Measurement-induced phase transitions are nonequilibrium transitions between phases characterized by distinct entanglement scaling behaviors, driven by the competition between unitary dynamics and measurements. Despite recent numerical efforts, how quenched disorder affects these transitions remains unclear. In this work, we study a $d$-dimensional noninteracting fermionic system subject to both quenched disorder and continuous monitoring of the local particle density, and derive an effective field theory describing its long-time universal behaviors. We find that the system is governed by the same nonlinear sigma model as in the case of clean monitored fermions, with disorder entering only through a modification of model parameters. This result suggests that the presence or absence of a measurement-induced phase transition is unaffected by the introduction of disorder: in spatial dimensions d>1, a transition occurs between an area x log law phase and an area law phase, whereas in d=1, the system exhibits only an area law phase and no transition. Numerical results further demonstrate that both clean and disordered one-dimensional free fermions exhibit area-law behavior when the system size is large enough.

The gravitational path integral can compute inner products between different states of open and closed universes. To have a well-defined Hilbert space, these inner products should be positive semi-definite, which is not manifest in the low-energy effective theory. In this letter, we analyze the constraints that the positivity of inner products imposes on gravitational theories coupled to axions. If the axion has an exact shift symmetry, we show that, under mild assumptions, a combined positivity constraint on closed and open universes is violated when one includes certain wormholes. In low-energy effective theories where these wormholes are perturbatively stable, positivity requires that the wormholes have a non-perturbative instability that breaks the shift symmetry. This leads to a sharp version of the axion weak gravity conjecture, including precise numerical constants. We relate the bound to possible extensions of other swampland conjectures, arguing for an imaginary continuation of the distance conjecture. We comment on how the bound applies to axions in string theory and discuss phenomenological implications.

We explore the coincidence of scales between cosmic inflation and right-handed neutrinos in seesaw models. We show that inflation models, which will be tested by next-generation CMB experiments, can produce right-handed neutrinos in sufficient abundance to explain the observed baryon asymmetry of the universe. The model can be tested by gravitational wave signatures from cosmic inflation and particle production.

We report the discovery and multi-wavelength characterization of the Galactic transient EP J174942.2$-$384834, first detected by the Einstein Probe during a faint X-ray outburst in March 2025. Coordinated follow-up observations revealed two major outbursts and a rebrightening over a seven-month period. Broadband X-ray spectral modeling shows that the outburst emission was dominated by thermal Comptonization of very soft seed photons. The absence of a detected thermal disk component, together with the low inferred seed-photon temperature, is consistent with a cool and possibly truncated accretion disk. The X-ray spectrum remained consistently hard throughout the outburst activity, with a power-law photon index of $Γ\approx 1$-2, gradually softening as the flux declined. The optical/UV counterpart brightened in tandem with the X-ray emission and exhibited a blue continuum with broad Balmer absorption features. Together with the optical/UV - X-ray luminosity correlation, this supports a disk-dominated origin of the optical/UV outburst emission, with viscous heating likely playing a major role and irradiation possibly contributing, especially in the UV. No radio counterpart was detected, implying at most very faint jet activity. Taken together, the observed properties support the classification of EP J174942.2$-$384834 as a very faint X-ray transient black hole candidate. This study demonstrates the ability of Einstein Probe to uncover and characterize the faintest accreting compact objects in the Galaxy.

Molecular clouds form stars from the interstellar medium via gravitational collapse, following a sequence from low-density gas to high-density cores and eventually the formation of stars. In classical density wave theory, gas clouds orbiting the galaxy experience gas compression and triggered star formation, while encountering the gravitational well of spiral arms. We aim to trace these different phases of the molecular cloud life cycle via tracers of molecular gas (CO), dense molecular gas (HCN), and star formation (H$α$, 24 $μ$m) within the spiral arms of two grand-design spiral galaxies: NGC 4321 and M51 (NGC 5194). In the spiral arms of these galaxies, we investigate the relation between molecular gas, dense gas, and star formation (CO-HCN-SFR) at matched physical resolutions of 270 pc and 125 pc in NGC 4321 and M51, respectively. We employed spiral arm masks for these galaxies and investigate trends of HCN/CO and SFR/HCN (SFR/CO), which serve as proxies for the dense gas fraction and dense (molecular) gas star formation efficiency, perpendicular to the spiral arm spines. We find that HCN/CO, SFR/CO, and SFR/HCN increase from the upstream towards the downstream side of both spiral arms of NGC 4321, while their trends are less prominent in M51. Our results indicate that large-scale galactic dynamics (e.g. density waves) can induce a sequence of gas density and star formation-to-gas density variations perpendicular to the spiral arms. This sequence contributes to the increased scatter seen among spectroscopic ratios such as HCN/CO and SFR/HCN at sub-kiloparsec scales.

Active galactic nuclei (AGN) showing dramatic spectral and flux variations, either due to changes in the accretion rate (changing-state, CS-AGN) of the supermassive black hole or in the line-of-sight column density (changing-obscuration, CO-AGN), have been classified as changing-look (CL) AGN. Here we present a peculiar source, 2MASX J0413-0050, first identified as a narrow-line Seyfert 1 (NLS1s) galaxy in 2004. When re-observed twice in 2021, it showed a transition in the spectral type (towards a Seyfert 1.9) and the complete and mysterious disappearance of the Hbeta line while source was in a high accretion state. In the meantime, the X-ray flux decreased between observations taken in 2020 and 2022, and again in the most recent spectrum of 2023. Shortly after this, another optical spectrum revealed the re-emergence of both the narrow and broad Hbeta components (Seyfert 1.8). Despite the fact that it was not possible to retrieve the line-of-sight column density from the X-ray spectra, which would have helped in assessing whether this event could be attributed to a CO AGN scenario, the observational evidence does not necessarily support such an interpretation. J0413-0050 may have undergone several switch-on switch-off phases over the past 20 years, on an unknown timescale, which could have affected the accretion power and, consequently, the optical continuum and so the emission lines coming from the broad-line region (BLR). For these reasons, it is reasonable to classify this source as a CS-AGN. The case of J0413-0050 supports the hypothesis that NLS1s can indeed experience CL phenomena.

The degree of black-hole spin-orbit misalignment ("tilts") in the astrophysical population could be a powerful diagnostic to distinguish between binary formation in isolation, in dynamical environments, or in hierarchical triples. However, robust population-level spin tilt measurements are complicated by model misspecification as well as numerical and Poisson variance, ultimately owing to poor single-event constraints on tilts. Motivated by reports of a possible peak in the spin tilt distribution, we analyze the fourth LIGO-Virgo-KAGRA gravitational-wave transient catalog to test for preferred spin orientations at different black hole masses. We find that a peak in spin tilts is not statistically significant nor model independent. Since the data cannot be used to reliably identify subpopulations based on their spin tilt properties, we also consider a complementary approach: measuring the spin magnitude and tilt distributions at fixed mass scales. We find no confident correlation between mass and spin tilt, but we do confirm a confident correlation between spin magnitude and mass, corroborating recent analyses.

Conventional approaches to simulating quantum many-body dynamics produce a single trajectory: if the Hamiltonian or the initial state is changed, the computation must be re-performed. Recent efforts toward foundation models have begun to address this limitation, yet existing methods transfer across either Hamiltonians or initial states, but not both. In this work, we introduce the Universal Neural Propagator (UNP), a single, unified model that learns the functional mapping from driving protocols to time-evolution propagators. Trained in an entirely self-supervised way, a single UNP model predicts dynamics across a function space of driving protocols and an exponentially large Hilbert space of initial states simultaneously. We benchmark on a two-dimensional driven Ising model and demonstrate the UNP's accuracy and transferability across product and entangled initial states, as well as for both in- and out-of-distribution driving protocols. The UNP remains accurate at system sizes beyond exact diagonalization, and can be efficiently fine-tuned across all initial states using observable data. By shifting the object of learning from quantum states to operators, this work opens a route toward transferable simulation of driven quantum matter.

We analyze the spectra of the central nuclei of extremely red quasars (ERQs) observed as part of the JWST ERS Q3D program. We focus on the complex kinematic structures of the prominent rest-frame optical emission lines. Our modeling allows us to deblend the lines and separate the emission into distinct kinematic components that imply velocity- and density-stratified gas structures on a range of physical scales within the ERQs. Supplementing the JWST data with archival data, we analyze the spectral energy distributions (SEDs) of the ERQs and find they are consistent with a significantly dust-obscured central source with a small amount of relatively-unobscured UV/optical flux that is scattered into our line-of-sight. While the kinematics of the UV and optical emission lines largely agree, the UV lines are dominated by scattered light. In contrast, the optical emission-line ratios indicate a combination of scattered and obscured emission. Our analysis focuses on one ERQ, J0834, because its distinct spectroscopic features allow the emission to be easily decomposed into separate kinematic components.

Quantum many-body scars in Rydberg atom arrays have thus far only been observed on bipartite lattices, leaving open the question of whether and how they survive frustration, and what the appropriate initial states are that lead to nonthermal dynamics. We introduce a graph-theoretic framework to find suitable candidates for scarring on arbitrary lattices. Our framework predicts two distinct mechanisms: type-I scars generalize the bipartite case by using locally entangled states to overcome mild frustration, while type-II scars exploit strong frustration to pin part of the lattice, leaving the remainder to oscillate freely. We numerically demonstrate both mechanisms and uncover an exponential family of scarred trajectories on the hexagonal lattice that can encode information protected from thermalization. Our results establish scarring as a generic feature of Rydberg systems beyond one dimension and provide an experimentally accessible route to systematically probing non-thermal dynamics in quantum simulators.

Quantum many-body scars enable persistent non-ergodic dynamics in otherwise thermalizing systems, yet their stabilization typically relies on fine-tuned initial states or engineered Hamiltonian perturbations. Here we show that lattice geometry alone can serve as a powerful and experimentally accessible control knob for inducing and enhancing scarring. By transforming a one-dimensional chain into a quasi-one-dimensional triangle-decorated lattice, we find that the fully polarized state -- normally thermalizing in the PXP model -- exhibits pronounced fidelity revivals, slow entanglement growth, and strong overlap with a tower of weakly entangled eigenstates. We trace this behavior to a geometry-induced restructuring of the constrained Hilbert space, whereby the adjacency graph decomposes into hypercube subgraphs that enforce coherent population transfer and stabilize an emergent approximate $\mathrm{su}(2)$ algebra. We propose a direct implementation in programmable arrays of tweezer-trapped Rydberg atoms, where the triangle-decorated geometry can be realized using spatial light modulators and the resulting scarring dynamics probed via time-resolved measurements of excitation density. Our results establish lattice connectivity as a design principle for engineering non-ergodic dynamics in constrained quantum systems.

We construct an $N=1$ supergravity action whose bosonic part contains an arbitrary function of the scalar curvature, the so-called $F(R)$ gravity. As in $R+R^2$ supergravity, it can be described in terms of two chiral superfields of no-scale supergravity: one contains the scalaron which plays the role of the Starobinsky inflaton and the other contains the goldstone fermion of spontaneously broken supersymmetry during the inflation plateau. Its (complex) scalar component acquires a non-tachyonic mass in the presence of the string dilaton and can be set to zero, together with the pseudoscalar partner of the scalaron, so that the scalar potential is reduced to the one of $F(R)$ gravity. In a perturbative expansion in powers of $R$, one obtains a small deformation of the Starobinsky cosmological model that solves the problem of initial conditions within the validity of the effective field theory, below the scale of tower of states predicted by the swampland distance conjecture. We also show that a particular example of an underlying microscopic theory with such properties is provided by a four-dimensional heterotic string model containing the Standard Model of particle physics.

Deep neural networks owe their expressive power to nonlinear activation functions. The effective field theory of signal propagation at initialization reveals a few distinct universality classes of activations that exhibit different depth scaling. Tuning across these, especially with analytical control, is an open problem. We show that a statistical mixture of activations, where each neuron independently and randomly draws its activation from a two-component distribution with mixing fraction $p$, provides a new mechanism for a continuous phase transition. Applied to a mixture of Tanh and Swish, the transition is sharp in the depth scaling of the preactivation variance, separating a variance-collapsing from a variance-inflating phase; at $p_c$, the network acquires statistical scale invariance, with depth-independent variance, without sacrificing smoothness. This resolves a longstanding tension, where scale-invariant propagation has previously required the non-smooth ReLU family, rendering such networks ill-suited to curvature-based optimizers, physics-informed architectures, and neural-network quantum states. We corroborate the transition through variance propagation, parallel and perpendicular susceptibilities, and Lyapunov exponents. Training multilayer perceptrons on real datasets reveals non-monotonic test performance as a function of $p$, with an optimum near the theoretically predicted $p_c$, confirming that the initialization-level transition has direct consequences for learned representations. The quenched activation disorder acts as a structural regularizer, suppressing memorization of corrupted labels while preserving generalization. Our framework establishes statistical activation mixtures as a controlled tool for navigating the phase diagram of deep network universality classes.

The majority of discovered exoplanets have been observed orbiting field stars as opposed to within a star cluster. To determine whether the lack of observed exoplanets in star clusters is due to gravitational perturbations or observational limitations, we consider the possibility of studying exoplanets in stellar streams. We present the results of direct $N$-body simulations of planetary systems around stars that orbit within a star cluster. Our simulations demonstrate that stars with early cluster escape times tend to retain all their planets as they spend most of their time orbiting in the cluster's low-density outskirts. Alternatively, stars with later escape times can have a wide range of survival fractions as they are subjected to a range of local densities and encounter types. With respect to the stellar stream that forms as the result of the cluster's dissolution, stars near the edge of the stream are therefore more likely to have unperturbed planetary systems. Conversely, stars near the centre of the stream have a higher chance of having planets pushed to eccentric orbits, inclined orbits, or stripped from the system entirely. From our suite of simulations, we provide an estimate of the probability that a star will host a planet with a given initial semi-major axis $a_0$ based on the star's location along a stellar stream $Δϕ$.

We develop a microscopic theory of charged excitations in an SU(2) Chern ferromagnet and obtain closed-form wavefunctions for a hierarchy of charge-$e$ spin polaron states binding an arbitrary number of spin flips. In an ideal Chern-$1$ band with a normal-ordered contact interaction, we show that these polarons are exact eigenstates of the Hamiltonian with the same energy as single-hole excitations. Away from this ideal limit, we promote these states to a variational family by introducing a single size parameter and a geometry-informed single-particle dressing. Our momentum-space wavefunctions admit two equivalent representations: a ratio of Jastrow factors of Weierstrass functions of relative momenta or an antisymmetrized geminal product of particle-hole wavefunctions. The latter enables efficient evaluation of overlaps and expectation values for large system sizes and many spin flips. Benchmarking in the lowest Landau level, the single-spin-flip ansatz achieves $\gtrsim 99\%$ overlap with exact diagonalization and accurately captures binding energies, while the multi-spin-flip energies interpolate smoothly toward the large-texture (skyrmion) regime. For Chern bands with tunable quantum geometry, we find that interaction-generated single particle dispersion quickly destabilizes the spin polarons once quantum geometry becomes sufficiently non-uniform. When such dispersion is suppressed, however, the bound states persist deeper into the non-uniform regime, with the binding energy slowly decreasing and the bound state becoming larger as the quantum geometry becomes more concentrated. Our results provide a microscopic foundation for analyzing doped Chern ferromagnets in moiré platforms and lay the groundwork for variational wavefunctions of multi-polaron excitations and phases.

We analyze three saddle points of the path integral computing the partition function of the SYK model with a Maldacena-Qi coupling in the double scaling limit. The three saddle points are holographically dual to three topologically different spacetimes: a pair of Euclidean black holes (two thermal disks), a thermal AdS$_2$ (a cylinder), and a thermal AdS$_2$ with a baby universe (a cylinder with a handle). We develop explicit chord rules that span and probe these three bulk geometries. We derive the rules by expanding the effective $G,Σ$ action in powers of the coupling $\mathcal{J}$ and writing the partition function as a weighted sum of chord diagrams. By slicing the diagrams open, we generate a Hilbert space description on a spatial slice for each saddle point. The Hartle-Hawking chord state for the third saddle point has genuine entanglement between the baby universe and the external spacetimes, providing evidence that a closed universe can support a nontrivial Hilbert space.

Some high-mass stars likely end their lives in underluminous implosions that leave behind a black hole, known as failed supernovae (FSNe). However, neutrinos radiated during proto-neutron star formation generate a weak (Mach $\gtrsim 1$) shockwave in the outer layers of the star, which produces a unique transient as it breaks out of the dying star and signals its imminent disappearance. It was recently shown that there are two self-similar solutions that describe the propagation of this weak shockwave, and these solutions simultaneously contain outward-moving ejecta and fallback accretion onto the black hole. Here we show that the larger Mach number solutions are unstable, such that the Mach number of the shock grows with time $t$ and deviates from the self-similar prediction as $\propto t^α$, with $α\lesssim 0.1$, whereas the smaller Mach number solutions are stable. We also show that, above a critical mass loss that is readily achievable in core-collapse supernovae, the shock asymptotically strengthens and approaches the strong limit. Our results imply that it is the mass lost to neutrinos \textit{relative} to the mass enclosed by the shockwave, as well as the stellar density gradient where the shock forms, that primarily dictate its strength and the amount of material it ejects. These criteria explain why red supergiants, which have relative mass losses well in excess of the critical value at the time of shock formation, more readily eject material and create more luminous explosions compared to more compact progenitors.

Strong-to-weak spontaneous symmetry breaking (SWSSB) is diagnosed by nonlinear correlators, but its direct static implication for conserved charge fluctuations is not automatic. We show that, for continuous symmetries, long-range Rényi-1 correlator, together with a sufficiently rapid approach to its nonzero asymptotic value, forces subsystem charge indefiniteness: the block-charge variance has an extensive lower bound; equivalently, the truncated symmetry expectation has extensive curvature. This gives a precise static fluctuation footprint of charge scrambling. We construct examples to show that the implication is conditional and non-reversible: dephased superfluids retain Rényi-1 SWSSB with subextensive charge variance when the Rényi-1 tail is too slow, while sparse fixed-charge projectors have extensive charge variance but no local charge-transfer Rényi-1 order or long-range conditional mutual information. Finally, we introduce a \emph{twist overlap} correlator, which serves as an analogue of charge variance applicable to both discrete and continuous symmetries. This naturally decomposes local block-charge fluctuations into strong- and weak-symmetry channels. We found that the weak-symmetry channel isolates coherent charge fluctuations and is directly related to the Wigner--Yanase skew information. Taken together, these results give a unified understanding for distinguishing nonlinear SWSSB order, local charge indefiniteness, and coherent charge fluctuations.

We present an exact black hole solution in anti-de Sitter (AdS) spacetime with a Kalb-Ramond field coupled to nonlinear electrodynamics (NLED), characterized by mass, magnetic monopole charge, and Lorentz-violating parameters. The geometry admits two horizons (inner and outer) that coalesce into a degenerate horizon at a critical monopole charge. Beyond this critical point, no black hole solutions exist. In the limit of vanishing Lorentz-violating parameters, the solution reduces to the modified Kalb-Ramond and Bardeen black holes, while suitable parameter choices reproduce the Reissner-Nordström-AdS and Schwarzschild-AdS geometries. We analyze the thermodynamics of the solution by computing the Hawking temperature, entropy, specific heat, and Gibbs free energy. The NLED source introduces nontrivial modifications: the Hawking temperature displays nonmonotonic behavior with possible local extrema, the entropy deviates from the standard area law, and the specific heat may assume negative values, signaling thermodynamic instabilities. The Gibbs free energy exhibits swallow-tail structures, indicative of first-order phase transitions. Furthermore, we derive the first law of black hole thermodynamics in the extended phase space, together with the Smarr relation, and confirm their validity for the Kalb-Ramond black holes with NLED sources. Our findings highlight the rich thermodynamic structure induced by Lorentz-violating effects and nonlinear electrodynamics in AdS black hole backgrounds.

This paper introduces and studies quasi sdf-absorbing ideals as a generalization of sdf-absorbing ideals. We investigate the stability of this property under various constructions, including localization, surjective images, Nagata idealizations, and amalgamations. We establish conditions under which the radical of such ideals is prime and discuss a specific class of rings where quasi sdf-absorption implies the sdf-absorbing primary property. The study concludes with a classification of these ideals in Z and examples distinguishing them from related ideal classes.

Production LLM systems require both safety moderation and PII detection under strict latency and cost constraints. This creates a trade-off: autoregressive moderators are accurate but expensive, while lightweight encoders are faster but less capable. We present GLiNER Guard (GLiGuard), a unified encoder that performs safety classification and PII detection in a single forward pass, simplifying safety pipelines. We introduce three variants: compact uni- and bi-encoders (145-147M) for high-throughput serving, and GLiGuard Omni (209M) for stronger moderation quality. Under dynamic batching on a single A100, the compact model reaches 193 requests/sec with P99 latency below 1s, achieving 1.6x higher throughput than GLiNER2. Omni remains competitive with much larger moderators on public safety benchmarks. We also release PII-Bench, a span-level benchmark for evaluating PII detection in end-to-end pipelines. Overall, encoder-based guardrails offer a practical low-cost alternative for always-on moderation. Models and benchmarks are released on HuggingFace.

In this paper, we expand the theory of depth-unbiased source localization to unbiased parameter estimation and signal reconstruction of an arbitrary number of non-zero parameters to be recovered. The topic touches on the concept of exact reconstructibility, most commonly known in compressed sensing and multisource estimation in various imaging problems. The theoretical results derive upper bounds on the number of recoverable parameters in the noiseless case, and a probability measure is defined to assess the probability of obtaining all non-zero parameters with correct magnitude order. The work provides a mathematical explanation of the open question regarding the noise robustness of standardized and unbiased methods. Also, the paper reveals a trade-off between the number of sensors and the signal-to-noise ratio. Numerical experiments demonstrate the theoretical findings.

Network-based Intrusion Detection Systems (IDS) are predominantly trained on tabular flow records, whose one-dimensional representations limit convolutional architectures from exploiting inter-feature spatial correlations. This paper presents a novel byte-level flow-to-image encoding method that converts each network-flow record into a fixed-size RGB image. Continuous features are serialised using IEEE-754 single-precision format and packed sequentially into pixels along an inverted-L shaped trajectory, while discrete features are mapped to byte values and placed contiguously in the middle image row's centre. The encoding is deterministic and reversible, preserving a fixed spatial layout across all samples. Four IDS models are evaluated on NSL-KDD and UNSW-NB15 datasets with both flow and image-based configurations. The image-based representation yields consistent accuracy gains of up to 15.6\% and 12.8\% for binary and multi-classification on UNSW-NB15, and up to 3.5\% and 3.2\% on NSL-KDD, highlighting the potential of byte-level visual encoding to strengthen AI-driven intrusion detection in local computer networks.

Large language model (LLM) ecosystems such as Claude Code and ChatGPT increasingly rely on skills: packages of natural-language instructions and executable tools. Once in the LLM's context, skill content cannot be reliably separated from trusted instructions, and a skill's executable side can invoke privileged actions, exposing the skill supply chain to injection, tampering, and rug-pull attacks. Existing defenses are stage-bound: centralized signing, audit reports unbound from the runtime artifact, or policy engines that cannot attest to what was approved. We present SIGIL, the first framework that seals the audit-runtime gap for LLM skills. SIGIL delivers verifiable hosting through a tamper-evident, decentralized on-chain registry from which LLMs fetch skills directly. The registry admits four publication types, Transparent, Licensed, Sealed, and Committed, spanning plaintext public distribution, monetized access, custodial use, and off-chain workflows; before admission, every skill is vetted by a Decentralized Autonomous Organization (DAO) audit committee that supports pluggable auditing methods under a stake-and-slash economic model. At load time, SIGIL delivers verified loading through a skill verification protocol executed by a Skill Verification Loader (SVL) embedded as the mandatory loading path: the SVL retrieves and decrypts the skill as its type requires, verifies its integrity against the on-chain record, and enforces its permission manifest before context injection. We evaluate SIGIL on a real-world deployment against 1,023 in-the-wild skills spanning six attack types. At load time, the SVL verifies each skill's integrity against its on-chain record and enforces its approved permission manifest, completing batched verification under 86 ms. Together, these results show that LLM skills can be cryptographically bound from publication through runtime at practical cost.

We develop a diagrammatic proof system for a fragment of structural semantics inspired by the Greimas semiotic square, using spider diagrams as the underlying formalism. The basic terms are represented as diagrammatic configurations, and the relations of contradiction and implication are interpreted as transformations governed by a set of inference rules. These transformations are realised as derivations, with proof trees serving as witnesses. Our main result shows that the construction of the four meta-terms can be captured uniformly: each is derivable from a conjunctive pair of basic configurations via a fixed derivation schema composed of contour introduction and habitat transformation rules. This yields a proof-theoretic account of the combinatorial operation underlying meta-term formation, and provides a semantic interpretation of the Greimasian operation `+' as a derivational construction rather than a logical combination. We further show that diagrammatic negation in this setting is not a Boolean complement, but a restricted, zone-determined semantic counter-position, reflecting the relational character of opposition in structural semiotics. The resulting framework provides a compositional, rule-based semantics in which complex configurations are generated constructively from simpler ones. In addition to extending the expressive scope of spider diagram calculi, the system illustrates how diagrammatic reasoning can be used to formalise non-classical semantic operations within a unified inferential setting.

This paper numerically investigates the statistical properties of rogue waves and their generation mechanisms in integrable turbulence, taking the Gerdjikov-Ivanov (GI) equation as the research object. The eigenvalue spectra of the analytical solutions and the chaotic wave field are calculated using the Fourier collocation method. Subsequently, taking a plane wave with random noise as the initial condition, the evolution of chaotic wave fields is simulated using the split-step Fourier (SSF) method. Numerical results show that the larger the initial disturbance intensity, the faster the wave field converges to a chaotic state, and the higher the peak amplitude after convergence, the higher the tail of the probability density function, and the significantly higher probability of rogue wave occurrence. Moreover, as the initial disturbance intensity increases, the turbulence type transitions from breather turbulence to soliton turbulence. In addition, the evolution of the wave-action spectrum is studied. The research has found that the wave-action spectrum of the GI equation shows an asymmetric distribution during the time evolution process, and this asymmetry persists even after the system reaches a steady state.

As 6G architectures transition toward decentralized Multi-Agent Systems (MAS), ensuring secure access to shared Knowledge Bases (KB) is critical. Traditional authorization models like RBAC fail to provide the granularity required for autonomous agents interacting with Semantic-based data. This work proposes a hybrid authorization framework that integrates roles and First-Order Logic (FOL) predicates to enforce zero-trust principles at the knowledge-graph level. We eliminate permission inheritance by enforcing authorization at the triple level (Subject-Predicate-Object), ensuring agents only access metadata required for their specific functional lifecycle.

We generalize proper scoring rules to the quantum domain, replacing probability distributions with density operators. We define Quantum Value Functionals via operator convex generators and establish a complete duality theory yielding proper quantum scoring rules. We derive minimax optimal bounds for quantum state tomography under McCarthy-type incentives, proving a Quantum Cramér-Rao-McCarthy Bound that explicitly links minimax risk to the curvature of the generating function and the Quantum Fisher Information. We quantify the economic value of quantum resources (coherence, entanglement, adaptivity) in forecasting tasks, establishing scaling separations between classical and quantum estimation strategies. Our results guide the design of quantum sensors, incentive-compatible quantum data markets, and robust quantum machine learning protocols.

We study the deflection of light in a homogeneous plasma medium around a BTZ-ModMax black hole, focusing on the effects of the ModMax nonlinear electrodynamics parameter and the cosmological constant. Using the Gauss-Bonnet theorem applied to the corresponding optical geometry in plasma, we derive a modified expression for the deflection angle and examine how plasma dispersion alters the gravitational lensing behavior. The influence of the ModMax parameter in the presence of homogeneous plasma is compared with its vacuum counterpart, as well as with the charged and static BTZ black hole cases, revealing distinct signatures arising from nonlinear electrodynamics. This work highlights the combined impact of homogeneous plasma, spacetime curvature, and nonlinear field dynamics on light deflection in lower-dimensional black hole geometries. We further study the greybody factor and analyze how the presence of homogeneous plasma and the ModMax parameter modifies the energy emission spectrum of the black hole. Our results demonstrate that both plasma effects and nonlinear electrodynamics significantly influence the transmission probabilities and emission rates, providing deeper insight into wave propagation and observational signatures in lower-dimensional black hole geometries.

We investigate the possibility that idealized quantum state-reduction processes may produce a local violation of charge conservation. If this occurs, the corresponding electromagnetic fields cannot be consistently described within Maxwell electrodynamics, and a natural alternative is provided by Aharonov-Bohm electrodynamics, which reduces to Maxwell theory when local charge conservation holds, but remains compatible with non-conserved sources. Within this framework we first analyze how state reduction may generate non-conserved local currents, including statistically compensated cases and biased tunnelling configurations with persistent average current. We then study the interaction of gauge waves with fermionic and bosonic quantum systems, the latter being described by a modified Schrödinger equation previously proposed for boson matter. As an application, we discuss the interaction of gauge waves with superconductors and show that they can effectively shield such waves. Finally, we present experimental proposals based on inverse-biased diodes and estimate the expected detector response.