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At least 145 records · Page 8

Phase Diagrams and Piezoelectric Properties of Wurtzite Al1-x-yScxGdyN Heterostructural Alloys

Ternary nitride alloys based on wurtzite AlN are a promising platform to realize functional materials, particularly ferroelectrics and optical emitters, that can smoothly integrate with conventional microelectronics. Here, a strategic design is presented to enable multifunctional materials by substituting multiple elements into AlN to create quaternary nitride alloys. By combining computational predictions and combinatorial thin film synthesis, the phase diagram of these quaternary Al-Sc-Gd-N alloys (or pseudo-ternary heterostructural AlN-ScN-GdN alloys) is successfully predicted as a function of effective temperature, and we experimentally grow Al1-x-xScxGdyN thin films for the first time. It is revealed that Al1-x-xScxGdyN crystallizes in a wurtzite-derived structure for X + y <~ 0.35, consistent with the calculated phase diagram. The computational investigation explores whether co-substitution induces cooperative effects on these alloys' piezoelectric and ferroelectric properties, finding that it is beneficial for reducing the polarization switching barrier. We calculate that Al1-x-xScxGdyN thin films should display ferroelectric switching. This is supported by our experimental measurements of a high optical bandgap, enhanced piezoelectric coefficient, and a change in the calculated polarization switching mechanism, and we achieve preliminary ferroelectric switching that experimentally realizes the prediction. Overall, our work sets the foundation toward quaternary wurtzite-nitride-based multifunctional materials, including piezoelectrics, ferroelectrics, and possibly even multiferroics.

36 MATERIALS SCIENCE↗

Heterogeneous Integration of Flipped Oxide Heterostructure Membranes for Nanoelectronics

Freestanding complex oxide membranes enable the release and transfer of epitaxial films, offering new design freedoms for next‐generation electronics. While the LaAlO 3 /SrTiO 3 (LAO/STO) heterostructure exhibits remarkable tunable conductivity at its interface, the active interface remains buried beneath the substrate, limiting access to this functionality. Here, we demonstrate how the LAO/STO heterostructure, in membrane form, can be flipped and precisely positioned on silicon and other platforms using polymer‐free micromanipulation. The transferred membranes preserve atomically smooth surfaces, high crystallinity, and key electronic properties. Through the 44‐nm insulating STO layer, ultra‐low‐voltage electron‐beam lithography (ULV‐EBL) writes conductive nanostructures at the now‐accessible STO/LAO interface, offering the potential to function as programmable local gates that modulate charge carriers in the underlying silicon. The platform establishes a general strategy for integrating complex oxide heterostructures with semiconductors, quantum materials, and flexible substrates, enabling new architectures for reprogrammable nanoelectronic devices.

36 MATERIALS SCIENCE↗

Manipulating Na/TM Ratio‐Driven Structural Heterogeneity of O3‐NaNi 1/3 Fe 1/3 Mn 1/3 O 2 Cathode for High‐Voltage Sodium‐Ion Batteries

The stability of O3-type NaNi 1/3 Fe 1/3 Mn 1/3 O 2 under high-voltage cycling is dictated by how synthesis encodes lattice strain and redox heterogeneity. Here, in this study, the role of Na:TM stoichiometry is systematically resolved by tuning the NaOH:precursor ratio during solid-state synthesis. The stoichiometric condition (Na:TM = 1.00) yields minimized microstrain, enabling uniform O3–P3 phase evolution and homogeneous multi-metal redox with preserved octahedral symmetry. In contrast, Na-excess compositions inherit disordered intermediates and heterogeneous distortion fields that trigger abrupt multiphase transitions and promote localized charge redistribution. In situ XRD captures the divergence in phase-transition pathways, TXM resolves particle-level redox heterogeneity, and XANES corroborates a stronger and more reversible Fe redox contribution at stoichiometry, shifting to diminished Fe participation and spatially inhomogeneous redox at higher Na content. These results establish Na:TM stoichiometry as a critical synthesis parameter controlling both structural coherence and redox stability. Electrochemically, the stoichiometric composition exhibits smooth voltage profiles with minimal polarization growth and retains nearly 80% of its initial capacity after 100 cycles even at an extended 4.2 V cutoff, whereas Na-excess compositions show significantly reduced initial coulombic efficiency and rapid voltage fade. Precise stoichiometric tuning provides a scalable route to defect-suppressed O3 frameworks, enabling structurally resilient, high-voltage sodium-layered cathodes.

36 MATERIALS SCIENCE↗

Facile Access to Organostibines via Selective Organic Superbase Catalyzed Antimony‐Carbon Protonolysis

Abstract The selective formation of antimony‐carbon bonds via organic superbase catalysis under metal‐ and salt‐free conditions is reported. This novel approach utilizes electron‐deficient stibine, Sb(C 6 F 5 ) 3 , to give upon base‐catalyzed reactions with weakly acidic aromatic and heteroaromatic hydrocarbons access to a range of new aromatic and heteroaromatic stibines, respectively, with loss of C 6 HF 5 . Also, the significantly less electron‐deficient stibines, Ph 2 SbC 6 F 5 and PhSb(C 6 F 5 ) 2 smoothly underwent base‐catalyzed exchange reactions with a range of terminal alkynes to generate the stibines of formulae PhSb(C≡CPh) 2 , and Ph 2 SbC≡CR [R=C 6 H 5 , C 6 H 4 ‐NO 2 , COOEt, CH 2 Cl, CH 2 NEt 2 , CH 2 OSiMe 3 , Sb(C 6 H 5 ) 2 ], respectively. These formal substitution reactions proceed with high selectivity as only the C 6 F 5 groups serve as a leaving group to be liberated as C 6 HF 5 upon formal proton transfer from the alkyne. Kinetic studies of the base‐catalyzed reaction of Ph 2 SbC 6 F 5 with phenyl acetylene to form Ph 2 SbC≡CPh and C 6 HF 5 suggested the empirical rate law to exhibit a first‐order dependence with respect to the base catalyst, alkyne and stibine. DFT calculations support a pathway proceeding via a concerted σ‐bond metathesis transition state, where the base catalyst activates the Sb‐C 6 F 5 bond sequence through secondary bond interactions.

Culvyhouse, Jacob↗

Self‐Standing Chiral Covalent Organic Framework Thin Films with Full‐Color Tunable Guest‐Induced Circularly Polarized Luminescence

Abstract Exploring self‐standing chiral covalent organic framework (COF) thin films with controllable circularly polarized luminescence (CPL) is of paramount significance but remains a challenging task. Herein, we demonstrate the first example of self‐standing chiral COF films employing a polymerization‐dispersion‐filtration strategy. Pristine, low‐quality chiral COF films were produced by interfacial polymerization and then re‐dispersed into COF colloidal solutions. Via vacuum assisted assembly, these COF colloids were densely stacked and assembled into self‐standing, pure chiral COF films ( L‐ / D‐ CCOF‐F) that were transparent, smooth, crack‐free and highly crystalline. These films were tunable in thicknesses, areas, and roughness, along with strong diffuse reflectance circular dichroism (DRCD) and cyan CPL signals, showing an intrinsic luminescence asymmetric factor ( g lum ) of ~4.3×10 −3 . Furthermore, these COF films served as host adsorbents to load various achiral organic dye guests through adsorption. The effective chiral transfer and energy transfer between CCOF‐F and achiral fluorescent dyes endowed the dyes with strong chirality and tunable DRCD, resulting in intense, full‐color‐tunable solid‐state CPL. Notably, the ordered arrangement of dye guest molecules within the preferentially oriented chiral pores of CCOF‐F contributed to an amplified | g lum | factor of up to 7.2×10 −2 , which is state‐of‐the‐art for COF‐based CPL materials. This work provides new insights into the design and fabrication of self‐standing chiral COF films, demonstrating their great potential for chiroptical applications.

Tang, Xihao↗

Facile Access to Organostibines via Selective Organic Superbase Catalyzed Antimony‐Carbon Protonolysis

The selective formation of antimony-carbon bonds via organic superbase catalysis under metal- and salt-free conditions is reported. Here, this novel approach utilizes electron-deficient stibine, Sb(C 6 F 5 ) 3 , to give upon base-catalyzed reactions with weakly acidic aromatic and heteroaromatic hydrocarbons access to a range of new aromatic and heteroaromatic stibines, respectively, with loss of C 6 HF 5 . Also, the significantly less electron-deficient stibines, Ph 2 SbC 6 F 5 and PhSb(C 6 F 5 ) 2 smoothly underwent base-catalyzed exchange reactions with a range of terminal alkynes to generate the stibines of formulae PhSb(C≡CPh) 2 , and Ph 2 SbC≡CR [R=C 6 H 5 , C 6 H 4 -NO 2 , COOEt, CH 2 Cl, CH 2 NEt 2 , CH 2 OSiMe 3 , Sb(C 6 H 5 ) 2 ], respectively. These formal substitution reactions proceed with high selectivity as only the C 6 F 5 groups serve as a leaving group to be liberated as C 6 HF 5 upon formal proton transfer from the alkyne. Kinetic studies of the base-catalyzed reaction of Ph 2 SbC 6 F 5 with phenyl acetylene to form Ph 2 SbC≡CPh and C 6 HF 5 suggested the empirical rate law to exhibit a first-order dependence with respect to the base catalyst, alkyne and stibine. DFT calculations support a pathway proceeding via a concerted σ-bond metathesis transition state, where the base catalyst activates the Sb-C 6 F 5 bond sequence through secondary bond interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A semi–automatic analytical methodology for characterizing the energy consumption of MRI systems using load duration curves

Background and purpose: Magnetic resonance imaging (MRI) scanners are a major contributor to greenhouse gas emissions from the healthcare sector, and efforts to improve energy efficiency and reduce energy consumption rely on quantification of the characteristics of energy consumption. The purpose of this work was to develop a semi-automatic analytical methodology for the characterization of the energy consumption of MRI systems using only the load duration curve (LDC). LDCs are a fundamental tool used across various fields to analyze and understand the behavior of loads over time. Methods: An electric current transformer sensor and data logger were installed on two 3T MRI scanners from two vendors, termed M1 (outpatient scanner) and M2 (inpatient/emergency scanner). Data was collected for 1 month (7/11/2023 to 8/11/2023). Active power was calculated, assuming a balanced three-phase system, using the average current measured across all three phases, a 480 V reference voltage for both machines, and vendor-provided power factors. An LDC was constructed for each system by sorting the active power values in descending order and computing the cumulative time (in units of percentage) for each data point. The first derivative of the LDC was then computed (LDC’), smoothed by convolution with a window function (sLDC’), and used to detect transitions between different system modes including (in descending power levels): scan, prepared-to-scan, idle, low-power, and off. The final, segmented LDC was used to measure time (% total time), total energy (kWh), and mean power (kW) for each system mode on both scanners. The method was validated by comparing mean power values, computed using the segmented 1-month LDC, for each nonproductive system mode (i.e., prepared-to-scan, idle, lower-power, and off) against power levels measured after a deliberate system shutdown was performed for each scanner (1 day worth of data). Results: The validation revealed differences in mean power values <1.4% for all nonproductive modes and both scanners. In the scan system mode, the mean power values ranged from 29.8 to 37.2 kW and the total energy consumed for 1 month ranged from 11 106 to 14 466 kWh depending on the scanner. Over the course of 1 month, the portion of time the scanners were in nonproductive modes ranged from 76% to 80% across scanners and the nonproductive energy consumption ranged from 8010 to 6722 kWh depending on the scanner. The M1 (outpatient) scanner consumed 99.9 and 183.9 kWh/day in idle mode for weekdays and weekends, respectively, because the scanner spent 23% more time proportionally in idle mode on the weekends. Conclusions: A semi-automatic method for quantifying energy consumption characteristics of MRI scanners was introduced and validated. This method is relatively simple to implement as it requires only power data from the scanners and avoids the technical challenges associated with extracting and processing scanner log files. Finally, the methodology enables quantitative evaluation of the power, time, and energy characteristics of MRI scanners in scan and nonproductive system modes, providing baseline data and the capability of identifying potential opportunities for enhancing the energy efficiency of MRI scanners.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Optimal Polynomial Smoothers and One‐Sided V‐Cycles for Poisson Problems

The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier‐Stokes equations needs robust preconditioning strategies. One such strategy is multigrid. To realize the potential of multigrid methods, effective smoothing strategies are needed. Chebyshev polynomial smoothers, in conjunction with pointwise Jacobi or additive Schwarz methods (ASMs), prove to be an effective smoother. Other polynomial smoothers, however, may provide superior convergence to the multigrid preconditioner. The authors compare the standard Chebyshev polynomial smoothers to both the novel fourth‐kind Chebyshev polynomial smoothers proposed by Lottes as well as smoothers based on the polynomial of best uniform approximation to as proposed by Kraus, Vassilevski, and Zikatanov. At the cost of symmetry, further improvements may be made. For example, a order polynomial smoother on both sides of the V‐cycle may be substituted with an order polynomial smoother on one side at no additional cost. The choice of omitting the postsmoother in favor of higher‐order polynomial presmoothing is advantageous in cases where the multigrid approximation property constant is large. The authors consider a 2D model problem based on finite differences to motivate the choice of polynomial smoother, order, and whether to apply postsmoothing for the target application of high‐order ‐geometric multigrid methods for GPU architectures. Results from both domains demonstrate the substantial improvement of these approaches over the standard Chebyshev polynomial smoother with a symmetric V‐cycle.

97 MATHEMATICS AND COMPUTING↗

Persistent Classification: Understanding Adversarial Attacks by Studying Decision Boundary Dynamics

ABSTRACT There are a number of hypotheses underlying the existence of adversarial examples for classification problems. These include the high‐dimensionality of the data, the high codimension in the ambient space of the data manifolds of interest, and that the structure of machine learning models may encourage classifiers to develop decision boundaries close to data points. This article proposes a new framework for studying adversarial examples that does not depend directly on the distance to the decision boundary. Similarly to the smoothed classifier literature, we define a (natural or adversarial) data point to be ( γ , σ)‐stable if the probability of the same classification is at least for points sampled in a Gaussian neighborhood of the point with a given standard deviation . We focus on studying the differences between persistence metrics along interpolants of natural and adversarial points. We show that adversarial examples have significantly lower persistence than natural examples for large neural networks in the context of the MNIST and ImageNet datasets. We connect this lack of persistence with decision boundary geometry by measuring angles of interpolants with respect to decision boundaries. Finally, we connect this approach with robustness by developing a manifold alignment gradient metric and demonstrating the increase in robustness that can be achieved when training with the addition of this metric.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Facile Synthesis of Rhodium‐Based Nanocrystals in a Metastable Phase and Evaluation of Their Thermal and Catalytic Properties

Abstract Controlling the polymorphism of metal nanocrystals is a promising strategy for enhancing properties and discovering new phenomena. However, previous studies on Rh nanocrystals have focused on their thermodynamically stable face‐centered‐cubic (fcc) phase. Herein, a facile synthesis of Rh‐based nanocrystals featuring the metastable hexagonal close‐packed (hcp) phase is reported by using Ru seeds in their native hcp phase to template the deposition of Rh atoms. The success of such phase‐controlled synthesis relies on the templating effect promoted by the small lattice mismatch between Ru and Rh and the slow dropwise titration of the precursor at an elevated temperature, ensuring the layer‐by‐layer growth mode and thus the formation of a conformal hcp‐Rh shell. Faster injection rate of Rh(III) precursor leads to the formation of a rough Rh shell in the conventional fcc phase due to accelerated reaction kinetics. Considering both thermodynamic and kinetic aspects of this system, the hcp‐Rh phase is favored when the low surface energy from smooth overlayers balances the high bulk energy of the metastable phase, achieved through tight control of reaction rates and deposition patterns. These Ru hcp @Rh hcp core–shell nanocrystals demonstrate thermal stability up to 400 °C, while exhibiting higher catalytic activity toward ethanol oxidation reaction compared to Ru hcp @Rh fcc counterparts.

Nguyen, Quynh N.↗

FLOWERS AEP: An Analytical Model for Wind Farm Layout Optimization

Annual energy production (AEP) is commonly used in objective functions for wind farm layout optimization. AEP is proportional to wind farm power production integrated over an annual distribution of free-stream wind conditions. Physics-based estimates of wind farm power production typically rely on low-fidelity engineering wake models that approximate the steady-state wind farm flow field. AEP estimates are then obtained by performing independent simulations for discrete wind conditions and using rectangular quadrature to account for each condition's expected frequency of occurrence. Depending on the number of simulated discrete wind conditions, this numerical integral could be hampered by poor accuracy or high computational costs. The FLOWERS AEP model instead poses an analytical integral of the engineering wake model over the variable wind conditions, yielding a closed-form, analytical function for wind farm AEP. This paper derives the analytical functions for FLOWERS AEP and its derivatives with respect to turbine position, which are useful for gradient-based wind farm layout optimization, in nondimensional form. We then analyze the benefits of the FLOWERS AEP model over conventional reference models, focusing on its low cost, adequate wake loss predictions, and smooth design space. Although the FLOWERS approach is found to predict the exact value of AEP with some error relative to the reference model (within 14% on average), it dramatically reduces computation time by an order of magnitude, produces a qualitatively similar design space at relatively low resolution, and yields comparable optimal layouts. This significant speed improvement is critical in layout optimization applications, where determining an optimal layout in an efficient manner is more important than precise AEP prediction.

17 WIND ENERGY↗

Lifting of superconformal descendants in the D1-D5 CFT

We consider D1-D5-P states in the untwisted sector of the D1-D5 orbifold CFT where we excite one copy of the seed CFT with a left-moving superconformal descendant. When the theory is deformed away from this region of moduli space these states can ‘lift’, despite being BPS at the orbifold point. For descendants formed from the supersymmetry $^{Gα}_{Å,–s}$ and R-symmetry $^{Ja}_{–n}$ current modes we obtain explicit results for the expectation value of the lifts for various subfamilies of states at second order in the deformation parameter. A smooth ~ √h behaviour is observed in the lifts of these subfamilies for large dimensions. Using covering space Ward identities we then find a compact expression for the lift of the above $^{Ja}_{–n}$ descendant states valid for arbitrary dimensions. In the large-dimension limit this lift scales as ~ √h, strengthening the conjecture that this is a universal property of the lift of D1-D5-P states. We observe that the lift is not simply a function of the total dimension, but depends on how the descendant level is partitioned amongst modes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for dijet resonances with data scouting in proton-proton collisions at $\sqrt{s}=13$ TeV

A search is presented for narrow resonances, with a mass between 0.6 and 1.8 TeV, decaying to pairs of jets, in proton-proton collisions at $\sqrt{s}=13$ TeV. The search is performed using dijets that are reconstructed, selected, and recorded in a compact form by the high-level trigger in a technique referred to as “data scouting”, from data collected in 2016–2018 corresponding to an integrated luminosity of 117 fb −1 . The dijet mass spectra are well described by a smooth parameterization, and no significant evidence for the production of new particles is observed. Model-independent upper limits are presented on the product of the cross section, branching fraction, and acceptance for the individual cases of narrow quark-quark, quark-gluon, and gluon-gluon resonances, and are compared to the predictions from a variety of models of narrow dijet resonance production. The upper limit on the coupling of a dark matter mediator to quarks is presented as a function of the mediator mass. The sensitivity of this search goes beyond what is expected from statistical scaling with the integrated luminosity alone, as a consequence of the use of fewer parameters in the background function within a more robust statistical procedure.

beyond Standard Model↗

Unveiling horizons in quantum critical collapse

Critical gravitational collapse offers a unique window into regimes of arbitrarily high curvature, culminating in a naked singularity arising from smooth initial data — thus providing a dynamical counterexample to weak cosmic censorship. Near the critical regime, quantum effects from the collapsing matter are expected to intervene before full quantum gravity resolves the singularity. Despite its fundamental significance, a self-consistent treatment has so far remained elusive. In this work, we perform a one-loop semiclassical analysis using the robust anomaly-based method in the canonical setup of Einstein gravity minimally coupled to a free, massless scalar field. Focusing on explicitly solvable near-critical solutions in both 2 + 1 and 3 + 1 dimensions, we analytically solve the semiclassical Einstein equations and obtain controlled, quantitative results for several long-standing questions within the dominant s-wave sector. We find that regularity uniquely selects a Boulware-like quantum state, encoding genuine vacuum polarization effects from the collapsing matter. Remarkably, the resulting quantum corrections manifest as a growing mode. Horizon-tracing analyses, incorporating both classical and quantum modes, reveal the emergence of a finite mass gap, signaling a phase transition from classical Type II to quantum-modified Type I behavior, thereby providing a quantum enforcement of the weak cosmic censorship. The most non-trivial aspect of our analysis involves dealing with non-conformal matter fields in explicitly time-dependent critical spacetimes. Along the way, we uncover intriguing and previously underexplored features of quantum field theory in curved spacetime.

2D Gravity↗

Soft algebras for leaf amplitudes

Celestial MHV amplitudes are comprised of non-distributional leaf amplitudes associated to an AdS3 leaf of a foliation of flat spacetime. It is shown here that the leaf amplitudes are governed by the same infinite-dimensional soft ‘S-algebra’ as their celestial counterparts. Moreover, taking the soft limit of the smooth three-point MHV leaf amplitude yields a nondegenerate minus-minus two-point leaf amplitude. The two- and three-point MHV leaf amplitudes are used to compute the plus-minus-minus leaf operator product coefficients.

79 ASTRONOMY AND ASTROPHYSICS↗

Celestial leaf amplitudes

Celestial amplitudes may be decomposed as weighted integrals of AdS 3 -Witten diagrams associated to each leaf of a hyperbolic foliation of spacetime. We show, for the Kleinian three-point MHV amplitude, that each leaf subamplitude is smooth except for the expected light-cone singularities. Moreover, we find that the full translationally-invariant celestial amplitude is simply the residue of the pole in the leaf amplitude at the point where the total conformal weights of the gluons equals three. This full celestial amplitude vanishes up to light-cone contact terms, as required by spacetime translation invariance, and reduces to the expression previously derived by Mellin transformation of the Parke-Taylor formula.

79 ASTRONOMY AND ASTROPHYSICS↗

Relational bulk reconstruction from modular flow

Abstract The entanglement wedge reconstruction paradigm in AdS/CFT states that for a bulk qudit within the entanglement wedge of a boundary subregion$$ \overline{A} $$ A ¯ , operators acting on the bulk qudit can be reconstructed as CFT operators on$$ \overline{A} $$ A ¯ . This naturally fits within the framework of quantum error correction, with the CFT states containing the bulk qudit forming a code protected against the erasure of the boundary subregionA. In this paper, we set up and study a framework for relational bulk reconstruction in holography: given two code subspaces both protected against erasure of the boundary regionA, the goal is to relate the operator reconstructions between the two spaces. To accomplish this, we assume that the two code subspaces are smoothly connected by a one-parameter family of codes all protected against the erasure ofA, and that the maximally-entangled states on these codes are all full-rank. We argue that such code subspaces can naturally be constructed in holography in a “measurement-based” setting. In this setting, we derive a flow equation for the operator reconstruction of a fixed code subspace operator using modular theory which can, in principle, be integrated to relate the reconstructed operators all along the flow. We observe a striking resemblance between our formulas for relational bulk reconstruction and the infinite-time limit of Connes cocycle flow, and take some steps towards making this connection more rigorous. We also provide alternative derivations of our reconstruction formulas in terms of a canonical reconstruction map we call the modular reflection operator.

Physics↗

The structure of quantum singularities on a Cauchy horizon

Spacetime singularities pose a long-standing puzzle in quantum gravity. Unlike Schwarzschild, a generic family of black holes gives rise to a Cauchy horizon on which, even in the Hartle-Hawking state, quantum observables such as ⟨T μν ⟩ — the expectation value of the stress-energy tensor — can diverge, causing a breakdown of semiclassical gravity. Because they are diagnosed within quantum field theory (QFT) on a smooth background, these singularities may provide a better-controlled version of the spacetime singularity problem, and merit further study. Here, I highlight a mildness puzzle of Cauchy horizon singularities: the ⟨T μν ⟩ singularity is significantly milder than expected from symmetry and dimensional analysis. I address the puzzle in a simple spacetime ${\mathcal{W}}_P$, which arises universally near all black hole Cauchy horizons: the past of a codimension-two spacelike plane in flat spacetime. Specifically, I propose an extremely broad QFT construction in which, roughly speaking, Cauchy horizon singularities originate from operator insertions in the causal complement of the spacetime. The construction reproduces well-known outer horizon singularities (e.g., in the Boulware state), and remarkably, when applied to ${\mathcal{W}}_P$, gives rise to a universal mild singularity structure for robust singularities, ones whose leading singular behavior is state-independent. I make non-trivial predictions for all black hole Cauchy horizon singularities using this, and discuss extending the results beyond robust singularities and the strict near Cauchy horizon limit.

black holes↗