured materials is crucial for device design, as optoelectronic and photovoltaic technologies require different considerations regarding the optimized excited state dynamics. Power-dependent photoluminescence is widely used to distinguish between excitons and free carriers, but the classical power-law analysis oversimplifies the underlying physics when the exponent lies between the linear (pure excitons) and quadratic (pure free carriers) limits. In this work, we present a complete study enabling a direct and quantitative analysis of the free-carrier fraction based on power-dependent peak photoluminescence and placing its analysis in the context of the Saha-equation. We study Ruddlesden-Popper perovskites with varying thickness as a model system, as they cover a wide range of exciton binding energies and the full range of free carrier fractions. Our results agree with previously reported values for the exciton binding energies in these materials, confirming the reliability of this approach and providing a simple and effective tool for probing the nature of optically excited states in semiconductors with intermediate exciton binding energies. We demonstrate that our method allows probing spatial variations in the fraction of free charges near grain boundaries or edges at micrometer spatial resolution. Finally, our results highlight the importance of performing optical characterization under excitation densities relevant to realistic operating conditions, as higher fluences can artificially enhance exciton formation and distort excited-state interpretation under solar-fluence conditions.

In anticipation of the new wave of ALICE experiments on particle-resonance correlation functions, we study the interaction of a kaon with the $D_{s0}^*(2317)$ resonance. Assuming the $D_{s0}^*(2317)$ to be a $DK$ molecular state in isospin $I=0$, we employ the fixed center approximation (FCA) to describe the kaon scattering off the $DK$ cluster, and implement elastic unitarity in the $K D_{s0}^*(2317)$ amplitude via an optical potential and the Lippmann-Schwinger equation. We evaluate the scattering length, effective range, and correlation function, which exhibits a shape characteristic of a strongly attractive interaction. Notably, the amplitude develops a narrow resonant peak about 40~MeV below the $K D_{s0}^*(2317)$ threshold, signaling a three-body bound state. We discuss the experimental feasibility of observing this state through the invariant mass distribution of $K D_s^+ π^0$, and argue that such three-body states, predicted by various theoretical approaches, offer promising targets for future experimental searches, providing valuable insights into the nature of exotic hadronic resonances.

Photocatalysis in atomically thin semiconductors is often limited by rapid electron-hole recombination, making it difficult to translate favorable band structures into efficient chemical function. Here we propose symmetry-defined periodic potentials as a strategy for photocatalysis: instead of modifying the chemistry of the active layer, one engineers a long-wavelength electrostatic landscape that spatially separates photoexcited electrons and holes. Applied to monolayer InSe, we show that experimentally accessible moiré patterns, such as those generated by twisted hBN, produce miniband formation, band-gap renormalization, and robust carrier separation. Using commensurate BN/InSe local registries, we further show that the moiré control layer transfers a measurable electrostatic modulation to InSe, providing the microscopic link between continuum potential engineering and the local surface environment. The key result is that the periodic potential strongly reorganizes carrier distribution while only weakly perturbing adsorption trends, thereby identifying a practically useful regime in which charge separation can be engineered without demanding major changes to the underlying surface chemistry. These results position periodic potentials as a broadly applicable design principle for photocatalysis and other light-driven interfacial phenomena in two-dimensional materials.

A multi-hop amplify-and-forward (AF) relay network can emulate a fully connected (FC) neural network layer via over-the-air (OTA) computation. However, achieving high emulation accuracy requires accurate channel state information (CSI) across all links in the multi-hop network. In this work, we investigate the impact of CSI errors on classification performance. We propose five heuristic schemes for allocating the total channel training time (pilots) across hops and compare their effectiveness. Numerical results reveal a clear trade-off between channel training overhead and classification accuracy. In particular, with sufficient pilot power and balanced allocation of channel training resources, the system can achieve classification accuracy close to that of the digital baseline.

This expository article is based on the author's talk at the Kinosaki Algebraic Geometry Symposium 2025. We discuss some recent progress surrounding stable degeneration in algebraic K-stability theory.

In this note, we prove a correspondence between filtrations and b-divisors over a general class of Noetherian local domains. As an application in the global setting, we prove a recent conjecture of Roé-Urbinati.

In this paper, we investigate the compactness of nonnegative solutions to a critical sub-elliptic equation with a nonnegative potential on the Heisenberg group. We establish that the solution set is compact provided the potential satisfies certain non-degeneracy conditions. Moreover, we show that if a sequence of solutions blows up, both the potential and its sub-Laplacian must vanish at the blow-up point. Our analysis overcomes the inherent geometric and analytical challenges posed by the Heisenberg group, including the degeneracy of the sub-Laplacian, its non-commutative structure, and the anisotropic dilation symmetry.

Synchronization in networks of coupled oscillators is classically studied via the Kuramoto model, whose intrinsic nonlinearity limits analytical tractability and complicates control design. Complex-valued extensions circumvent this by embedding phase dynamics into a higher-dimensional linear state space, where regulating complex-state moduli to a common value recovers Kuramoto phase behavior. Existing approaches to address this problem correspond, within a unified control framework, to state-feedback and hybrid reset-based strategies, each with performance constraints. We propose two switched control designs that overcome these limitations: a switched feedforward law ensuring exact phase correspondence at all times, and a feedforward plus sliding-mode law achieving finite-time convergence without spectral gain tuning. Additionally, we present a non-autonomous complex-valued MIMO sliding-mode controller that enforces phase locking at a prescribed frequency in finite time, independent of natural frequencies and coupling strengths. Simulations confirm improved transient response, steady-state accuracy, and robustness, including synchronization of heterogeneous networks where the classical real-valued Kuramoto model fails.

We study critical dynamics and phase-ordering kinetics in Active Model B (AMB) and its minimal extension, Active Model B$+$ (AMB$+$), using deterministic simulations in two dimensions. At criticality $r_c=0$, both models display identical mean-field scaling despite nonequilibrium currents, with order-parameter decay with time as $m(t)\sim t^{-α}$, with $α=\frac14$, and dynamical exponent being $z=4$. A generalized equal-area construction yields the binodal densities and phase diagram of AMB$+$. For supercritical quenches, domain size grows as $L(t)\sim t^{1/3}(1+c/\ln t)$, revealing logarithmic corrections to the classic $t^{1/3}$ growth-law; moreover it is consistent with the functional renormalization group predictions for marginal activity in $d=2$. While the logarithmic corrections are quite prominent in AMB, in AMB$+$ they are suppressed as the active current acts against the formation of macro-clusters; the growth is eventually arrested when a long-lived microphase-separated state appears.

Motivated by the need to develop fair and efficient schemes to facilitate the electrification of transport, this paper proposes a non-monetary karma economy for flexible Electric Vehicle (EV) charging, managing the intertemporal allocation of limited power capacity. We consider a charging facility with limited capacity that must schedule arriving EVs to charge in real-time. For this purpose, the facility adopts online karma auctions, in which each EV user is endowed with non-tradable karma tokens, places a karma bid in each time interval it is present in the facility, and capacity is allocated to the highest bidders, who must pay their bids. These payments are subsequently redistributed to the users to form a closed, indefinitely sustainable economy. The main contribution is to extend previous karma Dynamic Population Game (DPG) formulations to this setting which features novel State of Charge (SOC) dynamics and private trip deadlines in addition to urgency. A Stationary Nash Equilibrium (SNE) of the EV charging karma economy is guaranteed to exist, and it is demonstrated to provide pronounced benefits with respect to benchmark scheduling schemes as it balances between meeting deadlines and prioritizing high urgency.

The detection of Néel vector switching in a single-layer A-type antiferromagnet marks an important step toward functional two-dimensional spintronics. Here, Cr$_2$S$_3$-2D, grown on graphene on Ir(110), is established as a first single-layer A-type antiferromagnet. Spin-polarized scanning tunneling microscopy reveals hysteresis loops with a large switching field and a pronounced dependence on island size. X-ray magnetic circular dichroism at the Cr L$_{2,3}$ edges exhibits a tiny signal with a linear magnetic field dependence, consistent with a nearly compensated antiferromagnetic ground state and a Néel temperature of about 160 K. Quantitative analysis of the island-size dependence of the switching field, together with first principles calculations, indicates a slight imbalance between the magnetic moments of the two Cr planes of Cr$_2$S$_3$-2D when supported on a substrate. This imbalance results in a net magnetization for the A-type antiferromagnet, which enables the 180$^\circ$ rotation of the Néel vector. Moreover, Cr$_2$S$_3$-2D retains its magnetic properties after several days of exposure to air.

We investigate observational tests that can be used to distinguish between broad classes of cosmological models. This is achieved using curvature-consistency tests of the Friedmann-Lemaître-Robertson-Walker (FLRW) models, which we investigate in two scenarios where they can be violated; (i) when the optical properties of the cosmology deviate from the expectations of FLRW, and also (ii) when the large-scale expansion of the cosmology is different from FLRW. We identify useful ways to determine the properties of these alternative scenarios in terms of the violation of the curvature-consistency tests, and propose a new null test that can be used to isolate cosmologies with non-FLRW observational relations. The characteristic signatures we find can be used, together with the results of recent and upcoming cosmological observations, to probe and/or rule out large classes of cosmological models. This becomes an increasingly important task as the number of proposals in the literature increases, as cosmologists attempt to explain tensions, anomalies, and the dark sector of the Universe. Our approach provides a clear route for telling apart these different proposals, and offers a new opportunity for using precision cosmological data to efficiently discriminate between cosmological models.

This study explores an inertial-based contraction-type approach for addressing monotone variational inclusion problems (in short, MVIP) within real Hilbert spaces. Most contraction-type techniques assume Lipschitz continuity and monotonicity or co-coercivity (inverse strongly monotone) of the single-valued operator. However, the key advantage of the proposed method is that it does not rely on the coercivity condition and the Lipschitz continuity for the single-valued operator. A weak convergence result has been achieved for the proposed algorithm with a convergence rate $\mathcal{O}\left(1/\sqrt{k}\right)$. In addition, the maximal and strong monotonicity of the set-valued operator is used to establish a strong convergence result with the linear convergence rate. To demonstrate the effectiveness of our proposed method, we conduct numerical experiments focused on signal recovery problems.

In this paper, we introduce a generalised diagonal dimension. We explain why the generalised diagonal dimension extends the notion of diagonal dimension defined by Li, Liao, and Winter, and under which conditions these dimensions coincide. We prove permanence properties for the generalised diagonal dimension and compare it with the nuclear dimension. We investigate applications of the generalised diagonal dimension in large-scale geometry; specifically, we show that the generalised diagonal dimension of a noncommutative Cartan subalgebra in the C*-algebra of finite-propagation operators on a uniformly locally finite metric space is equal to the asymptotic dimension of the space.

We introduce the Random Subsequence Model, a spin glass model on pairs of random strings $(X,Y) \in \{0,1\}^N \times \{0,1\}^M$ whose partition function counts subsequence embeddings of $Y$ into $X$. We study two variants: the null model, where $X$ and $Y$ are independent and uniform, and the planted model, where $X$ is uniform and $Y$ is a uniformly-random length-$M$ subsequence of $X$. We connect the Random Subsequence Model to longstanding problems in various fields, including the best rate achievable by uniformly-random codes in the deletion channel, the longest common subsequence problem between two random strings, and models of directed polymers in statistical physics. In the regime where $N,M\to\infty$ at a fixed ratio $α= M/N \in (0,1)$, we exhibit strict asymptotic separations between the null annealed free energy and the quenched free energies of the null and planted models at all values of the density parameter $α$. This suggests that these models are in a spin glass phase at zero temperature throughout the entire dense regime. As a consequence, we show that uniformly-random codes achieve a positive rate in the deletion channel for all deletion probabilities $p\in [0,1),$ settling multiple conjectures of the second author, Isik and Weissman (2024) and proving the first such positive rate result for the regime $p \geq 1/2$. We also give an exact analytic formula for the annealed free energy of the planted model for all values of the density parameter. This implies a corresponding analytic upper bound on the best rate achievable by uniformly-random codes in the deletion channel, complementing the lower bound from our first result. Our upper and lower bounds for the capacity of the deletion channel under uniform codes are far closer to each other than the best known upper and lower bounds for the capacity of the deletion channel.

Meaningful social interaction is vital to well-being, yet Blind and Low Vision (BLV) individuals face persistent barriers when collaborating with sighted peers due to inaccessible visual cues. While most wearable assistive technologies emphasize individual tasks, smart glasses introduce opportunities for real-time, contextual support in social settings. To explore how smart glasses affect interpersonal dynamics and support inclusion in mixed-vision groups, we developed a smart glasses-based system, CollabLens, as a technology probe and employed it in four workshop sessions. We found that smart glasses can meaningfully support inclusive collaboration through expanding BLV participants' assistive networks with more flexible, independent access to visual information. While sighted participants viewed smart glasses as a promising medium that fosters interpersonal connection, they revealed uncertainty in adapting their helping behaviors. We concluded by discussing and synthesizing challenges and opportunities for designing smart glasses that provide seamless interaction experiences and enhance reciprocal mixed-vision social inclusion.

This chapter presents an ab initio perspective on giant resonances in atomic nuclei and surveys the principal theoretical frameworks that aim to describe these collective excitations from first principles. While the study of nuclear giant resonances has traditionally been dominated by the energy density functional approach, recent years have witnessed the development of advanced many-body approaches grounded directly in realistic nuclear interactions, namely, Hamiltonians that reproduce nucleon-nucleon phase shifts and accurately describe the binding energies of light nuclei. Within this modern framework, we review the main many-body methods currently used to compute nuclear response functions. These include the random phase approximation, the Lorentz integral transform coupled-cluster theory, the projected generator-coordinate method, and the self-consistent Green's functions approach. After giving a general conceptual and historical overview of giant-resonance phenomena, we outline the theoretical foundations and computational implementations of each method. We conclude with a critical comparison of their predictions for selected benchmark nuclei, $^{16}$O and $^{40}$Ca, emphasizing points of agreement and divergence, while maintaining a close connection to the relevant experimental observables.

Evolutionary game theory has provided substantial contributions to explain the emergence of cooperation under unfavourable conditions in ecology, economics, and the social sciences. Recently, inspired by newly available empirical evidence on group interactions, higher-order networks have emerged as a natural framework to properly encode multiplayer games in structured populations. Here, we study the emergence of cooperation in a nonlinear public goods game (PGG) on hypergraphs, where collective reinforcement captures the synergistic or discounting effect associated with each additional cooperator. In well-mixed populations, single-order PGGs, where all games have the same number of players, display a change in the nature of transition from continuous to discontinuous depending on the exact form of nonlinearity. By contrast, mixed-order PGGs, where games with different number of players coexist, exhibit a richer dynamical regime wherein a state of active coexistence of bistability and cooperation can arise. We further find that scale-free hypergraphs promote cooperation, highlighting the crucial role played by both the initial placement of cooperators and the presence of hyperdegree correlations. Overall, our results provide a comprehensive characterization of nonlinear PGGs on hypergraphs and open up new avenues for richer models of evolutionary dynamics of multiplayer interactions on structured populations.

The step-reinforced random walk (SRRW), where each step may replicate a randomly chosen past step, exhibits complex dependencies on the history. This paper introduces a generalized SRRW on groups, incorporating arbitrary transformations of past steps, which unifies several existing models in the literature. We develop a unified framework for establishing upper bounds on its transition probabilities for any reinforcement parameter $α<1$, linking the decay rate directly to the geometry of the underlying group. We prove that on Euclidean space, the walk is transient in all dimensions $d \geq 3$ for any $α<1$. On finitely generated groups, we derive the upper bounds using the isoperimetric profile of the Cayley graph, which in particular resolves an open problem regarding the exponential decay of the elephant random walk on Cayley trees.

The extraction of the static quark-antiquark potential from lattice QCD suffers from the poor signal-to-noise ratio of Wilson loops at large Euclidean times. To overcome this, smearing methods or the Coulomb gauge are used to improve the ground-state overlap with respect to the straight Wilson line trial state within the Wilson loop. To find excited states, complicated shapes are introduced to generate specific quantum numbers. Here, we introduce a neural-network parametrization of trial states, constructed with gauge-equivariant layers and optimized with a loss function that favors ground and excited states. In the quenched theory, we automatically obtain the interpolators for the ground and excited states.

We investigate the spontaneous meandering of slender rivulets in Hele-Shaw cells and identify the physical mechanism that selects the most unstable wavenumber, a quantity that has remained elusive even since the identification of the instability threshold [Daerr et al., Phys. Rev. Lett. 106, 184501 (2011)]. Earlier criteria did not distinguish between wavelengths and thus predicted an undiscriminated amplification of arbitrarily short perturbations. By incorporating viscous bending into the depth-averaged Navier-Stokes equations, we show that this effect is responsible for the selection of a fastest-growing mode, answering a question that has remained open for 15 years. We answer the open question of whether the meandering instability is absolute or convective. Our analysis also provides a simpler alternative derivation of the instability criterion, based on a low-viscosity assumption, and finally it yields a new physical interpretation of the mechanism: the destabilization arises directly from friction effects, instead of being caused by inertial forces. Together, these results complete the linear-stability picture of rivulet meandering in confined geometries, and establish viscous bending as a key parameter governing wavelength selection. They lay the groundwork for future exploration of the nonlinear features of the spontaneous meandering instability.

We compute the spectrum of light mesons, composed by up, down, and strange quarks, using a symmetry-preserving approximation that permits the inclusion of fully-dressed quark-gluon vertices in the key dynamical equations. This method is characterized by the use of the standard symmetric kinematic configuration as a seed in the corresponding Schwinger-Dyson equation, yielding finally the full kinematic dependence of all eight form factors composing the transversely-projected quark-gluon vertex. The extension of this approach to the case of distinct nonvanishing current quark masses is discussed, and the compatibility with the fundamental Ward-Takahashi identities demonstrated. The corresponding Bethe-Salpeter kernel is composed by three different diagrammatic structures, which may be deduced from the attendant quark gap equation by applying the standard "cutting" rules. The masses of the light mesons are computed by first determining the eigenvalue of the Bethe-Salpeter equation as a function of Euclidean momenta, and then using the Schlessinger extrapolation method to determine the Minkowski momentum for which this eigenvalue becomes unity. The resulting meson masses are in good agreement with experimental values, and substantially improve upon predictions from the rainbow-ladder approximation.

Multimodal retrieval models fail on reasoning-intensive queries where images (diagrams, charts, screenshots) must be deeply integrated with text to identify relevant documents -- the best multimodal model achieves only 27.6 nDCG@10 on MM-BRIGHT, underperforming even strong text-only retrievers (32.2). We introduce \textbf{HIVE} (\textbf{H}ypothesis-driven \textbf{I}terative \textbf{V}isual \textbf{E}vidence Retrieval), a plug-and-play framework that injects explicit visual-text reasoning into a retriever via LLMs. HIVE operates in four stages: (1) initial retrieval over the corpus, (2) LLM-based compensatory query synthesis that explicitly articulates visual and logical gaps observed in top-$k$ candidates, (3) secondary retrieval with the refined query, and (4) LLM verification and reranking over the union of candidates. Evaluated on the multimodal-to-text track of MM-BRIGHT (2,803 real-world queries across 29 technical domains), HIVE achieves a new state-of-the-art aggregated nDCG@10 of \textbf{41.7} -- a \textbf{+9.5} point gain over the best text-only model (DiVeR: 32.2) and \textbf{+14.1} over the best multimodal model (Nomic-Vision: 27.6), where our reasoning-enhanced base retriever contributes 33.2 and the HIVE framework adds a further \textbf{+8.5} points -- with particularly strong results in visually demanding domains (Gaming: 68.2, Chemistry: 42.5, Sustainability: 49.4). Compatible with both standard and reasoning-enhanced retrievers, HIVE demonstrates that LLM-mediated visual hypothesis generation and verification can substantially close the multimodal reasoning gap in retrieval. https://github.com/mm-bright/multimodal-reasoning-retrieval

Sub-terahertz (sub-THz) multi-user multiple-input multiple-output (MU-MIMO) systems unlock immense bandwidth for 6G wireless communications. However, practical deployment of wireless systems in sub-THz bands faces critical challenges such as increased atmospheric absorption, reduced channel coherence time due to increased Doppler spread at higher carrier frequencies, and hardware bottlenecks as low-loss sub-THz phase shifters are difficult to realize. To overcome the hardware and channel estimation challenges of sub-THz systems, this paper proposes a hybrid beamforming (BF) framework that integrates reconfigurable liquid crystal (LC) antennas with a liquid neural network (LNN) for transmitter. Specifically, we employ an LC antenna as the analog BF stage of a hybrid BF architecture, exploiting its voltage-driven permittivity tunability to achieve high-gain beam steering without the need for lossy phase shifters. For digital BF, we utilize an ordinary differential equations-defined LNN to learn temporal channel dynamics, and use a manifold optimization technique to compress the search space. We validated the proposed method on simulated site-specific 108 GHz ray-tracing channels in an urban scenario using NYURay, a ray-tracing simulator validated against 142 GHz propagation measurements. The 108 GHz carrier frequency matches the operating band of the LC antenna hardware. The proposed method achieves an 88.6\% spectral efficiency (SE) gain and higher robustness to imperfect channel estimation compared to the learning-aided gradient descent and gated recurrent unit machine learning baselines, and 1.9 times higher SE than the 3GPP TR~38.901 standard antenna model, highlighting the potential of LC-based hardware for sub-THz communications.

The Quantum Approximate Optimization Algorithm (QAOA) is a leading framework for quantum combinatorial optimization. The Vehicle Routing Problem (VRP), a core problem in logistics and transportation, is a natural application target, but it poses a major feasibility challenge for standard QAOA because feasible solutions occupy only a tiny fraction of the search space, and the conventional Pauli-$X$ mixer can disrupt partial solution structures that satisfy key local constraints. To address this issue, we propose a constraint-aware QAOA framework with two complementary components. First, we design a lightweight initialization strategy that encodes a selected subset of simple yet informative local one-hot constraints into the initial state, thereby reducing the initial superposition space and increasing the probability mass on states with important local structure. Second, we introduce a hybrid XY-$X$ mixer that preserves the constraint structure imposed at initialization while retaining exploratory flexibility over the remaining unconstrained degrees of freedom during QAOA evolution. We evaluate the proposed framework against standard QAOA under three progressively more realistic regimes: ideal statevector simulation, finite-shot sampling, and noisy finite-shot sampling. Across all regimes, the proposed method consistently achieves lower average energy and higher feasible-solution ratios than standard QAOA, indicating more effective guidance toward structurally valid, lower-cost VRP solutions. However, the performance gap narrows in the noisy regime. Because this setting adopts a hardware-inspired error model based on near-best-reported laboratory-level qubit gate and readout fidelities, the observed attenuation suggests that the practical advantage of the more structured mixer is likely to grow as quantum hardware improves and error rates decline.

We prove that the connection vector fields associated to ample Poisson line bundles are not locally hamiltonian unless the Poisson structure is zero. We use this result to provide further evidence on Bondal's conjecture regarding the dimensions of the degeneracy loci of a holomorphic Fano Poisson manifold.

We develop a trust-region method for efficiently minimizing the sum of a smooth function, a nonsmooth convex function, and the composition of a finite-valued support function with a smooth function. Optimization problems with this structure arise in numerous applications including risk-averse stochastic programming and subproblems for nonsmooth penalty nonlinear programming methods. Our method permits the use of inexact value and derivative information, enabling the solution of infinite-dimensional problems governed by, e.g., partial differential equations (PDEs). We prove global convergence of our method and under additional regularity assumptions, demonstrate that the sequence of iterates accumulates at a stationary point of our target problem. We demonstrate our method's efficiency on two PDE-constrained optimization examples, showing that its performance is invariant to the PDE discretization size.

In this paper, we provide a class of domains in $\mathbb{C}^3$, such that every holomorphic self-map of that domain either has a fixed point or the sequence of iterates is compactly divergent. In particular, it follows that the symmetrized bidisc, symmetrized tridisc, tetrablock, pentablock are in the aforementioned class of domains. We also give a description of the fixed point set of a holomorphic self-map of the symmetrized bidisc and tetrablock. For the symmetrized bidisc, given a holomorphic self-map such that the sequence of iterates is compactly divergent, we also provide a description of its target set.

Gibbs state preparation is an important subroutine in quantum computing. In this work we use the detectability lemma to improve Gibbs state preparation. Specifically, we design new Gibbs state preparation methods that do not rely on simulating Lindbladian evolution, thus avoiding the overhead from it. For local Lindbladians consisting of $M$ terms, this approach reduces the cost by a factor of $O(M)$. We also combine the detectability lemma operator and quantum singular value transformation to implement ground state projection operators of frustration-free Hamiltonians, resulting in a quadratic speedup in the spectral gap dependence. Applying this method to Lindbladians for the Gibbs state of local commuting Hamiltonians, we achieve quadratically better dependence on the Lindbladian spectral gap.

The definition of sixth-generation (6G) systems is being shaped by early standardization efforts, including the 3GPP TR 38.914 (Release 20) study on scenarios and requirements. This study introduces a comprehensive set of deployment environments, service classes, and performance targets that will guide the evolution toward IMT-2030. This article provides a design-oriented interpretation of these definitions, bridging the gap between standardized scenarios and system design. We first organize 6G deployment scenarios and emerging services into a unified framework. We then identify key design drivers derived from the 3GPP requirements, including terrestrial-non-terrestrial integration, GNSS-free operation, AI-native networking, and joint communication and sensing. Finally, we discuss the implications of these drivers on 6G architecture and highlight open challenges for future standardization and research.