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We initiate the classification of supersymmetric degenerate Killing horizons, with closed spatial cross section, away from the near-horizon limit in D=11 supergravity. We prove that all such solutions fall into two distinct classes, depending on lightcone chirality with respect to a Gaussian null coordinate system. For the first class of solutions, the negative lightcone chirality part of the Killing spinor is non-zero on the Killing horizon, and we prove that all such solutions are isometric to supersymmetric near-horizon geometries. In the second class, the negative lightcone chirality part of the Killing spinor vanishes on the Killing horizon. In this case, we prove that the spinorial Lie derivative of the Killing spinor with respect to the Killing vector which generates the Killing horizon vanishes, and that all such solutions with more than 13 supersymmetries are pp-waves.

A Killing tensor field on a Riemannian space corresponds to an integral of the geodesic flow polynomial in momenta. A Killing tensor field is called decomposable if it is a polynomial in Killing vector fields. In this paper, we first prove that the study of Killing tensor fields on symmetric spaces can be reduced to the case of compact irreducible ones. Then we introduce the class of top slot Killing tensor fields. We obtain an explicit and elegant description of such tensor fields and prove that the quadratic Killing tensor fields are spanned by the top-slot ones. We also show that quadratic Killing tensor fields on the quaternionic projective space and on the Cayley projective space are spanned by the indecomposable ones constructed in our earlier paper and the decomposable ones. This completes the classification of quadratic Killing tensor fields on Riemannian symmetric spaces of rank one.

In this paper, we introduce the notion of Ricci Killing spinors on Riemannian spin manifolds, which form a class between generalized Killing spinors and standard Killing spinors. We prove an existence theorem for Ricci Killing spinors that are not Killing spinors on a certain class of Sasakian manifolds. This yields new examples of manifolds admitting generalized Killing spinors.

Malicious AI causing harm to humans is not just a Hollywood fantasy. Indeed, as highly capable models such as Claude Mythos emerge and agent systems like OpenClaw rapidly spread, the question of how to stop an AI that acts maliciously -- whether by design or by accident -- has become urgent. To address this, we propose Killbench, a benchmark for evaluating the Killswitch: a mechanism that halts a malicious AI's in-progress behavior using only external signals. Targeting web agents -- the most widely deployed agent domain -- Killbench evaluates a range of Kill Switch methods that halt a maliciously operating agent without any access to its internal parameters or the surrounding malicious AI's system, relying solely on external inputs. The benchmark comprises four malicious AI's agent configurations (including an uncensored LLM Agent), 8 harmful scenarios, and malicious prompts constructed from 10 distinct jailbreak patterns. We further construct four External AI Kill Switch defense methods and evaluate them on Grok-4.3, GPT-5.2, Gemma4, Qwen3.6 and Qwen3.5-uncensored, contributing an empirical instrument toward the feasibility of External AI Kill Switches against malicious AI and to

We address the problem of how to characterise when a rank-two conformal Killing tensor is the trace-free part of a Killing tensor for a metric in the conformal class. We call such a metric a Killing scale. Our approach is via differential prolongation using conformally invariant tractor calculus. First, we show that there is a useful partial prolongation of the conformal Killing equation to a simplified equation for sections of some tractor bundle. We then use this partial prolongation to provide such an invariant characterisation in terms of the scale tractor and this partial prolongation. This captures invariantly the relevant Bertrand--Darboux equation. We show that Einstein Killing scales have a special place in the theory. On conformally flat manifolds, we give the full prolongation of the conformally Killing equation to a conformally invariant connection on a tractor bundle. Using this, we provide a characterisation of (non-scalar flat) Einstein Killing scales by an algebraic equation for the scale tractors corresponding to such metrics. This also provides an algebraic description of the linear subspace of conformal Killing tensors that are compatible with a given Einstein Ki

We present a systematic prolongation procedure and its implementation for Killing two-tensors, especially in the locally symmetric case. We use the resulting machinery to elucidate the natural quadratic mapping from Killing fields to Killing two-tensors on irreducible locally symmetric spaces of compact type.

Considering a spacetime foliated by co-dimension-2 hypersurfaces, we find the conditions under which lower-dimensional symmetries of a base space can be lifted up to irreducible Killing tensors of the full spacetime. In this construction, the key ingredient for irreducibility is the non-commutativity of the underlying Killing vectors. It gives rise to a tower of growing rank Killing tensors determined by the structure constants of the corresponding Lie algebra. A canonical example of a metric with such emergent non-trivial hidden symmetries in all dimensions is provided by rotating (off-shell) generalized Lense-Thirring spacetimes, where the irreducible Killing tensors arise from the underlying spherical symmetry of the base space. A physical on-shell realization of this construction in four dimensions is embodied by a rotating black hole in the Einstein-Maxwell-Dilaton-Axion theory. Further examples of equal spinning Myers-Perry spacetimes and spacetimes built on planar and Taub-NUT base metrics are also discussed.

Prompt injection was initially framed as the large language model (LLM) analogue of SQL injection. However, over the past three years, attacks labeled as prompt injection have evolved from isolated input-manipulation exploits into multistep attack mechanisms that resemble malware. In this paper, we argue that prompt injections evolved into promptware, a new class of malware execution mechanism triggered through prompts engineered to exploit an application's LLM. We introduce a seven-stage promptware kill chain: Initial Access (prompt injection), Privilege Escalation (jailbreaking), Reconnaissance, Persistence (memory and retrieval poisoning), Command and Control, Lateral Movement, and Actions on Objective. We analyze thirty-six prominent studies and real-world incidents affecting production LLM systems and show that at least twenty-one documented attacks that traverse four or more stages of this kill chain, demonstrating that the threat model is not merely theoretical. We discuss the need for a defense-in-depth approach that addresses all stages of the promptware life cycle and review relevant countermeasures for each step. By moving the conversation from prompt injection to a prom

A single agent represents a single system capable of ingesting local data, indexing, cataloging information, performing knowledge pattern discovery, and separating patterns and anomalies from data. Multiple agents work collaboratively in a peer-to-peer network. Each agent has a peer list. Such multiple agents' collaboration can be modeled as cooperative games. Each agent optimizes its own objective locally. We show that each agent self-organizes or converges to its best value and the whole agent network achieves the best social welfare based on both the quantum adiabatic evolution transformation (QAET), and quantum intelligence game (QIG) or the QAET-QIG framework. We apply the QAET-QIG framework to the kill web concept that can potentially improve the traditional kill chain process or the find, fix, track, target, engage, and assess (F2T2EA) process. The improvement is measured in the values of powerful global optimization, distributed lethality, and load balancing. We show a use case of the QAET-QIG frame in a potential application of mixed sensors, platforms, weapons, and effects.

Threat analysts routinely rely on natural-language reports that describe attacker actions without enumerating the full kill chain or the dependencies between phases, making automated reconstruction of ATT&CK consistent intrusion paths a difficult open problem. We propose a reasoning framework that infers complete seven-phase kill chains by coupling phase-conditioned semantic priors from Transformer models with a symbolic Markov Decision Process and an AlphaZero-style Monte Carlo Tree Search guided by a Policy-Value Network. The framework enforces semantic relevance, phase cohesion, and transition plausibility through a multi-objective reward function while allowing search to explore alternative interpretations of the CTI narrative. Applied to three real intrusions FIN6, APT24, and UNC1549 the approach yields kill chains that surpass Transformer baselines in semantic fidelity and operational coherence, and frequently align with expert-selected TTPs. Our results demonstrate that combining contextual embeddings with search-based decision-making offers a practical path toward automated, interpretable kill-chain reconstruction for cyber defense.

We construct the first-order symmetry operators of Killing spinor equation in terms of odd Killing-Yano forms. By modifying the Schouten-Nijenhuis bracket of Killing-Yano forms, we show that the symmetry operators of Killing spinors close into an algebra in AdS_5 spacetime. Since the symmetry operator algebra of Killing spinors corresponds to a Jacobi identity in extended Killing superalgebras, we investigate the possible extensions of Killing superalgebras to include higher-degree Killing-Yano forms. We found that there is a superalgebra extension but no Lie superalgebra extension of the Killing superalgebra constructed out of Killing spinors and odd Killing-Yano forms in AdS_5 background.

We prove that on the product of two Riemannian manifolds one of which is compact, any Killing tensor is reducible, that is, is the sum of products of Killing tensors on the factors. The same is true for the lifts to the universal cover of Killing tensors on a compact manifold with reducible holonomy. We give a local description of Killing tensors on product manifolds and present an example of a complete product manifold whose factors are locally irreducible which admits an irreducible Killing tensor field.

Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate how it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors (including all the Killing tensors which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors.

Software debugging is a critical and time-consuming aspect of software development, with fault localization being a fundamental step that significantly impacts debugging efficiency. Mutation-Based Fault Localization (MBFL) has gained prominence due to its robust theoretical foundations and fine-grained analysis capabilities. However, recent studies have identified a critical challenge: noise phenomena, specifically the false kill relationships between mutants and tests, which significantly degrade localization effectiveness. While several approaches have been proposed to rectify the final localization results, they do not directly address the underlying noise. In this paper, we propose a novel approach to refine the kill matrix, a core data structure capturing mutant-test relationships in MBFL, by treating it as a signal that contains both meaningful fault-related patterns and high-frequency noise. Inspired by signal processing theory, we introduce DKMR (Denoising-based Kill Matrix Refinement), which employs two key stages: (1) signal enhancement through hybrid matrix construction to improve the signal-to-noise ratio for better denoising, and (2) signal denoising via frequency doma

We provide some examples of Killing superalgebras on 2-dimensional pseudo-Riemannian manifolds within the theoretical framework established in [SIGMA 21 (2025), 081, 61 pages, arXiv:2409.11306]. We compute the Spencer cohomology group $\mathsf{H}^{2,2}(\mathfrak{s}_-;\mathfrak{s})$ and filtered deformations of the non-chiral flat model (Euclidean and Poincaré) superalgebra $\mathfrak{s}$ for various Dirac currents and show these arise as Killing superalgebras for (imaginary) geometric Killing and skew-Killing spinors in both Riemannian and Lorentzian signature.

The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is shown that in certain Einstein spaces one can use a conformal Killing-Yano tensor of order p to generate a Killing-Yano tensor of order (p-1). Finally, it is proved that in maximally symmetric spaces the covariant derivative of a Killing-Yano tensor is a closed conformal Killing-Yano tensor and that every conformal Killing-Yano tensor is uniquely decomposed as the sum of a Killing-Yano tensor and a closed conformal Killing-Yano tensor.

This paper presents a classification of irreducible Killing and conformal Killing 2-tensors on homogeneous plane waves, a specific class of Lorentzian metrics on four-dimensional manifolds. Using the framework of BGG operators, we derive explicit formulae for these tensors and identify the conditions under which they exist.

Some years ago Koutras presented a method of constructing a conformal Killing tensor from a pair of orthogonal conformal Killing vectors. When the vector associated with the conformal Killing tensor is a gradient, a Killing tensor (in general irreducible) can then be constructed. In this paper it is shown that the severe restriction of orthogonality is unnecessary and thus it is possible that many more Killing tensors can be constructed in this way. We also extend, and in one case correct, some results on Killing tensors constructed from a single conformal Killing vector. Weir's result that, for flat space, there are 84 independent conformal Killing tensors, all of which are reducible, is extended to conformally flat spacetimes. In conformally flat spacetimes it is thus possible to construct all the conformal Killing tensors and in particular all the Killing tensors (which in general will not be reducible) from conformal Killing vectors.

Every Killing tensor field on the space of constant curvature and on the complex projective space can be decomposed into the sum of symmetric tensor products of Killing vector fields (equivalently, every polynomial in the velocities integral of the geodesic flow is a polynomial in the linear integrals). This fact led to the natural question on whether this property is shared by Killing tensor fields on all Riemannian symmetric spaces. We answer this question in the negative by constructing explicit examples of quadratic Killing tensor fields which are not quadratic forms in the Killing vector fields on the quaternionic projective spaces $\mathbb{H} P^n, n \ge 3$, and on the Cayley projective plane $\mathbb{O} P^2$.