We develop a perturbative algorithm for constructing formal flat $F$-manifold structures on the cohomologies of dGBV (differential Gerstenhaber-Batalin-Vilkovisky) algebras associated with Landau-Ginzburg models. As an application, this approach provides a perturbative construction of formal flat $F$-manifold structures on two important objects: the Jacobian algebra of a homogeneous polynomial with an isolated singularity at the origin, and the primitive cohomology of smooth projective Calabi-Yau complete intersections.

A class of subcategories GP $B$ of the Grassmannian cluster category CM $C_{k, n}$ was constructed by Jensen--King--Su from certain superorders $B$ of $C_{k, n}$, which they showed are in bijection with Grassmannian positroids of type $(k, n)$. We prove that GP $B$ admits a cluster substructure of CM $C_{k, n}$, giving rise to a cluster algebra $A_{clu}$. This naturally raises questions regarding the relationship of $A_{clu}$ to $C[Gr(k, n)]$ and to the coordinate ring of the positroid variety associated to $B$. Using the cluster substructure, we show that the ice Gabriel quiver $Q^\circ_U$ of a cluster tilting object $U\in$ GP $B$, consisting of rank one modules, is a subquiver of $Q^\circ_T$ with $T$ a cluster tilting object in CM $C_{k, n}$ containing $U$ as a summand. We also deduce that $A_{clu}$ is a subalgebra of $C[Gr(k, n)]$. Moreover, applying a result of Canakci--King--Pressland on the Gabriel quiver $Q_U$ in the case where $B$ is connected (i.e., has no repeated direct summands), we deduce that $Q^\circ_U$, for arbitrary $B$, coincides with the quiver constructed by Muller-Speyer from a plabic graph whose face labels agree with the indices of the indecomposable summands of $U$. Consequently, the localised algebra $(A_{clu})_B$ is isomorphic to the cluster algebra $A_{MS}$ of Muller-Speyer. We then construct bases for certain subalgebras and for an ideal of $C[Gr(k, n)]$, and apply these to prove that $(A_{clu})_B$ is naturally isomorphic to the coordinate ring of the open positroid variety. As a consequence, we obtain a new proof of Galashin--Lam's Theorem, identifying $A_{MS}$ with the coordinate ring of the open positroid variety, which was originally conjectured by Muller-Speyer. In the connected case, we note also that Pressland gave a categorification of the cluster structure following Galashin-Lam.

A recent study by Gassner et al. [J. Sci. Comput. 90:79 (2022)] demonstrates that local energy stability--that is, ensuring the asymptotic numerical growth rate does not exceed the continuous growth rate--is crucial for achieving accurate numerical simulations of nonlinear conservation laws. While nonlinear entropy stability is necessary for numerical stability (i.e., ensuring the boundedness of nonlinear numerical solutions), local energy stability is essential to prevent unresolved high-frequency wave modes from dominating the simulation. Currently, it remains an open question whether high-order numerical methods for nonlinear conservation laws can be simultaneously entropy-stable and locally energy-stable. In this work, we examine the local energy-stability properties of recently developed entropy-stable, high-order accurate dual-pairing (DP) SBP methods, as introduced by Duru et al. [arXiv: 2411.06629], for nonlinear conservation laws. Our analysis indicates that the entropy-stable volume upwind filter inherent in these methods can ensure local energy stability. This approach offers a novel numerical strategy for designing reliable high-order methods for nonlinear conservation laws that are provably entropy-stable and locally energy-stable. The theoretical findings are supported by numerical experiments involving the inviscid Burgers equation and nonlinear shallow water equations, in 1D and 2D. Furthermore, we present accurate numerical simulations of 2D barotropic shear instability, with fully developed turbulence, demonstrating the efficiency of the DP SBP method in resolving turbulent scales.

Despite offering high sensitivity, a high signal-to-noise ratio, and a broad spectral range, single-pixel imaging (SPI) is limited by low measurement efficiency and long data-acquisition times. To address this, we propose a wavelength-multiplexed, spatially incoherent diffractive optical processor combined with a compact/shallow digital artificial neural network (ANN) to implement compressive SPI. Specifically, we model the bucket detection process in conventional SPI as a linear intensity transformation with spatially and spectrally varying point-spread functions. This transformation matrix is treated as a learnable parameter and jointly optimized with a shallow digital ANN composed of 2 hidden nonlinear layers. The wavelength-multiplexed diffractive processor is then configured via data-free optimization to approximate this pre-trained transformation matrix; after this optimization, the diffractive processor remains static/fixed. Upon multi-wavelength illumination and diffractive modulation, the target spatial information of the input object is spectrally encoded. A single-pixel detector captures the output spectral power at each illumination band, which is then rapidly decoded by the jointly trained digital ANN to reconstruct the input image. In addition to our numerical analyses demonstrating the feasibility of this approach, we experimentally validated its proof-of-concept using an array of light-emitting diodes (LEDs). Overall, this work demonstrates a computational imaging framework for compressive SPI that can be useful in applications such as biomedical imaging, autonomous devices, and remote sensing.

The temperature and strain dependences of the optical conductivity spectrum of hexagonal manganese telluride (MnTe) were measured, revealing absorption in the terahertz (THz) region from spin-split bands to acceptor levels. The temperature dependence of the THz absorption peak is consistent with that of a ferromagnetic phase transition, even though MnTe exhibits no net magnetism. The temperature dependence was attributed to a change in the altermagnetic electronic structure. A Fano-like antisymmetric line shape in the optical phonon absorption was observed, which originates from the interaction between optical phonons and the spin-split bands. Additionally, under negative uniaxial pressure, the THz peak shifts away from the Fermi level (EF), suggesting that spin-splitting bands at energies away from EF, consistent with the theoretical prediction that the spin-splitting angle decreases. The observed behavior of the THz peak clearly shows that MnTe has the altermagnetic electronic structure.

This is a note on the graphs of two smooth real-valued functions in the plane with no intersection and the natural map onto the region surrounded by them with the canonical projection to the line composed, yielding its Reeb space. The Reeb space of a real-valued function on a topological space is the set of all connected components of all level sets and topologized naturally. Such spaces have been fundamental and strong tools in theory of Morse functions and its generalization and variants, since the former half of the 20th century. They are graphs for tame functions such as Morse(-Bott) functions. The author has launched and has been studying this problem since 2020s, interested in Reeb spaces of smooth or non-analytic non-proper functions. For smooth closed manifolds and nice compact spaces, topological properties and combinatorial ones on Reeb spaces have been investigated by Gelbukh, Saeki, and so on.

Atomic-scale disorder can create hidden optical anisotropy even in crystals that are structurally cubic on average. Here, we show that CuInSnS$_4$ single crystals host locally symmetry-broken environments arising from intrinsic In/Sn cation disorder, which affect vibrational and excitonic properties in markedly different ways. Combining polarization- and temperature-dependent Raman spectroscopy, infrared near-field microscopy, steady-state and time-resolved photoluminescence, and first-principles calculations, we find that phonons remain largely symmetry-averaged and locally homogeneous on the nanoscale. In contrast, photoluminescence reveals a lower-energy band-tail emission with pronounced polarization anisotropy following a well-defined angular symmetry, highlighting the strong sensitivity of excitonic states to local symmetry breaking. This phonon-exciton decoupling reveals that intrinsic disorder can localize excitons while preserving vibrational coherence and dielectric homogeneity, thereby opening new opportunities for polarization-sensitive light sources, anisotropic photodetectors, and exciton-based optical functionalities even in nominally cubic multinary semiconductors.

Recent biological evidence suggests the presence of a two-phase ageing process in several species. We introduce a system of two age-structured partial differential equations (PDE) representing two phases of ageing of a wild population. The model includes a coupling of both equations through birth and transition between phases and non-linearities due to competition. We show the existence, positivity and uniqueness of weak solutions in a general setting. For a simplified system of ordinary differential equations (ODE), we show existence and uniqueness of a strictly positive steady state attracting all trajectories. We study another simplification, a coupled PDE-ODE model, for which we prove existence, uniqueness and local asymptotic stability of a strictly positive steady state. Under further assumptions, but without assuming weak non-linearities, we show the global asymptotic stability of that steady state. The uniqueness of steady states and absence of oscillations in these systems show that the proportion of individuals in each phase at equilibrium is a unique feature of the model. This paves the way to ecological applications as the experimental measure of such a proportion could help gain some insight on the health of a wild population.

In this paper, we study two-dimensional steady solitary gravity waves propagating along the surface of a fluid of finite depth. In particular, we can deal with general vorticity distributions and overhanging wave profiles. By conformal mappings, we reformulate the problem into an overdetermined elliptic system coupled with an elliptic boundary value problem in a fixed strip domain. To avoid imposing extra constraints on vorticity function, we further reformulate the problem into the form of an abstract operator. Based on the formulations, the existence of small-amplitude solitary waves is proved by the center manifold reduction method, while the large-amplitude waves are obtained based on the analytic global bifurcation theorem.

Converting mid-infrared (MIR) radiation to visible or near-infrared wavelengths is essential for imaging and sensing, yet achieving sensitive, low-power, and scalable detection remains challenging. Lanthanide nanocrystals provide an alternative through ratiometric luminescence but are typically constrained by Boltzmann statistics, which tie population distributions to lattice temperature and limit signal contrast. Here we show that MIR irradiation rebalances dissipative relaxation pathways, driving lanthanide emitters into a non-Boltzmann steady state that enables non-thermal control of population distributions. This allows emission behaviors inaccessible under thermal equilibrium. We exploit this regime to achieve linear MIR detection with respect to MIR power across 6.8 to 8.6 micrometers. The ratiometric response is intrinsically independent of the pump power, enabling operation at an ultralow excitation power of 10 uW, several orders of magnitude lower than conventional approaches. Using standard silicon photodetectors, we then demonstrate room-temperature MIR imaging with detection limits approaching 4 nW um-2. Our results establish lanthanide nanoparticles as an efficient platform for MIR conversion and sensing in nanophotonic systems.

We report emergent magnetic behavior in heterostructures composed of (111)-oriented La$_{0.7}$Sr$_{0.3}$MnO$_3$ (LSMO) and (00$l$)-oriented Bi$_2$Te$_3$ (BT), controlled by interfacial reconstructions. When BT is deposited directly onto LSMO, an intermediate interfacial layer forms between the two materials. Polarized Neutron Reflectometry modeling reveals that this reconstructed region stabilizes a secondary magnetically ordered phase that is coupled to the underlying ferromagnetic LSMO layer. As a consequence, the heterostructures exhibit unconventional self-crossing magnetic hysteresis loops at room temperature, characterized by a reversal of the net magnetization at low applied fields. In contrast, the introduction of a tellurium seed layer results in a sharper LSMO-BT interface, while preserving the anomalous hysteresis behavior and enhancing the saturation magnetization. Element-specific X-ray absorption spectroscopy suggests that the emergent magnetic phase originates from the chemical reconstruction of manganese species. These results demonstrate that interface engineering in magnetic oxide-topological insulator heterostructures provides a pathway to control emergent magnetic coupling and emergent magnetic states in oxide-topological insulator heterostructures.

Confidential databases (CDBs) are essential for enabling secure queries over sensitive data in untrusted cloud environments using confidential computing hardware. While adoption is growing, widespread deployment is hindered by high performance overhead from frequent synchronous cryptographic operations, which causes significant computational and memory bottlenecks. We present FEDB, a novel CDB design that removes cryptographic operations from the critical path. FEDB leverages crypto-free mappings, which maintain data-independent identifiers within the database while securely mapping them to plaintext secrets in a trusted domain. This paradigm shift reduces the runtime overhead by up to 78.0 times on industry-standard benchmarks including TPC-C and TPC-H.

We introduce the CaRBM algorithm for fixed-depth thermal state preparation. Our algorithm is based on thermal state purification and uses the Restricted Boltzmann Machine (RBM) block-encoding scheme to implement the imaginary-time propagator $e^{-βH}$, which is implemented in the quantum circuit in a fixed-depth manner via Cartan decomposition. Our algorithm performs best at high temperatures, with the success probability of the block encoding decreasing as the temperature decreases. To increase the success probability, we have devised a correction scheme for the block-encoding that increases the temperature range our algorithm reliably probes. We demonstrate our algorithm by calculating the partition function zeros of the XXZ model and the phase diagram of the Gross-Neveu model, which is a model of strongly interacting relativistic fermions.

We consider solutions of the Einstein vacuum equations which arise from smooth initial data on a hypersurface slightly inside a dynamical black hole settling down to a subextremal Kerr black hole, and satisfying a precise non-linear Price's law-type estimate (which we expect to hold generically). We prove that the corresponding maximal globally hyperbolic development admits a non-trivial piece of future null boundary - the Cauchy horizon - emanating from timelike infinity $i_+$, which exhibits a kind of curvature blow-up, and across which the spacetime metric is Lipschitz-inextendible. Our results thus imply a Lipschitz version of Strong Cosmic Censorship for Kerr spacetimes near timelike infinity under this Price's law-type assumption. The analysis relies on the proof of the $C^0$ stability of the Kerr Cauchy horizon by Dafermos and Luk, on the non-integrable formalism of Giorgi-Klainerman-Szeftel and principal temporal gauge of Klainerman and Szeftel used in the proof of the exterior stability of slowly rotating Kerr black holes, on the linearized analysis for the Teukolsky equation inside subextremal Kerr black holes by the author (following an earlier paper on the scalar wave equation by Ma and Zhang), and on Sbierski's criterion for Lipschitz inextendibility. More precisely, we proceed by decomposing the black hole interior into different regions equipped with appropriate gauges, allowing for a proof of stability estimates and a thorough analysis of the non-linear analog of the Teukolsky equation, from which we infer our instability results.

It is now common to describe classical backgrounds involving dynamical black holes with the production of gravitational radiation using the methods of scattering amplitudes. In that light, we revisit the standard formulation of quantum field theory on a background. We discuss the interpretation of Bogoliubov coefficients as generalised amplitudes, and explain how crossing, analyticity, and causality relate the relevant set of amplitudes. When the background is itself a coherent state, we map these statements onto standard results in flat-space quantum field theory.

In sports analytics, player tracking data have driven significant advancements in the task of player evaluation. We present a novel generative framework for evaluating the observed frame-by-frame player positioning against a distribution of hypothetical alternatives. We illustrate our approach by modeling the within-play movement of an individual ball carrier in the National Football League (NFL). Specifically, we develop Bayesian multilevel models for frame-level player movement based on two components: step length (distance between successive locations) and turn angle (change in direction between successive steps). Using the step-and-turn models, we perform posterior predictive simulation to generate hypothetical ball carrier steps at each frame during a play. This enables comparison of the observed player movement with a distribution of simulated alternatives using common valuation measures in American football. We apply our framework to tracking data from the first nine weeks of the 2022 NFL season and derive novel player performance metrics based on hypothetical evaluation.

Dynamic pricing is commonly used to regulate congestion in shared service systems. This paper is motivated by the fact that in the presence of users with varying price sensitivity (responsiveness), conventional monotonic pricing can lead to unfair outcomes by disproportionately excluding price-elastic users, particularly under high or uncertain demand. We therefore develop a fairness-oriented mechanism under demand uncertainty. The paper's contributions are twofold. First, we show that when fairness is imposed as a hard state constraint, the optimal (revenue maximizing) pricing policy is generally non-monotonic in demand. This structural result departs fundamentally from standard surge pricing rules and reveals that price reduction under heavy load may be necessary to maintain equitable access. Second, we address the problem that price elasticity among heterogeneous users is unobservable. To solve it, we develop a robust dynamic pricing and admission control framework that enforces capacity and fairness constraints for all user type distributions consistent with aggregate measurements. By integrating integral High Order Control Barrier Functions (iHOCBFs) with a robust optimization framework under uncertain user-type distribution, we obtain a controller that guarantees forward invariance of safety and fairness constraints while optimizing revenue. Numerical experiments demonstrate improved fairness and revenue performance relative to monotonic surge pricing policies.

Sensemaking is an important preceding step for activities like consensus building and decision-making. When groups of people make sense of large amounts of information, their understanding gradually evolves from vague to clear. During this process when reaching a conclusion is still premature, if people are presented with others' insights, they may be directed to focus on that specific perspective without adequate verification. We argue that similar phenomena may also exist in AI-assisted sensemaking, in which AI will usually be the one that presents insight prematurely when users' understandings are still vague and ill-formed. In this paper, we raised three questions that are worth deliberation before exploiting AI to assist in collaborative sensemaking in practice, and discussed possible reasons that may lead users to opt for insights from AI.

A substantial body of research has focused on formalising what constitutes a ``secure'' messaging system, recognising that end-to-end encryption alone is insufficient to capture the full range of security, privacy, and usability properties that are expected by modern users. Several solutions have been proposed recently, including their own drawbacks, making the need for a direct secure messaging system a necessity. This paper presents Ember, a serverless peer-to-peer messaging system providing end-to-end encrypted communication over a decentralised IPv6 mesh network. Ember operates without central servers, enforces data minimisation through ciphertext-only local storage and time-based message expiration, and prioritises architectural clarity, explicit trust boundaries, and practical deployability on Android. The paper describes the system architecture, cryptographic design, network model, and security properties. Ember includes a ciphertext-only persistence model using an encrypted local database, ensuring that message plaintext is never written to disk. Through the integration of a time-to-live (TTL) mechanism for automatic message expiration, Ember enforces data minimisation on mobile devices. Ember is a layered and analysable system architecture with explicit trust boundaries separating user interface logic, cryptographic operations, storage, and networking components. The paper presents dynamic testing results demonstrating that no plaintext information can be recoverable from captured network traffic, and finally discusses limitations and future work.

Defective chalcopyrites have recently emerged as promising thermoelectric materials because their ordered intrinsic vacancies can profoundly reshape both lattice dynamics and electronic structure. Here, we present a comprehensive theoretical investigation of the lattice thermal and carrier transport properties of II-III$_2$-VI$_4$ defective chalcopyrites by combining first-principles calculations with machine-learning interatomic potentials. We show that vacancy ordering enhances lattice distortion, leading to strong anharmonicity and metavalent bonding. The interplay of soft low-frequency phonons, strongly negative Grüneisen parameters, and a substantially enlarged four-phonon scattering phase space results in four-phonon-scattering-dominated heat transport, yielding ultralow lattice thermal conductivity. Meanwhile, systematic anion substitution at the VI-site provides an effective route to tune the electronic structure: reduced anion electronegativity weakens metal-anion hybridization, shifts anion $p$ states upward, narrows the band gap, and thereby improves electrical transport. Benefiting from this synergy between vacancy-induced phonon suppression and anion-regulated electronic optimization, CdGa$_2$Te$_4$ exhibits an ultralow lattice thermal conductivity of 0.19 W$\cdot$m$^{-1}$K$^{-1}$ and a high room-temperature $ZT$ of 0.957. This work not only predicts defective chalcopyrites as a promising platform for high-performance thermoelectrics but also provides a practical design strategy by integrating vacancy ordering, higher-order phonon scattering, and anion-dependent band engineering.

Accurate reconstruction of global Sea surface temperature (SST), which dominates the air-sea coupling and global climate variability, underpins climate monitoring and prediction. Existing SST reconstruction products primarily provide one deterministic field derived from heterogeneous satellite data and in situ observations, limiting their ability to represent observation uncertainty and to support probabilistic forecasting. Here, we introduce Satellite and in situ Adaptive Guided Estimation (SAGE), a diffusion-based uncertainty-aware generative framework for probabilistic SST reconstruction. SAGE learns a physically consistent prior from historical SST data and performs observation-conditioned posterior sampling without requiring satellite or in situ data during training, enabling flexible state inference from heterogeneous observations. Through a progressive data-fusion strategy, observations from two FengYun-3D polar-orbiting satellites constrain basin-scale structures, while sparse in situ measurements serve to refine local anomalies and extremes. The resulting ensemble SST fields well capture observational uncertainty and scale-dependent variability. Validation against independent in situ observations shows that SAGE substantially reduces reconstruction errors compared with widely used operational products. When used to initialize forecasting systems, SAGE-generated SST fields substantially reduce 10-day SST forecast errors relative to current operational analyses. At the climate scale, SAGE-driven forecasts of the 2023-2024 El Nino event show added value in capturing its onset and intensity evolution compared to conventional approaches. Our results demonstrate that SAGE represents a step toward a new paradigm for ocean state estimation and climate prediction.

We extend the Weak Adversarial Neural Pushforward Method (WANPM) to the McKean--Vlasov mean-field Fokker--Planck equation, covering both the stationary and time-dependent cases. The key observation is that the mean-field nonlinearity -- an expectation under the solution distribution -- is naturally estimated by Monte Carlo sampling from the pushforward network, requiring no change to the architecture and only minor modifications to the training loop. For the quadratic (granular media) interaction kernel, the interaction term reduces to the batch sample mean, eliminating secondary sampling entirely. We also identify a dimension-dependent frequency initialization rule for the adversarial test functions, necessary to avoid spurious minimizers. Numerical experiments on linear McKean--Vlasov benchmarks in 2, 5, 20, and 100 dimensions confirm accurate recovery of the exact Gaussian stationary and transient distributions, with training times ranging from 27 seconds (2D) to 10 minutes (100D) on a single GPU.

We present results and compare the behavior of two fluctuation-induced forces pertinent for their corresponding ensembles: the critical Casimir force in the grand canonical (fixed external field $h$) one and the critical Helmholtz force in the canonical (fixed average value of the order parameter $m$) one. We do so by deriving exact results for their behavior near the bulk critical point at $T=T_c$ in the three-dimensional Gaussian model. We consider Dirichlet-Dirichlet, Neumann-Dirichlet, Neumann-Neumann, and periodic boundary conditions. For every boundary condition examined, we confirm that both forces follow a finite-size scaling. We find that for Dirichlet-Dirichlet and Neumann-Dirichlet boundary conditions the Casimir and the Helmholtz force differ from each other. For Dirichlet-Dirichlet boundary conditions the Casimir force is always attractive, while the Helmholtz force can be both attractive and repulsive as a function of $T$ and $m$. For Neumann-Dirichlet boundary conditions the Casimir force changes sign from repulsive to attractive with increase of $h$, while the Helmholtz force stays always repulsive. Under periodic and Neumann-Neumann boundary conditions the Casimir force and the Helmholtz force coincide - the first does not depend on $h$, while the latter does not depend on $m$; they are always attractive.

Real-time captioning is vital for Deaf and Hard of Hearing (DHH) and neurodivergent learners (e.g., those with ADHD), yet it often omits emotional and non-verbal cues essential for comprehension. This omission is particularly consequential in STEM education, where cognitively demanding material can exacerbate the challenges faced by caption users across diverse ability profiles. In this paper, we present a design-oriented exploration of four captioning prototypes that embed emotional and multimodal cues, including facial expressions, body gestures, keyword highlighting, and emoji. Across a pilot and a main study with 24 participants, we found that certain prototypes reduced self-reported cognitive load and improved comprehension scores compared to traditional captions. Qualitative feedback reveals the importance of customizable caption features to accommodate neurodivergent users' preferences (e.g., ADHD or different levels of comfort with emojis). Our findings contribute to ongoing conversations in accessible technology research about how best to integrate emotional cues into captions in a way that is both usable and beneficial for a wide range of learners.

The FDA's Project Optimus initiative emphasizes patient-centered dose selection in oncology that balances efficacy and safety. We develop a framework for randomized dose optimization studies that uses clinically interpretable utility scores to integrate binary efficacy and safety endpoints and select the optimal dose for a follow-on confirmatory trial. The framework provides: (i) a systematic method for eliciting utility scores that reflect clinical priorities; (ii) closed-form sample size formulas to achieve prespecified Probabilities of Correct Selection (PCS) under clinically relevant scenarios; and (iii) analytical expressions characterizing the propagation of selection-induced bias to confirmatory trials, including time-to-event endpoints correlated with the selection endpoint. Extensive simulations (10^6 replications per scenario) confirm that the sample size methods achieve target PCS and that the bias and Type I error formulas closely match empirical estimates. An R package DoseOptDesign and an interactive Shiny application are publicly available.

We study whether an aperiodic hierarchy can provide a structural advantage for lossless compression over periodic alternatives. We show that Fibonacci quasicrystal tilings avoid the finite-depth collapse that affects periodic hierarchies: usable $n$-gram lookup positions remain non-zero at every level, while periodic tilings collapse after $O(\log p)$ levels for period $p$. This yields an aperiodic hierarchy advantage: dictionary reuse remains available across all scales instead of vanishing beyond a finite depth. Our analysis gives four main consequences. First, the Golden Compensation property shows that the exponential decay in the number of positions is exactly balanced by the exponential growth in phrase length, so potential coverage remains scale-invariant with asymptotic value $Wφ/\sqrt{5}$. Second, using the Sturmian complexity law $p(n)=n+1$, we show that Fibonacci/Sturmian hierarchies maximize codebook coverage efficiency among binary aperiodic tilings. Third, under long-range dependence, the resulting hierarchy achieves lower coding entropy than comparable periodic hierarchies. Fourth, redundancy decays super-exponentially with depth, whereas periodic systems remain locked at the depth where collapse occurs. We validate these results with Quasicryth, a lossless text compressor built on a ten-level Fibonacci hierarchy with phrase lengths ${2,3,5,8,13,21,34,55,89,144}$. In controlled A/B experiments with identical codebooks, the aperiodic advantage over a Period-5 baseline grows from $36{,}243$ B at 3 MB to $11{,}089{,}469$ B at 1 GB, explained by the activation of deeper hierarchy levels. On enwik9, Quasicryth achieves $225{,}918{,}349$ B $(22.59\%)$, with $20{,}735{,}733$ B saved by the Fibonacci tiling relative to no tiling.

It has long been a puzzle why, despite sustained reform efforts, many applied scientific fields remain dominated by Null Hypothesis Significance Testing (NHST), a framework that dichotomizes study results and privileges "statistically significant" findings. This paper examines that puzzle by situating the development and rise of NHST within its historical and institutional context. Taking Actor-Network Theory as a point of entry, the analysis identifies the conditions under which particular inferential technologies stabilize and endure. The analysis shows that, although NHST does not resolve the technical problem of statistical inference, it came to dominate as a social technology that addressed the most pressing institutional challenge of the postwar period: the mass expansion of scientific networks. Under conditions of rapid institutional growth, NHST's technical slippages--purging research context and replacing epistemic judgment with mechanical procedures--became functional features rather than flaws. These features enabled procedural self-sufficiency across settings marked by heterogeneous goals and uneven expertise, thereby sealing NHST's position as the obligatory passage point in many postwar scientific fields.

We propose an enhanced hyperbolic square-root (HSQRT) deformation of the Starobinsky model in the context of $f(R)$ gravity. The original HSQRT construction provided a globally regular modification of $R^2$ inflation, curing the strong-coupling singularity at negative curvatures while preserving the exponential slow-roll plateau at large positive curvatures. Motivated by recent cosmological data (ACT DR6 and DESI), we introduce a structurally minimal, rational-logarithmic enhancement. This enhancement modifies the deep UV asymptotic regime while preserving global tachyon-free stability, ghost freedom, and the recovery of general relativity at low curvatures. In the Einstein frame, the scalaron dynamics is described by a globally defined, Padé-regulated effective potential, $V_{\text{Padé}}(ϕ) = V_{\text{Staro}}(ϕ) \left(1+ \frac{4β}{\frac{2}{3}κ^2ϕ^2 + 1}\right)^{-1} + \frac{1}{4ακ^2} \left[1 - \left( 1 + \sqrt{\frac{2}{3}}κϕ\right) e^{-\sqrt{\frac{2}{3}}κϕ} \right] e^{-\sqrt{\frac{2}{3}}κϕ}$, which exhibits the inverse-power asymptotic form at high curvatures, $V(ϕ) \simeq \frac{1}{8ακ^2} \left( 1 - \frac{6β}{κ^2ϕ^2} \right)$, with the strength of the deviation from the baseline HSQRT geometry governed by dimensionless parameter $β$. We derive analytic expansions for the slow-roll observables, yielding a leading-order spectral index $n_s \simeq 1 - 3/(2N)$ and a tensor-to-scalar ratio $r \simeq 2\sqrt{3β}/N^{3/2}$. For standard e-fold durations ($N \in [50, 60]$), this model drives the spectral index directly into the newly favored observational window ($n_s \simeq 0.970\text{--}0.975$) and predicts an exceptionally small spectral running $α_s \simeq -3/(2N^2) \in [-0.00060, -0.00042]$, establishing a viable target for next-generation CMB observatories.

We prove a general reduction theorem for stabilizer absolutely maximally entangled states in composite local dimension. If a stabilizer $\mathrm{AME}(n,D)$ state exists and $D=\prod_{i=1}^m q_i$ is the prime-power factorization of $D$, then for every nonempty subset of factors there exists a stabilizer $\mathrm{AME}\bigl(n,\prod_{i\in M} q_i\bigr)$ state. Thus any obstruction at a prime-power factor immediately obstructs stabilizer AME states in the composite dimension.

An ordered graph is a graph whose vertex set is equipped with a total order. The ordered complete graph $K_N^<$ is the complete graph with vertex set $[N]$ equipped with the natural ordering of the integers. Given an ordered graph $H$, the ordered Ramsey number $R_<(H)$ is the smallest integer $N$ such that every red/blue edge-colouring of $K_N^<$ contains a monochromatic copy of $H$ with vertices appearing in the same relative order as in $H$. Balko, Cibulka, Král, and Kynčl asked whether, among all ordered paths on $n$ vertices, the ordered Ramsey number is minimised by the alternating path $\mathrm{AP}_n$ -- the ordered path with vertex set $[n]$ such that the vertices encountered along the path are $1, n, 2, n - 1,3, n-2,\dots$. Motivated by this problem, we make progress on establishing the value of $R_<(\mathrm{AP}_n)$ by proving that \[ R_{<}(\mathrm{AP}_n)\leq \left(2+\frac{\sqrt{2}}{2}+o(1)\right)n. \] We then use similar methods to determine the exact ordered Turán number of $\mathrm{AP}_n$, and study the ordered Ramsey and Turán numbers of several related ordered paths.