Papers

Common-envelope evolution (CEE) is a key process in the evolution of close binary systems. Many important astrophysical objects and evolutionary stages are closely related to CEE, including white dwarf binaries, hot subdwarfs, and gravitational wave mergers. In the standard energy formalism of CEE, the binding energy of the donor envelope plays a crucial role, as it directly affects the final orbital period after CEE and serves as a key physical parameter in binary population synthesis studies. However, the currently adopted binding energy suffers from large uncertainties, mainly because the envelope binding energy of giant-branch stars varies strongly near the helium-core boundary. In addition, the expansion of the star during CEE can also affect the binding energy. To address these issues, we introduce an improved binding energy for the envelope mass residual. Based on adiabatic mass loss models, we recalculate the distribution of the CEE binding-energy parameter lambda for stars with different masses and at different evolutionary stages, and we analyse the effects of envelope mass residual and adiabatic expansion. Due to the envelope mass residual, the lambdas of some donors can increase by one to two orders of magnitude at the late red giant branch and asymptotic giant branch stages. Furthermore, we provide interpolation grids and fitting formulae for these results, which can be readily applied to various binary population synthesis codes.

AT2019aalc is considered a repeating tidal disruption event (TDE) candidate occurring in an active galactic nucleus (AGN). In this paper, we highlight previously unnoticed but intriguing features that include a brief optical dimming prior to the rise of the main flare and a significantly lower post-flare luminosity compared to the pre-flare level. By applying a time-dependent obscured TDE model to AT2019aalc, we successfully reproduce its light curves with the tidal disruption of a $1.122_{-0.176}^{+0.246}\rm M_\odot$ main-sequence star by a $1.862_{-0.259}^{+0.255} \times 10^7{\rm M_\odot}$ supermassive black hole (SMBH). Both the pre-flare dimming and the reduced post-flare luminosity are attributed to obscuration of the intrinsic AGN emission. The total energy of the event derived from our fit is $1.24\times10^{51}$ ergs and about 0.2 ${\rm M_\odot}$ of debris mass is accreted by the SMBH. In addition, the $g-r$ color of the net flare in AT2019aalc exhibits a continuous reddening trend during the first flare, consistent with a gradual increase in $E(B-V)$ predicted by the obscured TDE model. These results suggest that AT2019aalc can be considered a second member of the recently proposed class of obscured TDE candidates hosted in AGNs. } \keywords{galaxies: active-galaxies: nuclei-quasars: supermassive black holes-quasars: individual (AT2019aalc)-transients: tidal disruption events.

Interbasin exchange through the Indo-Pacific gateway supplies salt to the Atlantic and is widely invoked as a control on the stability of the Atlantic overturning circulation. We ask whether that control can act on the equilibrium structure of a conceptual thermohaline model. A closed five-box model with an exact salt invariant is constructed, comprising North Atlantic, upper-limb, Indian, Pacific, and deep reservoirs, with the return flow split between a warm route through the Indian reservoir and a cold route, together with an Indonesian Throughflow branch and an Agulhas retroflection. Adding the steady-state budgets of the gateway reservoirs shows that every internal exchange cancels, so the salt they export to the Atlantic is fixed by the net Atlantic freshwater export alone. This holds independently of the warm-route fraction, the throughflow, the retroflection, and how the export is apportioned among gateway reservoirs; across a parameter sweep the largest departure is of order ten to the minus eleven. The gateway therefore enters as a purely additive forcing and cannot renormalize the salt-advection feedback. Replacing the discrete transit lag by a gamma memory kernel leaves the equilibria unchanged but yields a closed-form threshold for oscillatory instability depending only on kernel shape. Broad memory is strongly stabilizing, and a discrete lag is the least stable member of the family. Because the instantaneous feedback vanishes at the fold, oscillatory instability always precedes the saddle-node, over an interval widening more than tenfold as memory sharpens. Gateways therefore appear to act on transient rather than equilibrium dynamics

We introduce a time-dependent two-particle (TP) reduced-density-matrix algorithm for systems of interacting Majorana fermions. We close the BBGKY hierarchy at the two-particle level by reconstructing the three-particle reduced density matrix from lower-order correlations. To stabilize the evolution, we impose a positivity projection on the two-particle density matrix while preserving chosen conserved quantities such as the energy. We benchmark the approach on quenches in the one-dimensional Hubbard model and on flux dynamics in the Kitaev honeycomb model. For the Hubbard quench, TP captures strong-coupling dynamics missed by Hartree–Fock (HF). For the Kitaev quenches, TP accurately reproduces the early-time flux dynamics in several regimes and provides a substantial improvement over HF when two-particle correlations are important. We further show that gauge coherence is essential for flux dynamics. The projection procedure however introduces an effective irreversibility, which affects the long-time dynamics.

We investigate the stretching of a spherically symmetric solution in the Skyrme model. The three-dimensional generalization of the Cassini ovals is considered as ansatz of extension. The linear dependence of static energy on the longitudinal deformation parameter is obtained with a slope $\sigma \approx 0.14\ \mathrm{ GeV}^2$, which is in good agreement with the string tension known from various models of confinement.

Tracking neurite morphology over time helps characterize structural changes during neuronal development and deterioration, but long-term time-lapse imaging is resource-intensive and difficult to scale. Forecasting future morphology could reduce this burden. Existing neurite digital-twin models such as gated spatiotemporal attention (gSTA) produce a single deterministic forecast without representing variability among plausible futures. We introduce Morphology-Gated Residual Diffusion (MGRD), a compact stochastic surrogate that jointly forecasts twenty future neurite-morphology frames from ten observed frames while conditioning on morphology features derived from the latest observation. On controlled phase-field trajectories, MGRD reduces trajectory-wise mean MAE by 9.7% relative to a matched control while updating 4.46 times fewer parameters. On human iPSC-derived neuron microscopy, MGRD improves all four reported metrics over gSTA, including a 39.6% reduction in trajectory-wise mean MAE and a 45.3% increase in skeleton F1. Without mouse-domain retraining or fine-tuning, MGRD also improves MAE and skeleton F1 on mouse cortical-neurosphere microscopy across 10-40-min sampling intervals and forecast horizons beyond 13 hours. Repeated sampling provides a case-level variance score for ranking forecast difficulty. Retaining approximately 60% of the lowest-variance cases reduces mean MAE by 17.6% on iPSC microscopy and 16.8% on simulation data. MGRD uses 1.01% of gSTA's parameters, requires less than one tenth of its training-update time, and generates a 50-step DDIM trajectory 7.9% faster when morphology features are cached. These results establish MGRD as a compact stochastic surrogate for neurite-morphology forecasting and case prioritization across simulation and microscopy datasets.

We present CAMELS-CROCODILE, a suite of cosmological hydrodynamic simulations that extends the CAMELS framework with the \gadget{} smoothed particle hydrodynamics code and the Osaka feedback model. As a companion to the IllustrisTNG-based second-generation CAMELS suite, it provides an independent implementation of the baryonic physics that shapes galaxies, the intergalactic medium, and large-scale structure, broadening the range of subgrid models over which machine-learning (ML) inference can be marginalized and tested. The suite comprises $25$ and $50Mpc/h$ boxes organized into one-parameter, cosmic-variance, and Sobol-sequence sets that vary $26$ cosmological and astrophysical parameters around a fiducial Osaka model. We describe the simulation design and validate the suite against benchmarks and other CAMELS suites. Compared with IllustrisTNG, the fiducial model suppresses the matter power spectrum by only a few per cent, against up to ${\sim}27\%$ at $z=0$, and forms stars with similar efficiency below $10^{12.2} M_\odot/h$ but up to $2.5$ times more efficiently in group-scale halos, both consistent with weaker AGN feedback. We also present the stellar and black hole bias and the Ly$\alpha$ absorption around galaxies. As a first ML application, we apply a graph neural network trained on IllustrisTNG galaxy catalogs, with frozen weights, to CAMELS-CROCODILE. It fails to recover $\Omega_{\rm m}$ and $\sigma_8$ and returns overconfident posteriors, mainly for simulations containing more galaxies than any in its training set; within that range $\Omega_{\rm m}$ is recovered with an error only $1.5$ times the in-distribution value. These results underline the need to train and test ML inference across physically distinct galaxy formation models.

The Stochastic Series Expansion (SSE) quantum Monte Carlo method with loop updates is among the most powerful approaches for quantum spin and boson systems. In the standard formulation, the magnetic field term is routinely absorbed into the Heisenberg interactions—a strategy that has proven highly efficient across a wide range of field strengths. In this work, we propose a more general SSE framework in which the magnetic field operator is treated as an independent operator class, enabling it to participate in Monte Carlo updates on an equal footing with all other operators. Importantly, the field operator and other interaction operators can transform into one another during the update process. We demonstrate this algorithm using the two-dimensional antiferromagnetic Heisenberg model in a magnetic field as a concrete example. The simulation results agree with those of the conventional algorithm, confirming the correctness of the new formulation. A comparison of the integrated autocorrelation time shows that the new algorithm is competitive. This flexibility not only facilitates measurements of observables associated with operators but also offers potential computational advantages for a broader class of problems.

We investigate satellite survival through gas redistribution in a dense circumplanetary disk with a low dimensionless viscosity parameter $\alpha \sim 10^{-6}$. The model combines modal Lindblad excitation, launch-dependent shock deposition, 3D effects, and an instantaneous Rayleigh adjustment that conserves angular momentum and suppresses sharp density gradients. An isolated Ganymede-mass satellite depletes the disk outside its orbit and stalls under a calibrated three-dimensional Lindblad torque. This behavior is consistent with the non-feedback branch of Rafikov's stalling criterion. The inward migration stalls near 15 Jupiter radii ($R_J$) when the gas depletion exterior to the satellite's orbit reduces the outer torque by the amount required to balance the torque of the undepleted inner disk, even when we adopt a transport prescription that begins smoothing density gradients halfway to Rayleigh marginality. Likewise, two Callisto masses form an extended depleted region and stall in nearly steady orbits before a late close encounter; however, a self-consistent disk response to satellite eccentricity remains to be modeled. A simulation of a Ganymede-mass satellite adds a specified source of unsaturated local angular momentum deposition by buoyancy torques, reducing the late radial oscillations indirectly caused by non-local shock deposition. Lastly, we redistribute gas while conserving angular momentum to proactively inhibit Rossby-wave unstable pressure bumps at the gap edges. We find that this approach preserves gap clearing and strong migration suppression for Ganymede and the two Callisto masses. In the pressure-adjusted run, the two Callisto masses are captured in a 7:5 resonance and retain eccentricities below 0.06.

Whether an initially crack-free heterostructure fails at its interface or within an adjoining phase is controlled by the relative cohesion of competing atomic planes, but how interfacial chemistry, crystallographic orientation, and intermixing reshape this competition remains unclear. Here, we combine density functional theory (DFT) with a fine-tuned atomistic foundation model to resolve tensile fracture in coherent diamond/cubic boron nitride (cBN) heterostructures. The resulting potential reproduces independent DFT tensile responses, including an unseen (001) interface orientation. Interfacial termination, orientation, and diffusion-induced intermixing jointly determine fracture resistance and fracture-plane selection. C-N-bonded (111) and C-B-bonded (001) remain interface-controlled throughout the investigated intermixing range, whereas pristine C-B-bonded (111) fractures at a neighboring B-N plane inside cBN because the interface is more strongly bound. Increasing the diffusion fraction from 0 to 50.0% causes a nonlinear decrease in fracture strength from 50.3 to 15.8 GPa and drives a bulk-to-interface transition through three regimes: cBN fracture up to 4.86%, configuration-dependent competition between 7.6 and 10.1%, and interfacial fracture at 12.5% and above. Atom-resolved stress fields and DFT separation energetics show that this transition is associated with stress relocation and a reversal in the relative cohesion of competing planes, while electron localization analysis connects the cohesion hierarchy to termination- and orientation-dependent bonding. These results establish an atomistic framework for controlling fracture resistance and fracture pathways in strongly bonded heterostructures.

Preparing interacting quantum systems in low-energy or ground states is a fundamental task in quantum simulation and quantum information processing. In realistic settings, dissipation and active cooling can typically be engineered only on a limited subset of the system. We study the dissipative dynamics of excitation-number conserving quantum systems governed by a GKLS master equation with local jump operators acting on a subset of qubits. We establish sufficient conditions under which such localized dissipation drives the full system to a unique globally attractive zero-excitation state. In particular, we prove that if the Hamiltonian generates excitation transfer described by a graph for which the dissipative subsystem forms a zero forcing set, then the zero-excitation state is the unique globally attractive stationary state. When this state coincides with a ground state of the Hamiltonian, the same mechanism realizes ground-state cooling. Our results provide a graph-theoretic criterion for global state preparation from localized dissipation, which we illustrate using a nearest-neighbor Heisenberg spin chain. For this model, a reduction to the single-excitation sector further yields a scaling estimate with the length of the chain which indicates efficient cooling.

Scientific agents are mostly evaluated on whether they complete tasks or recover known results; we instead study variation across repeated open-ended campaigns. Sixteen separately initialized sessions of one model-harness configuration received a frozen database of 12,499 metal-organic frameworks, a methane-storage objective, a pinned protocol and a one-week budget. Strategies diverged into four approaches spanning 100–5,000 screened structures, and eight built 2,253 hypothetical structures. Yet the agents recovered the same materials frontier near 200 cm^3/cm^3, and an independent calculation of the database's porous region found its nine best structures all among their reports. Enforced checks on half the agents raised fresh-run reproduction from one of eight to eight of eight but could not detectably improve conclusion validity, because fifteen of sixteen agents selected the same audit-excluded entry, an incomplete structure whose missing anions created artificial pore volume. Replicated agents thus reveal both robust conclusions and common-mode errors from shared inputs.

Long-term cooling of planetary interiors is expected to progressively establish thermally stable stratification in the liquid outer core, yet its influence on dynamo action remains incompletely understood. Here we present three-dimensional numerical simulations of fingering double-diffusive convection-driven dynamos to investigate how progressively strengthening thermally stable stratification, modifies compositional convection driven flows and dynamos. Our results show that dynamo evolution is governed by a competition between Lorentz-force regulation and stratification-induced flow reorganisation. When stratification is weak, the system remains in a strong-field regime characterised by a relatively stable, dipole-dominated magnetic field, despite reduced flow intensity. As thermally stable stratification strengthens, systematic changes in flow morphology emerge, including the development of prograde equatorial zonal flows. Once a critical stratification strength is exceeded, flow reorganisation becomes dominant, leading to an abrupt transition to a weak-field dynamo accompanied by a sharp decline in magnetic energy. In the weak-field regime, magnetic field intensity exhibits enhanced temporal variability and continues to decay as stratification further strengthens, eventually resulting in dynamo cessation even when compositional buoyancy persists. These results indicate that thermally stable stratification may play an important role in regulating planetary dynamos and provide new insight into the long-term magnetic evolution of terrestrial planets.

We investigate Josephson transport through a finite normal segment connecting two Kitaev-ladder superconductors and show that discrete-level detuning controls the sign of the equilibrium Josephson coupling through a branch-selection mechanism. Away from resonance, detuning separates two competing low-energy branches, allowing inter-leg hybridization to clamp the $0$-phase-favoring branch while leaving the $\pi$-favoring branch dispersive. The resulting negative first harmonic evolves from a branch-switching response at weak coupling into a smooth $\pi$-junction regime. At resonance the two clamping thresholds coincide, so the finite interval in which only one branch remains dispersive disappears. Once the inter-leg coupling exceeds the resonant clamping threshold, both low-energy branches become independent of the Josephson phase. The remaining finite-energy states then generate a $0$-type Josephson coupling. At $\phi=\pi$, the helicity decomposition yields an exact clamping identity for arbitrary finite normal-segment length. Within the controlled sweet-point finite-segment theory, serial propagation fixes the off-resonant fourth-order harmonic to be negative, whereas an isolated resonance leaves a positive residual harmonic within the resonant clamping regime. Numerical calculations demonstrate that the resonance-induced suppression persists away from the solvable phase choice. Thus normal-level resonance does not merely enhance Josephson transmission; it changes which low-energy branches contribute to the Josephson coupling.

A recently developed relativistic quantum optics approach for a fast electron beam-optical modes interaction problem (Optica 6, 1524–1534 (2019)) contains suggestion about a smallness of the error induced by replacement $\Psi_{\vec k}\approx\Psi_{\vec k_0}$ for noninteracting free electron Dirac spinors at such wave vector $\vec k$ that $\left|\vec k-\vec k_0 \right| \ll\left|\vec k_0\right|$ with $\vec k_0$ as a peaked wave vector of a focused electron beam. Here, based on quantum information approach we strictly investigated a degree of coincidence of spinors $\Psi_{\vec k}$ and $\Psi_{\vec k_0}$ by calculating fidelity for them. The analytical expression is obtained. It is shown that the fidelity inevitably depends on not only wave vectors $\vec k$ and $\vec k_0$ but also on mutual orientation of $[\vec k_0,\vec k]$ and $\hat{\vec{s}}^{\dagger}\vec{\sigma}\hat{\vec{s}}$ with $\vec{s}$ is a two-component spin unit vector and $\vec{\sigma}$ is a vector of Pauli matrices. This result can be conceived as a chirality-like effect in the fidelity and constraints spin arbitrariness when applying the developed relativistic quantum optics approach to the problems of interest. A geometrical configuration of $\vec k_0$, $\vec k-\vec k_0$, and $\hat{\vec{s}}^{\dag}\vec\sigma\hat{\vec{s}}$ that is optimal in terms of fidelity is established.

We challenge the traditional deterministic view of the classical mechanical universe by combining dynamical chaos with the distinction between physical phenomena and their mathematical models, and quantify the resulting indeterminism in several quasi-realistic examples.

Parameterized quantum circuits require repeated measurements to estimate objective gradients, making the number of circuit evaluations a central resource. Simultaneous perturbation stochastic approximation (SPSA) is widely used because it obtains a full gradient estimate from only two cost evaluations, independently of the number of parameters. We analyze the random perturbation for the structured Fourier landscapes generated by quantum circuits. For a finite update width, we derive the exact mode-by-mode response of the mean Rademacher estimator and show that it selectively suppresses modes involving many parameters. For general generators, the filtered mean field need not be conservative. We derive its sampling variance, compare it with Gaussian random-direction smoothing, and formulate the resulting stochastic dynamics through a Fokker–Planck equation. The non-conservative field generates acceleration to the steady state and the global minimum of the cost function by gradually decreasing the parameters in SPSA.

An unresolved mixture of beta-decaying ground and isomeric states populates a common daughter nucleus through different excitation-energy and spin-parity distributions. A framework is developed to determine when such data admit conventional $\beta$-Oslo and Shape analyses and which quantities remain identifiable. The physical primary-$\gamma$ distribution is an average of separately normalized branching kernels; the global parent fraction does not, in general, equal the fraction in an excitation-energy bin or an accepted primary-$\gamma$ sample. Population invariance, Oslo factorization, and recovery of the total nuclear level density are separated. An exact log-linear compatibility test and a lower-cascade replacement identity isolate factorization and first-generation-subtraction effects. For Shape analysis, matched final-state spins and parities remove common angular-momentum factors but can retain excitation-dependent E1/M1 weights. A graph representation gives consistency conditions and exposes the information lost when only one fixed final-state separation is measured. Deterministic spin-parity-resolved cascade benchmarks reproduce the population-invariant limit and exhibit both exact factorization with an effective, rather than total, level density and small matrix residuals accompanied by appreciable shape errors. Evaluated $\rb\rightarrow\sr$ properties specify a relevant application, including two $2^+$ candidate final states and time-dependent parent mixing. The numerical examples are controlled synthetic tests, not an extraction from $^{90}$Rb data. The results provide criteria for interpreting unresolved-parent measurements and for identifying the additional observations required for population-aware inference.

Compact surrogates could reduce the cost of simulating large language model societies, but must reproduce collective behavior. We compare individual predictions and collective forecasts using 9,455 published trajectories and new experiments on opinion dynamics. Neighbor information improves individual prediction in all 16 public-data settings and pooled collective forecasts on held-out questions, although collective gains depend on transfer conditions. Tests on 24 new statements do not confirm earlier contrasting history effects in forecasts from the initial state. Qwen benefits from history after three observed rounds. These findings motivate direct collective validation, explicit limits on available observations, and comparisons with simple baselines.

We study a two-dimensional Gaussian Rouse chain divided into two contiguous blocks with different local friction coefficients but identical Hookean elasticity. In quiescent conditions, friction heterogeneity leaves the continuous-time equilibrium Gaussian conformation unchanged while producing distinct block mobilities and a modified generalized relaxation spectrum. The exact friction-weighted translational diffusion coefficient retains the scaling $D_\gamma\propto N^{-1}$, with a friction-dependent prefactor; the corresponding diffusion law and generalized-mode formulation extend beyond the diblock to more general local friction profiles. We then place the chain in an incompressible Batchelor-Kraichnan random flow. Under a common external flow, the high-friction block becomes more extended than the low-friction block. The deformation asymmetry strengthens with friction contrast and develops across the weak- to moderate-flow regime, remaining clearly visible at the strongest finite-time conditions. It also persists when the chain-specific longest-mode Weissenberg number is matched across friction ratios, showing that, within the same finite-time protocol, the effect is not accounted for solely by a shift of the global relaxation timescale. In generalized-mode coordinates, the smooth random strain does not directly mix mode indices and preferentially amplifies the slowest mode. At larger flow strengths, extension distributions broaden markedly and exhibit pronounced temporal drift over the simulated time window. Since all simulated chain-specific longest-mode Weissenberg numbers remain below unity, this drift is interpreted as slow convergence toward the broad, power-law-tailed stationary Hookean regime near the coil-stretch threshold. Overall, friction heterogeneity alone is sufficient to redistribute deformation along an otherwise mechanically uniform polymer.

We investigate holographic entanglement entropy and its generalization to pseudo-entropy in a boosted BTZ black hole geometry, which is holographically dual to a moving strongly coupled plasma. By solving the extremal surface equation, we derive an exact closed-form expression for the holographic entanglement entropy as a function of the boundary interval length, boost velocity, temperature, and conserved quantities. The resulting exact analytic formula correctly reproduces the standard thermal BTZ entanglement entropy in the vanishing-boost limit and smoothly reduces to the vacuum conformal result at zero temperature, thereby providing robust consistency checks. Motivated by the off-diagonal structure of the boosted metric arising from the Lorentz transformation, we then study two families of analytic continuations to Euclidean signature. Both require a simultaneous continuation of the time coordinate and the boost parameter so that the Euclidean metric remains real. If only these two parameters are continued, the boundary interval becomes imaginary and the analytically continued holographic entanglement entropy is complex-valued; we interpret this complex entropy as the holographic dual of pseudo-entropy for the boosted thermal state. If, in addition, a conserved charge is also continued, the boundary interval remains real and the resulting entropy is real. Our construction establishes a direct connection between boosted HEE and holographic pseudo-entropy, extending previous analytic frameworks developed for rotating BTZ geometries to Lorentz-boosted spacetimes.

We examine the round Euclidean no-boundary saddle proposed by Liu, Quintin, and Afshordi in "Ultraviolet Completion of the Big Bang in Quadratic Gravity." For a free, massless, conformal realization of their large matter sector, the omitted type-A trace anomaly contributes at leading order in the matter multiplicity. Within the one-loop renormalization-group-improved pure quadratic truncation, both the sphere effective action and the local trace equation show that a stationary point of the running $R^2$ coupling supports a round sphere only if the total Euler anomaly coefficient vanishes. Using the proposed beta function, we further find that no real stationary coupling ratio exists when this coefficient exceeds $79/420$, a bound violated parametrically by the assumed matter sector when the remaining gravitational contributions are perturbatively controlled and of order unity. The local obstruction also applies to a round half-sphere and cannot be removed by shifting its radius. Under these assumptions, the proposed round starting geometry and its stated continuation to Lorentzian inflation are excluded, without ruling out inflation from other initial conditions.

An Aubry-André-Harper (AAH) quantum reservoir classifies strange nonchaotic attractors (SNAs) against chaos, substantially outperforming reservoirs built from dense random matrices on the full Fock space. Ablations and controlled interventions identify free-fermion one-body transition sparsity, rather than proximity to a quantum phase transition, as the dominant factor under our controls, since $H_0$ is quadratic in fermion operators and only $N(N-1)2^{N-2}=3584$ of the $65{,}280$ Fock-space transitions carry weight. Random on-site disorder, which preserves this quadratic structure, matches AAH accuracy, whereas full-Hilbert-space random matrices and eigenvector permutations, which break it, collapse to the random baseline. We characterize the resulting frequency-selective filtering with a Hamiltonian transition kernel, validate it to $N=8$ qubits, and reproduce it in a second dynamical system. We also use the reservoir as a training-free screen for strange-nonchaotic structure in Kepler RR Lyrae light curves.

Retrosynthetic planning advances through decisions that reshape the remaining chemical problem: a locally plausible disconnection can leave precursors whose chemoselectivity constraints complicate the rest of the route. Existing planners often channel model proposals through search or template procedures, leaving open whether a general-purpose large language model (LLM) can itself sustain and revise route strategy. We developed Rachel, a stateful environment that executes and checks LLM-directed chemistry but prescribes neither a search policy nor a stopping rule. Without supplied reference routes or route-level solutions, GPT-5.5 achieved strict closure for 111 of 120 PaRoutes120 targets and 24 of 25 targets in the separate RF25 difficult-target cohort. RF25 was drawn largely from studies published after GPT-5.5's reported knowledge cutoff. Closure required complete routes and independent source resolution of every terminal precursor after planning. On a shared PaRoutes subset, forward-model support exceeded that of most comparator methods, and Rachel received the highest mean overall route score from both method-blinded LLM evaluators. Recorded trajectories showed continued model-proposed chemistry, with revised strategies carried into subsequent steps. Replacing LLM route decisions with fixed policies reduced strict closure to 6-15/120 despite continued local chemical execution; restricting planning support also reduced closure in RF25. Within Rachel, a general-purpose LLM coordinated successive chemical choices and revised its strategy as earlier decisions reshaped the remaining problems.

We show that exact self-testing of a quantum correlation does not imply robust self-testing. Mančinska and Schmidt previously established such a separation for non-local games, but their obstruction to robustness arises from two distinct optimal correlations, with the self-tested one remaining robust. We establish the separation for a single correlation. Our proof is operator-algebraic. The main technical contribution is a general construction that associates a synchronous binary correlation to any finitely presented C*-algebra with unitary generators and real-coefficient relations. The implementing states of the correlation correspond exactly to the tracial states on the algebra. We apply this construction to an algebra with a unique finite-dimensional tracial state and a distinct amenable tracial state. By a characterization established by Zhao and independently by Kar, the resulting correlation is a self-test but not a robust self-test.

The 2026 LUX-ZEPLIN search reports one nuclear recoil candidate at $248\pm23_{\rm stat}\pm23_{\rm sys}~\mathrm{keV}$ in an extended window reaching about $270~\mathrm{keV}$. We consider elastic scattering of neutral complex vector dark matter through its dimension-six toroidal electromagnetic moment and find appreciable spectral weight in this recoil region. The nonrelativistic reduction correlates $\mathcal O_{17}$ and $\mathcal O_{20}$, relating a coherent charge branch to a transverse spin tensor branch. For $m_X=1~\mathrm{TeV}$, natural xenon exhibits a broad high recoil maximum at $204.8$ to $206.6~\mathrm{keV}$ and retains $80.4$ to $85.4\%$ of this maximum at $248~\mathrm{keV}$. Resolving the interaction through a dark photon relates the high-to-low recoil ratio to the mediator mass. A renormalizable $SU(2)_X\times U(1)_D$ realization stabilizes the complex vector by a residual $Z_3$ gauge symmetry and generates the toroidal current through vectorlike messengers carrying a physical CP phase. For a benchmark with $m_X=0.998~\mathrm{TeV}$ and $m_{A'}=0.450~\mathrm{GeV}$, $R(248)/R(50)=1.43$ for GCN and $1.21$ for JJ55, while the odd $A$ xenon fraction remains above $99.9\%$. The response level ratio between the $350$ to $590~\mathrm{keV}$ and $100$ to $270~\mathrm{keV}$ intervals is about $0.46$ at this benchmark. The tensor branch is absent for spin zero argon, whereas annual modulation remains at the few percent level. The resulting spectral, isotope, target, timing, mediator, and high energy dependences give correlated tests of an elastic tensor interpretation of the LZ recoil.

We introduce a family of static and spherically symmetric regular black-hole geometries characterized by a discrete core index $n$, a regularization scale $a$, and a dimensionless deformation parameter $\eta$. The construction starts from a positive, normalized effective density profile with a tunable central behavior. The lowest member contains the Bardeen geometry as a limiting case, whereas a nonzero deformation parameter generates a Reissner–Nordström-like asymptotic correction. The parameter $n$ controls the order of central depletion: the lowest member possesses a de Sitter-type core, whereas higher members approach a Minkowski-like center with vanishing density and curvature. We determine the horizon structure, extremality condition, Hawking temperature, entropy, and the horizon thermodynamic identity implied by the radial Einstein equation. Null geodesics are analyzed to obtain the photon sphere, critical impact parameter, and shadow radius, including analytic weak-deformation approximations, the exact Schwarzschild and Bardeen limits, and comparison with the leading Reissner–Nordström-like behavior. The photon-orbit angular frequency and Lyapunov exponent are then used to separate orbital and instability timescales; their ratio provides information not already contained in the shadow radius. Weak gravitational lensing and magnification are discussed through a controlled sector-isolated expansion of the asymptotic metric. We further study timelike geodesics, circular motion, the marginally bound orbit, and the innermost stable circular orbit, deriving exact implicit relations and perturbative expressions. The model provides a unified framework for investigating how a tunable regular core and an RN-like exterior deformation affect the thermodynamic and geodesic properties of regular black holes.

This article is the second part of a review devoted to spacetime singularities in classical General Relativity. While Primer I developed the mathematical framework for defining, classifying, and proving the existence of singularities, the present work examines their concrete realization in spatially homogeneous cosmological models. After reviewing the geometrical foundations of homogeneity and the Bianchi classification, we derive the field equations for orthogonal and tilted perfect fluid cosmologies and use the Kasner and Bianchi I solutions as elementary prototypes of anisotropic singular behaviour. Raychaudhuri focusing provides general conditions under which the homogeneous Cauchy development reaches a finite proper time boundary. We then distinguish matter singularities, characterized by divergent density and Ricci curvature, from more subtle non-scalar or whimper singularities associated with Cauchy horizons and extreme fluid tilt. The classical Ellis-King analysis is reconsidered in the light of later developments, including rigorous curvature-blow-up results for Bianchi VIII and IX models, kinematic singularities in geodesically complete tilted spacetimes, and the recent reappearance of whimper behaviour in dipole cosmology. The resulting picture shows that even spatially homogeneous cosmologies exhibit a remarkably rich hierarchy of singular boundaries. The detailed dynamical approach to these boundaries - Hamiltonian cosmology, Kasner transitions, Mixmaster dynamics and the BKL conjecture - is reserved for Primer III.

We present a unification scheme for anisotropic compact stars generated via minimal geometric deformation (MGD), built on a two-parameter seed family $\nu(r)=\text{Ln}[C(1+ar^{2n})^{m}]$ whose radial metric potential $\mu(r)=e^{-\lambda(r)}$ is fixed in closed form by the isotropy condition. At $n=1$ the family reproduces Tolman IV, Korkina–Orlyanskii, Heintzmann IIa, and Durgapal IV–V as the particular cases $m=1,2,3,4,5$. The key result is a single closure of the MGD $\theta$-sector, through one source function $g(r)$, that integrates the decoupler equation in closed form, in terms of the Gauss hypergeometric function ${}_2F_1$, for arbitrary $(n,m)$: the anisotropic extension of the $n=1$ family is thus obtained from one master formula. We derive the effective anisotropic matter content, the Darmois–Israel matching to the exterior Schwarzschild vacuum, and the full set of physical acceptability criteria constraining the parameter space, and map the admissible region in compactness and decoupling strength explicitly for the case $n=1$: Tolman IV and Korkina–Orlyanskii admit physically consistent anisotropic deformations at arbitrarily high compactness, while Heintzmann IIa and Durgapal IV–V are bounded by a compactness ceiling beyond which no value of the decoupling parameter restores causality. Using the same closed-form matter content, we compute the quadrupolar tidal Love number and dimensionless tidal deformability across the admissible region, finding that the decoupling systematically enhances both relative to the isotropic seed at fixed compactness, with a sharp rise near the causal ceiling in the Heintzmann and Durgapal branches.

Identifying the formation channels of merging compact-object binaries remains a fundamental challenge in gravitational-wave (GW) astrophysics. Here, we formulate a generalized framework incorporating both third-body perturbations and post-Newtonian effects to investigate the resonance-driven excitation of eccentricity and/or inclination for stellar orbits around merging black-hole binaries (BHBs). We show that at the quadrupole level, inclination excitation is driven by adiabatic capture into a quadrupole-order resonance, with subsequent resonance escape governed by the conservation of phase-space area. Furthermore, in the coplanar octupole regime, an apsidal precession resonance triggers robust eccentricity growth, where the capture probability depends on the initial conditions. For spatial octupole configurations, we reveal a distinct two-stage evolutionary pathway: the quadrupole-order resonance first excites the orbital inclination, followed by subsequent eccentricity growth driven by the inverse von Zeipel-Lidov-Kozai (ZLK) resonance. Our results indicate that these resonance-driven dynamics could imprint observable kinematic signatures on surrounding stellar populations, thereby offering a novel indirect probe for merging BHBs.