Papers

The problem of inverting the Radon integral transform in finite-dimensional Euclidean space is considered. The relevance of this topic for probing issues is indicated. It is noted that for the latter direction, it is natural to consider the integrand as discontinuous function. However, the available inversion formulas are only proven for differentiable functions. Therefore, the question of obtaining formulas for discontinuous functions arises. It is set that the required results can be obtained by some modification of available proofs for smooth functions.

Measures on function spaces arise throughout Bayesian inverse problems and generative modeling, often with low-dimensional structure relative to a tractable reference measure. We introduce the class $\mathcal{P}_\psi(\mu)$ of measures that differ from a reference measure $\mu$ only through a finite-dimensional map $\psi$ while preserving the reference conditionals on its fibers. Class members are determined by their $d$-dimensional pushforwards under $\psi$ and admit convenient block-triangular transport map representations. Draws are taken from this $d$-dimensional distribution and then completed to function space through sampling of the reference conditionals. For Gaussian references, these transport maps are finite rank perturbations of the identity. In contrast, optimal transport maps do not preserve this low-dimensional structure. For covariance perturbations that are trace class in the Cameron-Martin geometry of the reference, we show the optimal map is a trace class perturbation of the identity. Even finite rank perturbations yield corrections whose rank, governed by an invariant subspace, is typically infinite. We develop approximation theory for $\mathcal{P}_\psi(\mu)$ and error analysis for fitting within it, splitting the total error into an irreducible class error and a finite-dimensional marginal term set by the dimension of $\psi$ rather than the ambient discretization. We present numerical results including inference from low-dimensional nonlinear observation maps, deconvolution under a jump process prior, and state estimation for Navier-Stokes flows.

Epigenetic clocks estimate age and aging-related phenotypes from DNA methylation at selected CpG sites, but the extent to which these inputs are influenced by germline genetic variation is unclear. Because methylation at many CpGs is genetically regulated, some between-person variation in clock estimates may reflect inherited genetic differences rather than aging-related change alone. Here we developed GIA (Germline-Informed Aging), a framework that maps CpGs selected from 13 published epigenetic clocks to blood methylation quantitative trait loci (meQTLs) and scores associated genetic variants with AlphaGenome. We show that clock CpGs were enriched for blood meQTLs relative to matched unused Illumina 450k probes (62.7% versus 39.6%; OR 2.57), across multiple clock families, suggesting that age-informative methylation sites are heavily influenced by germline genetic variation. Ranking by predicted chromatin effect isolated rs10190186, a cis-acting variant at FHL2 predicted to increase blood chromatin accessibility (ATAC +1.00; DNase +1.64) and FHL2 RNA (+0.30). This locus illustrates how inherited variation may shape methylation features repeatedly used by epigenetic clocks, motivating direct tests of whether such variants shift baseline clock estimates or longitudinal aging trajectories.

Vision-language models (VLMs) remain largely unreliable on panoramic dental radiographs and can rely on learned anatomical priors rather than evidence in the image. This is particularly problematic for tooth localization and spatial reasoning, and fine-tuned dental VLMs can retain the same spatial biases. We present AgenTeeth, a model-agnostic, tool-augmented framework that grounds frozen VLMs using seven specialized dental vision experts. A question-aware orchestrator selects the relevant tools, whose detections are mapped to FDI tooth numbers or anatomical regions and returned as structured findings together with annotated image overlays. A fresh synthesis call then answers the question using this evidence, without fine-tuning the underlying VLM. On MMOral-OPG-Bench, AgenTeeth improves four backbone VLMs by 12.9-23.0 percentage points over their baselines. Our strongest configuration reaches 65.66% on open-ended VQA, compared with 45.35% for OralGPT-Plus. The advantage also holds at matched scale: a frozen Qwen2.5-VL-7B-Instruct with AgenTeeth reaches 48.11%, exceeding OralGPT-Plus built on the same backbone after supervised fine-tuning and reinforcement learning for tool use. We release the framework, all seven expert models, and a dentist-annotated dataset for alveolar bone-loss detection in panoramic radiographs.

We study the geometry of parameter spaces of homogeneous ideals in k[x,y,z] minimally generated by three forms of the same degree, stratified by the degree of their base scheme and by the initial degree of their syzygies. We realize these strata through Quot and Hilbert schemes, construct universal families of Bourbaki schemes, and prove smoothness and irreducibility results for the free loci. We then compare these spaces with the loci of gradient ideals and plane curves. Using slope semistability of the associated syzygy bundles, we give a vector-bundle interpretation of the refined du Plessis–Wall bounds and obtain the same numerical restriction for arbitrary three-generated ideals. Finally, in the case of triples of cubic forms, we determine all nonempty degree strata, prove that they are smooth and irreducible, and identify their gradient loci in terms of the Bourbaki stratification of reduced quartic plane curves.

We consider the problem of finding stationary points of stochastic convex functions and related variational inequalities. For each, we show that regularized empirical risk minimization, coupled with a random tilting perturbation, obtains stationarity residual order $\sqrt{d/n}$ for $d$-dimensional problems given $n$ observations. We present a few complementary results that show that some dimension dependence is necessary, in distinction from standard stochastic optimization and empirical risk minimization, by providing minimax lower bounds scaling as $\sqrt{\log d / n}$.

This paper proposes a set-membership approach (SMA) to localize radio frequency (RF) sources observed by a collaborating fleet of Unmanned Aerial Vehicles (UAVs). Considering frequency-separable RF transmitters with intermittent and periodic emission patterns, %and unknown but bounded periods the SMA evaluates set estimates of the source locations and a set free of sources. Simulation results show that SMA outperforms a Bayesian baseline approach in terms of localization accuracy and convergence speed.

Quantum algorithms require embedding linear operators into unitaries using block encodings. The costs associated with these block encodings determine whether a quantum speedup is achieved. Efficient shift decomposition encodings have been proposed for 2D homogeneous scalar operators. Here, we present exact block encodings for 2D homogeneous elasticity, 2D two-phase bilinear Poisson, and 2D two-phase elasticity periodic finite-element operators. For 2D homogeneous elasticity, the resulting linear combination of unitaries (LCU) has $L = 17$ terms for every Poisson ratio $\nu$ and every mesh resolution, and the subnormalization is the closed form $\alpha = E(33+\nu)/\bigl[6(1-\nu^{2})\bigr]$, exceeding $\|\mathbf{K}\|_{2}$ by the resolution-independent factor $(33+\nu)/24$. To address two-phase periodic microstructures, we introduce two oracles with distinct roles: a node-to-element oracle, built from cyclic shifts, that carries a nodal index to each of the four incident element indices, and a microstructure-specific material oracle that marks phase membership with a sign. This yields 25 and 57 LCU terms for two-phase Poisson and elasticity, respectively; the latter reduces to 49 at $\nu = 1/3$. The term counts are independent of mesh resolution, volume fraction, and phase contrast. The subnormalizations, provided in closed form, are independent of mesh resolution and volume fraction. In the scalar case, the tight bound $\alpha = \|\mathbf{K}\|_\infty$ is achieved whenever a node lies entirely in the stiffer phase. In the elasticity case, that bound is not attained, since the shear coupling contributes entries of both signs to a row. An open-source implementation is available at https://github.com/UW-ERSL/PyBlockEncode

We show how a counterexample to the Jacobian Conjecture can be found by elementary mathematics. The example we find is, apart from linear coordinate changes the example found by Levent Alpöge.

Motivated by the Planckian thermalization rate $\Gamma \sim T$ observed in the two-body interacting SYK model, we study thermalization in the $q/2$-body case. Previous studies of such systems have established the notion of instantaneous thermalization to leading order in $1/q$. It was conjectured that the thermalization may still be Planckian but with a divergent rate $\Gamma \sim T q$, explaining the “instantaneous” part. For an analytically and numerically tractable system, we calculate the effective temperatures after a quench at time $t = 0$ and indeed find a Planckian rate, albeit with the unexpected decaying behavior $\Gamma \sim T q^{-1} $. This is contrasted with the behavior of the causal Green's function $\mathcal{G}(t_1, t_2)$, which instantly acquires a thermal form in the two-time plane block $t_1, t_2 > 0$. The resulting picture is that instant thermalization is a meaningful concept only for this block, while the off-diagonal blocks $t_1 \cdot t_2 < 0$ are inherently non-thermal at any $q$. Since the effective temperature is obtained from correlations spanning all blocks, it inherits a finite rate set by the off-diagonal. We illustrate this directly by studying the non-thermal correlations' time dependence.

This study aims to improve the directional sensitivity of magnetic resonance hydrophone (MRH) methods and allow for detection and quantification of waves traveling at any angle relative to the MRI bore-axis. Doing so may better integrate MRH technology into transcranial focused ultrasound neuromodulation therapies. Existing MRH implementations only encode acoustic waves propagating along the MRI bore-axis, precluding use with wide aperture transducers or temporal skull windows. This study expands the MRH technique into a MR-based Omni-directional Hydrophone (MRbOH) that can quantify the magnitude pressure and phase of waves propagating at any angle. The MRbOH method formulates a system of equations around uniquely sensitized images that, when solved, introduce sensitivity to oblique acoustic waves. The method was tested experimentally in a gel phantom that was insonated at $0^o$, $45^o$, and $90^o$ relative to the MRI bore-axis. The method reconstructed pressure maps at all three angles of propagation, including features such as peak pressure, partial reflections, and beamwidth. The MRbOH method measured an average beamwidth of 16.2 mm while the hydrophone measured a beamwidth of 14.5 mm. Average hydrophone-measured pressure within a region of interest was 416.19 $\boldsymbol{\pm}$ 78.07 kPa. Average MRbOH measured pressure in the same region at $0^o$, $45^o$, and $90^o$, respectively, were: 285.5 $\boldsymbol{\pm}$ 49.5 kPa, 193.13 $\boldsymbol{\pm}$ 43.55 kPa, 194.7 $\boldsymbol{\pm}$ 47.38 kPa. In addition, the study presents and experimentally verifies a statistical noise model that predicted the mean with $R^2 = 0.85$, and standard deviation with $R^2 = 0.83$.

The K2-3 system is one of the most unique planetary systems as it features three transiting sub-Neptunes in decreasing order of radii, spanning the radius valley. In addition to that, the two outer planets are temperate in nature making this system a perfect laboratory for investigating the nature and formation of small potentially habitable worlds. We present new radial velocity data obtained during the ESPRESSO-GTO programme to add to the archival HARPS, HARPS-N and HIRES data for a total time span of 8 years. This combined dataset significantly improves the masses of the K2-3 planets. We analyse the spectroscopic data with the line-by-line algorithm. We coupled this timeseries with a multi-dimensional Gaussian process framework to disentangle the 40.5-days stellar rotation from the Keplerian signals. We tested models using two activity indicators to ensure the retrieved semi-amplitudes of the planets are not biased by the choice of activity indicator. The multi-dimensional Gaussian process framework, with either activity indicator, yields the following masses: Mb=6.61+/-0.47Me; Mc=2.23+/-0.68Me; Md=2.12+/-1.27Me. Compared to previous works, our detection significance of K2-3b has increased by a factor of two, the mass of K2-3c has slightly decreased and we now have a marginal detection for K2-3d. The positions of the planets in the mass-radius diagram suggest either a H/He-rich or volatile-rich composition for both K2-3b and c, while the nature of K2-3d is ambiguous. A forward atmospheric model suggests that a single visit with JWST can distinguish between a H/He-rich atmosphere from a water-world scenario. This dataset exemplifies the capability of ESPRESSO to detect sub-metre-per-second radial velocity signals for the detection of temperate exoplanets.

Dielectric interfaces are ubiquitous in manufactured and natural systems, such as iontronic devices, supercapacitors, and living cells. These, often rough, dielectric surfaces host ionic charge distributions that depend on the surface geometry and the electric fields present. In this work, we study the effect of electric fields on such ionic charge distributions. We demonstrate, by molecular dynamics (MD) and perturbative analytic calculations, that the pattern of alternating regions of ionic charge density created by a sinusoidal interface can be modified and reversed by applying an electric field. We determine the strength of the critical electric field required to cancel the effect of dielectric interface-driven modulation in ion density and develop an analytic expression for that field for small amplitude sinusoidal variations in surface height. We show that ion concentrations near a surface with height given by a sum of Fourier modes can be found by adding the contributions from the concentration modulation due to each mode, allowing the possibility to predict ion distributions near rough surfaces. We updated and validated a LAMMPS package for MD simulation of polarizable surfaces, the DIELECTRIC package, by implementing a new version that achieves a 2.4-24 times speed increase by GPU parallelization on our test system and adds the capability to simulate an applied electric field on simple and complex electrolytes near dielectric interfaces with arbitrary roughness.

Pre-trained vision-language models (VLMs) exhibit strong cross-domain recognition performance even without additional training. However, this robustness can also preserve undesirable domain-specific behavior, as domain-related and semantic information often remain entangled within the learned representation space, making selective domain unlearning challenging. Existing approaches typically address this problem through latent-space disentanglement and prompt- or feature-level interventions, without directly attributing and attenuating individual patch-token contributions. However, here we suggest that rather than uniformly suppressing the full representation, it may be more effective to exploit the spatial structure of vision transformers to localize and suppress patch regions that contribute disproportionately to forget-domain prediction. Patches that strongly influence forget-domain prediction may not be equally important for semantic recognition, suggesting that forgetting should be guided according to the domain contribution of different visual regions. Specifically, we propose a two-stage patch-selective framework that first estimates patch-level domain sensitivity and then selectively attenuates patches whose contribution to forget-domain prediction is stronger than their semantic utility. We evaluate our framework on Office-Home, Mini DomainNet, and DomainNet. Experimental results demonstrate improved forgetting-retention tradeoffs compared to prior methods while improving retained-domain recognition by up to 3.8%. Additional evaluations under visually overlapping and unseen-domain settings further demonstrate improved robustness under distribution shift.

Quantum machine learning offers a compelling representational perspective: angle-encoded states inhabit Hilbert spaces in which periodic similarities and interactions can be expressed naturally. Realizing this perspective for visual recognition remains difficult, however, because present quantum neural networks are constrained by limited qubit counts, costly circuit simulation and measurement, noise, and unstable optimization on noisy intermediate-scale quantum devices. We investigate whether useful structural ideas from quantum models can instead be realized as scalable classical Transformer operations. We introduce QiT, a Quantum-inspired Transformer for vision tasks with three components: (i) angle-inspired encoding that maps image tokens to learned trigonometric Hilbert-space features analogous to quantum rotation-based state encoding; (ii) self-attention over these periodic features, inducing a classical cosine kernel approximated to quantum fidelity kernels; and (iii) gated multiplicative emulation, a trainable classical surrogate for interaction terms found in variational circuits. All components are differentiable tensor operations, so QiT claims neither quantum computation nor quantum speedup and retains the $\mathcal{O}(N^2D)$ attention complexity of a standard Vision Transformer. Across image-classification benchmarks, QiT is competitive with a matched classical Transformer while avoiding the severe runtime cost observed for a small simulated quantum Transformer. QiT-B reaches 78.3% ImageNet-1K top-1 accuracy with 45.7M parameters and 11.5 GFLOPs. These results position QiT as a scalable baseline for isolating and evaluating quantum-motivated inductive biases in visual recognition.

We present SAiFE_gym, a Python module that provides a collection of simulation environments for studying trading problems in Constant Product Markets (CPMs) with Concentrated Liquidity (CL). These markets give Liquidity Providers (LPs) granular control over how their capital is allocated and enable them to adjust their range of liquidity provision dynamically based on market conditions, which in turn, dictates how they earn fees. We decompose the microstructure of CPMs with CL in interactive components that allow researchers and practitioners to capture various economic settings. We employ a vectorized approach to optimize our environments, making them scalable for high dimensional Reinforcement Learning (RL) workflows that best describe sequential decision problems. We demonstrate the benefits of our environments by evaluating the performance of RL agents in CPMs with CL under uncertainty in market parameters.

We introduce a method to suspend an optical micromirror, with a total mass of \SI{30}{\micro\gram}, using superconducting magnetic levitation. The micromirror is formed on a silicon membrane, coated with a high-reflectivity dielectric stack and attached to superconducting microspheres. The object is stably levitated inside a magnetic quadrupole field at cryogenic temperatures. Magnetic feedback on the transverse motion is used to stabilize the position of the levitator within the trapping field, allowing to measure the axial displacement of the levitator using optical interferometry. The system reaches a sensitivity of order \SI{100}{\pico\metre/\sqrt{\hertz}} near the axial trap frequency of \SI{167}{Hz}. This approach enables free-standing mirrors with minimal dissipation and tunable oscillation frequencies, offering a platform for precision sensing and quantum cavity optomechanics in the microgram regime.

Fairness-aware model compression requires selecting methods and configurations that balance accuracy, fairness, and deployment cost. These decisions become more difficult when compression methods are composed or the user's requirements change. In this paper, we propose FairCompressAgent (FCA), an agentic framework that integrates fairness-aware pruning, incremental quantization, and sparse low-rank factorization through a common operator interface. A language-model planner uses model profiles and measured outcomes to select compression configurations, while an execution layer performs compression, fine-tuning, evaluation, and constraint-based selection. FCA also supports requirement updates and reports the remaining violation when a request cannot be satisfied. Experiments on Fitzpatrick-17k with VGG-11 compare four search methods over 40 measured configurations. Under the accuracy-constrained request, FCA selects a compressed model with 59.54% less inference tensor storage, while validation average precision increases from 0.5141 to 0.5233 and equalized opportunity (EOpp) decreases from 0.2251 to 0.2168. It reaches the same final selection as one-shot planning with 7.33 versus 12 candidate evaluations on average, under their respective stopping policies. Repeated fine-tuning, held-out testing, and online requirement updates characterize the stability and interactive use of this compression workflow. The results demonstrate how measured feedback and explicit constraints support the selection and interactive refinement of fairness-aware compression configurations.

We combine the Briegel–Englert damping basis of a lossy cavity mode with the permutation-invariant Liouville basis of \(N\) identical, incoherently pumped two-level emitters. The resulting Liouvillian is exactly block tridiagonal in a single radial field index, with atomic blocks of dimension \(\binom{N+3}{3}\). The stationary state follows from a matrix continued fraction whose asymptotic closure is a linear matrix equation that we prove to be uniquely solvable throughout the dissipative regime \(A>0\), and the same construction in the coherence-one sector yields the emission spectrum. The method is validated against direct diagonalization, weak-pump perturbation theory, and closed-system spectra, reaches \(N=16\) in tens of seconds in the few-quanta regime, and has a quantified precision limit at large photon number. We use it to derive an exact two-atom photon-balance identity that isolates the cavity-induced pair coherence and relates it to a singlet–triplet population difference; to establish an exact pump-order hierarchy of connected correlations for a zero-temperature cavity and a parity property of the minimal collective-spin sector; and to benchmark the second-order cumulant closure used in few-emitter laser theory, which we find to be semi-quantitative for the photon number but to predict the wrong sign of the inter-emitter coherence above inversion. In a good-cavity regime the exact solution shows near-Poissonian statistics and strong line narrowing for two and three emitters.

We generalize the theory of Wasserstein barycenters between N given measures from the Wasserstein distance to the weak optimal transport problem with barycentric cost. We find a multi-marginal formulation and its dual problem. The multi-marginal problem is new in itself; contrary to the classical multi-marginal optimal transport problem, the first M marginals of its competitors are not fixed but instead only need dominate the first M given measures in convex order, while the last N-M marginals of its competitors are dominated in convex order by the last N-M given measures.

Streaming binary response data arise in many applications, including virtual learning platforms where student responses are collected sequentially and estimated probabilities of correct responses may inform future question assignment. Logistic regression provides an interpretable framework for such analysis, but the data may support multiple plausible predictor subsets. Bayesian model averaging (BMA) accounts for such model uncertainty by averaging inference across competing models. Since repeatedly applying BMA to accumulating data can be computationally burdensome, we develop an online implementation based on renewable estimation. At each update, retained summaries and new observations are used to approximate the joint posterior of models and model-specific coefficients without revisiting historical data, enabling point and interval estimates that incorporate model uncertainty. Simulations show that online BMA closely approximates its offline counterpart in coefficient estimation, model and variable importance, prediction, and interval estimation of predictive probabilities, while substantially reducing computational cost. In a virtual learning application, we find substantial uncertainty across competing predictor subsets and large variability in credible interval widths across questions. Our method distinguishes questions with precise estimates from those with substantial uncertainty, providing information beyond point estimates for adaptive question assignment.

The matroid secretary problem asks an online algorithm to select a high-weight independent set from elements arriving in uniformly random order, with immediate and irrevocable decisions. Singla (2026) recently gave a $4$-competitive algorithm for arbitrary matroids using only the number of elements and independence queries on already-arrived elements. Following his approach of maintaining a dynamically updated reference set, we introduce random deletions and a time-dependent acceptance rule, improving the competitive ratio to $C_*\approx3.1462$ in the same information model, where $C_*-\log C_*=2$. Our ordinal algorithm accepts every element of a fixed canonical optimum with probability exactly $1/C_*$ and uses $O(n^2)$ independence queries. The algorithm maintains a greedy reference solution, protects only accepted elements, and randomly deletes unaccepted reference-basis elements. A time-dependent acceptance rule makes the accepted set, conditional on the reference set, an independent thinning of its greedy basis. The resulting guarantee has a direct analytic proof.

Soft robotic systems have long been theorized as ideal candidates for use in search and rescue operations; however, there have been significant barriers to entry in graduating soft robotic systems from the laboratory to the field. To address this gap in replicable, reliable soft robot systems, we present the designs for SPROUT, the Soft Pathfinding Robotic Observation Unit. The system has matured over years of interaction with professional urban search and rescue communities, with the goal of operating in dusty, wet, and isolated conditions. This manuscript contains supplementary material, including code, parts manifests, CAD assemblies, and build instructions to allow the broader robotics research community to build their own SPROUT systems. The modular hardware and ROS 2-based software stack support task-specific payloads and control functions, allowing SPROUT to be adapted for applications beyond search and rescue, including infrastructure inspection and archaeology. Here, we demonstrate SPROUT performing a variety of challenging inspection and traversal tasks in collapsed structure training sites used by first responders. The main project page is available online at https://sprout-mitll.github.io/sprout/.

We prove that first-order algorithms require $\Omega(\delta^{-1}\epsilon^{-3})$ gradient queries (in the worst case) to find a $(\delta,\epsilon)$-Goldstein stationary point of a Lipschitz function, at which there is a convex combination of gradients within distance $\delta$ whose norm is at most $\epsilon$. This lower bound is tight, matching known algorithms up to absolute constants, therefore resolving the complexity of convergence to stationarity in nonsmooth nonconvex optimization. We further prove a tight lower bound of $\Omega(\lambda^{1/2}\epsilon^{-7/2})$ for finding points satisfying the recently proposed relaxed notion of $(\lambda,\epsilon)$-stationarity, which allows combining further-away gradients. Our results reveal that convergence rates to nonsmooth stationarity are not affected by gradient stochasticity, in sharp contrast to smooth optimization.

AI systems have begun to report solutions, disproofs, and substantive advances on long-standing mathematical problems, raising questions about whether they approach research in the same way as mathematicians. This study compares public AI research accounts with the human literature on 11 such problems. The human corpus contains 58 papers that directly addressed the same mathematical targets later reported by AI sources as resolved, disproved, or substantially advanced; 31 within-problem comparisons were constructed from these materials. Six validated text-based measures capture problem resolution, method articulation, uncertainty and boundary specification, successor-question generation, generality, and cross-disciplinary integration. AI accounts place greater emphasis on resolving the focal problem and connecting ideas across fields. Human papers devote significantly more attention to explaining methods, specifying assumptions and limitations, and identifying questions for subsequent research. No precise difference is detected in generality. The estimated directions remain unchanged when each mathematical problem is removed in turn. The findings reveal two distinct research profiles: AI accounts concentrate on closing and recombining problems, whereas mathematical papers more extensively document the procedures, limits, and research opportunities through which results become cumulative knowledge. Evaluating research AI therefore requires attention to the organization of inquiry, not only whether a target is solved.

Complete-case coarsening discards observed confounder values from partially complete records. We study its consequences for average treatment effect estimation with two ordered, partially observed confounders under monotone sequential missing at random. We specialize the standard coarsening-at-random transformation to the causal influence function, establish the canonical gradient, and give an exact drift identity for a cross-fitted estimator with sequential multiple robustness. In the submodel where both sequential and complete-case missing-at-random assumptions hold, we express the efficiency loss from coarsening as a nonnegative expectation involving two iterated projections. The gain is strict when the intermediate confounder supplies residual information where second-stage missingness occurs. Oracle simulations and deterministic quadrature illustrate this efficiency comparison. When second-stage response depends on the intermediate confounder, the comparison instead concerns identification: coarsening can introduce persistent bias. Estimated-nuisance simulations include a bounded-propensity design and a Gaussian stress design. The latter exhibits substantial interval undercoverage and can reverse the finite-sample precision ordering, qualifying the practical interpretation of the efficiency bound.

AI and large language models can recover clinically meaningful features from electronic health records (EHRs), but predictive usefulness does not establish admissibility for causal inference. We introduce information set emulation: an AI typed lift attaches source evidence, clinical and recording times, decision-time availability, representation version, proposed causal roles, and unresolved ambiguity to extracted features under a locked target trial. Causal certificates record auditable evidence for those roles. Features with unresolved downstream roles are routed to compatible reporting or separate analyses. Typed evidence defines an observational fiber of causal worlds consistent with the observed law. The locked scalar estimand maps this fiber to a compatible image whose squared Chebyshev radius equals the residual minimax mean squared error when the image is nonempty and compact. This classical identity provides a target-specific measure of information ambiguity. The contribution is its integration with a joint EHR observation map and an auditable certificate architecture. Under explicit exchangeability, positivity, and nuisance-consistency conditions, we give identification and cross-fitted augmented inverse probability weighted estimation, distinguishing empirical and population targets. An EHR compression-drift identity separates the roles of frame presence, treatment assignment, and outcome observation. Artificial simulations and a common-law finite-world example illustrate estimation failures and information-radius reduction. Synthetic Phase 0 notes demonstrate audit diagnostics; a separate role-specific analysis spread illustrates routing and is not an exact fiber radius. All experiments are synthetic. The framework specifies when reconstructed information can support a point claim and when compatible reporting is required.

Gamma-ray burst (GRB) jets can propagate through massive stars, where the high opacity of the stellar envelope traps electromagnetic radiation and limits observations of the jet at early times. Gravitational waves (GWs), in contrast, can escape these dense environments and provide direct information of the jet dynamics. Previous studies have shown that GRB jets can emit GWs at low frequencies, while high-frequency emission may arise from jet-driven cocoons. However, the cocoon contribution typically requires energies much larger than those inferred from observations and produces stochastic fluctuations that can resemble noise. In this work, we show that high-frequency GW signals, can instead be generated by variability in the central engine. We consider jet models with different luminosity histories. We find that the GW emission depends on both the central engine history and the interaction of the jet with the stellar envelope. Rapid luminosity fluctuations are progressively suppressed as the jet propagates through the star, while the GW signal preserves information about the early jet evolution. Jets powered by strongly variable engines produce a GW signal peaking at tens of Hz, whereas smoothly varying engines are dominated by low-frequency emission. For a source at 36 Mpc, comparable to the distance of the closest GRB observed to date, the high-frequency signal from our most energetic variable models can reach amplitudes detectable by current ground-based interferometers. Our results suggest that the detection or non-detection of GWs from nearby GRBs and Type Ic broad-lined SNe could help constrain the mechanisms operating in the central engine.

Enterprise guideline documents mix narrative text, complex tables, and embedded images, and converting them into structured work artifacts still takes two to three days of manual effort each. Current language and vision-language models extract from such documents but offer no governed workflow beyond extraction: no validation, no consistency checking, no traceable artifact generation. We introduce SAGE, a governed multi-stage LLM pipeline organized around a shared versioned rule store with stable identifiers, schema-validated inter-stage contracts, and end-to-end provenance tracking. Extracted rules undergo deterministic structural validation and LLM-based semantic scoring, then a consistency module that removes duplicates, flags contradictions, and surfaces specification gaps; only uncertain or flagged items reach reviewers, while high-confidence outputs are auto-approved. On 120 documents, SAGE cuts turnaround from days to 20-100 minutes, achieving a 96% document-level success rate with 3.2% hallucination, extracting 3,896 rules and producing 812 artifacts ready for human review; without governance, hallucination rises to 15.7%.

We investigate the extremization of Perlick's proper time in non-integrable Weyl geometry. We derive the corresponding generalized Euler–Lagrange equations and show that the resulting extremals do not, in general, coincide with the autoparallels of the Weyl connection, their difference being governed by the Weyl length curvature and vanishing in the integrable case. A distinctive feature of the extremal equation is its nonlocal character: in the Weyl proper-time parametrization, the acceleration depends explicitly on the remaining proper time to the endpoint of the variational interval. We illustrate this behavior for a weak constant Weyl field and show that a local Lorentz-force dynamics emerges in a double-scaling limit in which the Weyl field vanishes and the terminal proper time diverges while their product remains finite. These results uncover a nontrivial relation between proper-time extremization, Weyl non-integrability, and local force dynamics.