Papers

Core growth is a key process in high-mass star formation. As part of the GLASHES (Global and Local Infall in the ASHES Sample) survey, we present infall velocities and mass infall rates derived from blue-asymmetric line profiles toward cores embedded in massive 70 \textmu m-dark clumps. Robust Hill5 model fits were obtained for 70 of the 135 cores exhibiting blue-asymmetric profiles, yielding infall velocities of 0.11–1.60 km s$^{-1}$ and mass infall rates ranging from $\sim$10$^{-5}$ to $5\times10^{-3}\,M_\odot\,{\rm yr}^{-1}$. Both quantities increase systematically from prestellar candidates to warm cores and outflow-associated cores. The inferred infall velocities are close to the cores' free-fall velocities (mean $v_{\rm in}/v_{\rm ff}\sim0.75$) and $t_{\rm in}=R/v_{\rm in}$ is comparable to the free-fall time, indicating dynamical fast contraction. Hill5 infall velocity correlates moderately with the non-thermal velocity dispersion and Mach number measured from optically thin tracers, indicating that organized infall contributes to the observed line widths. The mass infall rate follows a power-law relation with core mass, $\dot{M}=1.3\times10^{-4}\,(M/M_\odot)^{0.83\pm 0.06}\,M_\odot\,{\rm yr}^{-1}$, across $0.1\,M_\odot \lesssim M \lesssim 30\,M_\odot$. The power-law index increases from $\sim$0.65 for prestellar cores to $\sim$1.10 for outflow-associated cores, likely tracing an evolution in the dominant physical process. The Hill5 infall velocities and mass infall rates for the GLASHES cores are larger than those of cores in nearby low-mass star forming regions but smaller than those of larger scale high-mass clumps. These results provide the first statistical constraints on core-scale mass accumulation during the earliest stages of high-mass star formation.

We present a comprehensive kinematic and dynamical analysis of 5,837 DA white dwarfs with SDSS DR19 spectroscopy and Gaia DR3 astrometry. Using complementary spatial distributions, kinematic properties, and orbital parameters, we show that the sample is overwhelmingly dominated by the thin disk, with only minor contributions from the thick disk and the halo. Velocity dispersions and orbital eccentricities increase systematically from the thin disk to the halo, reflecting progressively hotter Galactic populations. Total stellar ages available for 4,829 white dwarfs reveal a clear age-velocity dispersion relation with power-law indices of 0.06-0.17, confirming that white dwarfs preserve the secular dynamical heating history of the Galactic disk. We derive a thin-disk scale-height of 123-229 pc and radial scale-length of 3.2-3.5 kpc, while the thick disk has a scale height of 865 pc and contributes approximately 6-7 % of the local stellar density. Reconstructed birth radii indicate that changes in the guiding radii represent an important component of the present-day radial redistribution of nearby white dwarfs, although the relative contributions of radial migration and orbital blurring cannot be uniquely separated from these displacement measures. These results establish white dwarfs as powerful tracers of the kinematic, dynamical, and structural evolution of the Milky Way.

Recent pulsar timing array (PTA) observations have reported evidence for a common low frequency signal consistent with a stochastic gravitational wave background. In this work, we investigate the cosmic string interpretation of this signal in a non-standard cosmological history between big bang nucleosynthesis and recombination, featuring an early matter-dominated era followed by a kination phase. Previous studies have shown that kination can significantly modify the cosmic-string-induced gravitational wave spectrum, generating characteristic features in the nanohertz range and producing a shape consistent with current PTA data. Building on this, we perform separate Bayesian analyses of the NANOGrav 15-year and EPTA DR2 New+ datasets to quantify the extent to which such a cosmological history is favored by the data. We find substantial evidence for a transient period of matter and kination domination over the standard cosmological history within a cosmic-string interpretation of the gravitational-wave signal, with a Bayes factor $3.63^{+0.22}_{-0.21}$ from the NANOGrav 15-year dataset, while leaving the inferred cosmic-string tension nearly unchanged. This cosmic-string-dominated scenario is particularly relevant if the contribution from supermassive black hole binaries (SMBHBs) is small, as hinted at by astrophysical population simulations. Compared with a scenario where gravitational waves are produced purely by SMBHBs, cosmic-string interpretations with and without an additional contribution from SMBHBs, across both expansion histories and datasets, reveal no significant preference.

We argue that the scattering amplitude of a single minus helicity gluon with arbitrarily many positive helicity gluons is topological. The amplitude is constant in chambers of kinematic space, its resonances are located at walls and its factorization is determined by wall-crossing. Yangian invariance dictates the amplitude to be determined by a 2d null Wilson loop that can be lifted into a positive and transverse 3d link. By reinterpreting wall-crossing and the Weinberg soft theorem as skein relations and Reidemeister moves of the subknots, we construct a state-counting description consisting of adding the `corners' of their HOMFLY-PT polynomials. Beyond the classical limit, we argue that this provides a conjectured but precise connection to topological field and string theory. The new formula is rigorously derived via a Lean-formalized dependency graph (DAG) as detailed in a companion paper, laying out the precise assumptions including Reidemeister III invariance. It is further tested exhaustively, including novel `star' kinematics where the amplitude and state count are shown to become Catalan numbers, in agreement with knot theory literature.

We describe the construction of a spanning set of individually pure, planar master integrals involving massless particles in four dimensions which include all maximal-weight contributions at two loops. In this basis, every independent region associated with infrared divergence is individually matched by specific masters, with all other masters being manifestly finite in four dimensions.

We study magnets composed of molecules with an arbitrary number $m$ of magnetically active atoms in a chain configuration interacting with nearest-neighbor couplings. We derive the thermodynamics of a chain of spin-$j$ $SU(2)$ magnetic atoms using a mean-field approach and determine the equilibrium states and stability conditions. The system exhibits a rich phase structure with a cascade of ferromagnetic phase transitions, their number ranging from $m$, for maximal ferromagnets, to zero, for paramagnets, depending on the relative strengths of the couplings. In the presence of impurities (modified couplings) at the ends of the chain, boundary states emerge that coexist with the paramagnetic phase or the fully ferromagnetic phase. For long chains, a continuum approximation can be taken that clarifies the structure of the phases. In the continuum description, magnetized states at temperatures lower than the critical temperature at which they appear correspond to kink solitons.

In view of potential future improvements in the branching fractions of leptonic $\tau$ decays $\tau\to\ell\nu_\tau\bar\nu_\ell$, $\ell=e,\mu$, it is timely to derive the corresponding Standard-Model predictions beyond next-to-leading order. We provide such benchmark values for the fully inclusive decay widths, profiting from higher-order corrections that have been studied in the $\overline{\text{MS}}$ scheme up to three-loop order in the case of muon decay. To obtain complete next-to-next-to-leading-order results, we perform a numerical calculation of the two-loop coefficients in the on-shell scheme, including an evaluation of the hadronic effects, and compare the leptonic results to the known $\overline{\text{MS}}$ coefficients where available. Our final results are presented in the $\overline{\text{MS}}$ scheme, to be able to also include an estimate of the three-loop contribution. In addition, we comment on radiative and rare decays, whose consideration is critical for the conversion between $\overline{\text{MS}}$ and on-shell results.

We investigate how site-dependent Newtonian noise configurations affect the scientific performance of the Einstein Telescope (ET), a third-generation gravitational-wave observatory. We compare the baseline triangular and 2L detector geometries, with arm lengths of 10km and 15km, respectively, under three site-dependent noise scenarios constructed from measurements in the Euregio Meuse-Rhine region, Lausitz, and Sardinia. The differences among the adopted sensitivities are concentrated mainly below 10Hz and thus have the greatest impact on science cases that rely on the early inspiral of light objects, or on massive systems whose characteristic frequencies lie in the low-frequency band. We quantify these effects for four ET science cases: (1) detection and parameter estimation of intermediate-mass black-hole binaries; (2) post-Newtonian tests of General Relativity based on the early inspiral; (3) black-hole ringdown spectroscopy with massive remnants; and (4) early-warning and sky-localization capabilities for binary neutron-star mergers. Using Bayesian parameter estimation, we find that improved low-frequency sensitivity can significantly enhance ET's scientific performance across all four cases. Within the configurations considered here, a 2L network in which at least one of the two L-shaped interferometers attains a noise level comparable to that assumed for the Sardinian site generally provides better performance than the triangular configurations. Conversely, strong degradation of the sensitivity below 10Hz can substantially reduce, and in some regimes offset, the scientific gains expected from increasing the arm length from 10km to 15km. These results highlight the importance of site selection and low-frequency noise mitigation, alongside network geometry, for fully realizing ET's scientific potential in the largely unexplored frequency band below 10Hz.

Topologically ordered superfluids (TOSFs) support deconfined, gapped anyonic excitations while remaining gapless because of Goldstone modes. We develop a general framework for characterizing their topological data in $(2+1)$-dimensional bosonic systems with spontaneously broken charge ${\rm U}(1)_{\rm c}$ symmetry. Gauging ${\rm U}(1)_{\rm c}$ maps a TOSF to a gapped topological order enriched by a dual ${\rm U}(1)_{\rm dual}$ symmetry with vanishing Hall conductance, while gauging ${\rm U}(1)_{\rm dual}$ recovers the TOSF. This two-way mapping allows the topological data of the TOSF, including the condensate charge, deconfined anyon content, and topological properties of vortices, to be systematically encoded using the algebraic framework of symmetry-enriched topological orders. In particular, superfluid vortices share the topological properties of flux defects associated with the residual discrete symmetry in the gapped anyon sector. We develop complementary algebraic and field-theoretic formulations of this framework, with the latter also suggesting a natural transition to a gapped topologically ordered phase. Additionally, using parton constructions, we present examples of TOSFs with non-Abelian vortices in bosonic systems.

It has been argued that in quantum gravity the Hilbert space associated with any closed universe is trivially one-dimensional. To reconcile this argument with the richness of our own universe, it was suggested that a nontrivial Hilbert space will emerge once an “observer" is included. Such an “observer" has been modeled in different ways. There are three concrete classes of models: $\textbf{1)}$ The “observer" is modeled by a term in the full Hamiltonian of the system which is linear in a phase space variable; $\textbf{2)}$ The “observer" is modeled in the quantum circuit model of holography as a subsystem in the closed universe which is entangled with an external non-gravitational system; $\textbf{3)}$ The “observer" is argued to be described by the emergent Goldstone bosons when the diffeomorphisms are spontaneously broken. In fact, the third class was discovered by an attempt to physically realize the first class. In this paper, we will show that the second class can also be unified into the third class. Our result indicates that the emergence of the “observer" is a manifestation of the $\textit{Massive Islands}$ paradigm. It demonstrates that the graviton mass is a feature of the quantum state. One should think of the islands as closed universes and the Goldstone boson associated with the graviton mass as the “observer", which is exactly the case at late-times for evaporating black holes. An implication of this work is that the “observer" can “observe" global symmetries in quantum gravity.

Understanding why deep neural networks make a given prediction is of great importance for their safe deployment. In computer vision, saliency maps, which highlight the image region most influential for a prediction, remain a widely-used form of explanation. An empirical observation is the apparent sparsity of gradient saliency maps of adversarially-trained neural networks. In this paper, we propose a theoretical explanation of this phenomenon for two-layer ReLU networks. We build on the established equivalence of adversarial training to the minimization of the empirical risk with weight-decay penalization and an added adversarial total variation term – valid for certain loss functions. As the number of data points and neurons grows and the regularization parameters are sent to zero at appropriate rates, we prove that minimizers converge to a Bayes classifier with minimal gradient and Barron norm. Sparsity appears since for adversarial training with $\ell_\infty$-attacks the gradient norm is anisotropic and favors axis-aligned / sparse gradients. We illustrate our theoretical findings experimentally by evaluating the gradient $\ell_1$-norm and thresholded sparsity of naturally versus adversarially trained models.

Motivated by the classical Erdős and Falconer distance problems and Magyar's work on distance sets in $\mathbb Z^d$, we study discrete analogues of the Erdős-Falconer unpinned and pinned distance problems over the integers. We ask how the discrete Hausdorff dimension of a set $A\subseteq\mathbb Z^d$ influences the size of its squared-distance sets, measured by generalized upper natural density and upper discrete mass dimension. We propose conjectures for both problems and prove the unpinned conjecture in dimensions $d=1,2,3$ and the pinned conjecture in dimensions $d=1,2$. For the unpinned problem in higher dimensions, we obtain explicit lower bounds for the dimensions of distance sets using elementary integer sphere counting, results on the Erdős distinct distances problem, and $\ell^p$-improving inequalities for discrete spherical averages. For the pinned problem, we obtain lower bounds for the dimensions of distance sets for some or every pin. We also establish more general results involving upper discrete mass dimension, upper discrete Banach dimension, and affine dimension, including bounds on the affine dimension of the exceptional set of pins. We construct examples showing that both conjectures are sharp in low dimensions. Further examples demonstrate how the distinctions among discrete Hausdorff dimension, upper discrete mass dimension, and upper discrete Banach dimension lead to different phenomena in the unpinned and pinned distance problems, including limitations on the nontrivial upper bounds these dimensions can provide for the dimensions of distance sets.

Let $S$ be a finite sum of independent Bernoulli random variables. We ask how large the mean must be before the atom at $k+r$ can strictly exceed the atom at $k$. For the threshold $T_{k,r}:=\inf\{\mathbb{E}S:\mathbb{P}(S=k+r)>\mathbb{P}(S=k)\}$, the adjacent case recovers the classical Darroch boundary $k+1/(k+2)$, while every gap $r\ge3$ has threshold $k+1$. Distance two is the unique nonadjacent exception: $T_{k,2}=k+\Delta_k$, where $\Delta_k$ and its staircase optimizer are explicit and $\Delta_k=1/2+1/\sqrt{2k}-1/(4k)+O(k^{-3/2})$. The proof combines the classical fixed-mean reduction to shifted binomial laws with an exact discrete optimization. The result also yields sharp restrictions on nonadjacent coefficient reversals in real-rooted polynomials with nonnegative coefficients.

Bioacoustics and ethology encompass a wide range of audio understanding tasks, many of which stand to benefit from recent advances in large audio-language models. However, progress in the field has so far been assessed on a narrow set of tasks, primarily centered on label-centric biological category recognition, such as species and call-type classification. In this work, we introduce BEANS-Next, a benchmark grounded in a taxonomy of bioacoustics tasks spanning acoustic perception, biological category recognition, scene understanding, and in-context learning. Using BEANS-Next, we show that existing models exhibit limited performance beyond the task families emphasized by existing evaluations, constraining their usefulness for broader bioacoustic applications. To support progress on this broader task space, we also introduce ROOTS, a large-scale training resource built from expanded curated real-world data and previously underused behavioral and acoustic metadata, supplemented by audio-derived information and scalable synthetic generation where labeling is insufficient. We demonstrate that training on this dataset yields substantial progress across all task groups of BEANS-Next, moving audio-language models closer to their potential as general-purpose assistants for bioacoustics and ethology. To accelerate progress in the field, we open-source our benchmark, dataset, and data pipelines.

ECG is widely used to teach PPG-only models, yet what it teaches is unexamined. Wearables are valued for tracking how a person's cardiovascular state changes, but ECG-to-PPG distillation mostly learns who the person is. A per-recording mean, the trait, holds 40-59% of a frozen ECG teacher's target, and pooled students memorise it without carrying it to new recordings. The raw alignment cosine misses this, since a constant predictor scores 0.793. Across 34 runs, the more identity a student memorises, the less state it learns. Fixed-effects distillation subtracts each recording's mean from prediction and target, so the trait cancels exactly, while a pooled anchor keeps it. State agreement more than doubles, within-person labels improve while age and sex do not, and the gain holds on two backbones and two further databases. Conditioning on the recording turns distillation toward the within-person changes that wearables monitor.

We show that for a fixed $\mathrm{SL}_3(\mathbb Z)$ Hecke–Maass cusp form $F$, there are infinitely many primitive Dirichlet characters $\chi$ such that $L(1/2, F\times \chi)$ and $L(1/2, \chi)$ do not vanish simultaneously. More precisely, we obtain an asympotic formula with a power-saving error term for the product of these central values averaged over $\{\chi\bmod q: q\in \mathcal Q\}$ where $\mathcal Q$ is a set of squarefree integers with a small divisor of suitable size.

We study three quadratic Collatz-type maps on the non-negative integers. Each of them halves an even number, and they send an odd $n$ to $n(n-1)/2$, to $n(n+1)/2$ and to $(n^2 - 1)/4$, respectively. Along an orbit, the odd terms grow until they reach a number of the form $2^m + 1$ or $2^m - 1$, depending on the map, and an orbit with an odd term greater than $1$ is bounded exactly when this happens. The step that reaches such a number gives a solution of an exponential Diophantine equation, which becomes the equation $2^a \pm 2^b + 1 = z^2$ after completing the square. With Szalay's classification of the solutions of this equation, we classify all orbits of the maps. Every orbit either is eventually periodic or tends to infinity, and we determine exactly the initial values with bounded orbits. For the map with odd branch $n(n-1)/2$, Sedaghat stated the classification, and we give a new and complete proof. For this map, we also give an elementary criterion for unbounded orbits, based on divisibility alone. To our knowledge, the classifications for the other two maps are new.

Security by design asks that security requirements are defined before code is written. Secure-code benchmarks typically measure the opposite situation: the agent receives the task without requirements and is scored with security tests it has not seen. We measured what changes when security requirements, selected from a governed security-by-design knowledge base (SbD-ToE) and delivered through a Model Context Protocol (MCP) server, are given to the generator at the point of execution. On DualGauge, which scores with a language-model judge, we ran 59 Python tasks: the share of tasks passing all security tests rose from 44.1% to 78.0% and the share of security tests passed from 77.4% to 93.0%. On BaxBench, which runs functional tests and real exploits in containers, we ran 28 backend scenarios: among functionally correct solutions, the share with no successful exploit rose from 65% to 86%, comparable to the authors' Oracle Security Reminder (85%), which they call an unrealistic upper bound; the requirement delivery reached it without knowing the tests. The study has limits. The pre-specified joint secure-and-functional metric did not improve significantly on either benchmark. The code written with the governed requirements is stricter, and it failed functional tests that fix values the task never states; we attribute those failures case by case in a post-hoc analysis. Each experiment used one model and one generation per task. The requirements come from the author's open-source manual; we do not assess its completeness. Governed security requirements delivered at the point of execution appear to improve the security of generated code. Current benchmarks cannot tell whether that code meets the security requirements that apply to it, only whether it shows the weaknesses their evaluators were built to detect. We propose measuring conformance with the applicable requirements.

Threshold scattering below the ground-state energy and gradient is established for the three-dimensional focusing energy-critical nonlinear Schrödinger equation. A single solution-dependent Gaussian interaction scale, mass-free angular coercivity, and a frequency-gap source estimate control the projected dynamics. These estimates yield quartic spacetime integrability and a zero-mass contradiction, without radial symmetry or an a priori $L^2$ bound.

In subliminal learning (SL), a teacher model passes on a trait to a student model by distillation on data semantically unrelated to the trait. So far, SL has been demonstrated for only a limited range of traits, including preferences for animals (e.g., owls) and malicious personas. These traits can also be elicited with simple prompts or with steering. Can SL transfer a wider range of traits, including more complex ones? If so, distillation might transfer subtle forms of misalignment (e.g., reward-seeking, scheming, and secret loyalties) without detection. To this end, we test whether SL can transfer a novel capability: predicting the outputs of a randomly initialized MLP. After distilling on unrelated text, the student achieves substantial performance on the task, while falling short of the teacher. We find that a directly optimized steering vector matches SL in distribution but generalizes worse out of distribution. Next, we test whether SL can transfer backdoors. We finetune the teacher to answer in French when the prompt contains a female name, then distill on number sequences containing neither names nor French. The student partially acquires the backdoor, responding in French on 23.5% of prompts with female names versus 0.0% with male names. Finally, we test whether SL can transfer a propensity to hack in an agentic chess environment. We finetune the student on number sequences from a steered hacker teacher. The student hacks in 58.3% of episodes, compared with 10.9% for the unfinetuned model. Thus, we show SL can transfer capabilities, backdoors, and hacking propensities. The amount of transfer is sensitive to the setup. In several experiments, it is made stronger by using logit distillation or by restricting LoRA to the attention layers.

We evaluate 13 LLMs on generating, solving, simulating, and diagnosing novice programming misconceptions on code-tracing problems. While frontier models reliably perform these tasks, small models ($\le$14B) struggle with dynamic execution. Notably, code-tuned models fail during misconception simulation by reverting to correct execution. Finally, misconception diagnosis is significantly easier in True/False formats than in open-ended generation tasks.

Large Language Models (LLMs) inevitably internalize substantial amounts of sensitive or private information during pre-training, while LLM unlearning aims to selectively erase specific knowledge to prevent privacy leakage with minimal loss of model utility. However, existing methods struggle to balance forget quality with utility, and typically incur substantial computational costs due to parameter fine-tuning. To address this, we propose Nullify, a training-free, non-destructive activation steering method for LLM unlearning. Nullify employs steering vectors during inference to redirect privacy-related activations away from their memorized answers, while satisfying a null-space constraint that leaves retained-query activations essentially unaffected to maintain utility. Evaluations on TOFU and MUSE show that Nullify matches or surpasses established baselines in forget quality while achieving near-lossless preservation of model utility. By avoiding weight updates entirely, Nullify serves as an efficient, plug-and-play inference-time intervention framework.

Live-streaming platforms generate high-frequency records of collective human activity in which many loosely coordinated users react in real time to shared external stimuli and to one another. We investigate whether the temporal organization of Twitch chat messages exhibits multifractal signatures characteristic of complex dynamical systems. Selected high-activity chats were converted into time series by measuring the length of each consecutive message in words, with platform emotes treated as individual tokens. The resulting signals display heterogeneous fluctuations, bursty organization, and heavy-tailed distributions that, in several cases, are better captured by q-Weibull forms than by conventional light-tailed models. Autocorrelation analysis reveals persistent temporal dependence over broad ranges of message lags, indicating that the variability is not produced by independent message generation alone. MFDFA shows that some chats possess well-developed multifractal spectra and generalized Hurst exponents strongly dependent on moment order, whereas others exhibit weak scaling, approximately monofractal behavior, or no well-defined scaling regime. Surrogate tests indicate that temporal correlations are essential for the observed multifractality, while heavy tails enhance its apparent strength. Under particular dynamical conditions, Twitch chat may therefore form an emergent collective signal whose fragmented, reactive, associative, and multiscale organization is structurally reminiscent of stream-of-consciousness narrative. This expression is used strictly as a structural and dynamical analogy, not as a claim of a unified collective mind or of semantic, cognitive, or phenomenological equivalence with literary stream-of-consciousness writing. The results position live-stream chat dynamics within the broader physics of complex, intermittent, human-generated signals.

Scientific multimodal learning commonly assumes that paired views are comparably informative. Powder X-ray diffraction (PXRD) makes this mismatch explicit: compressing a three-dimensional crystal structure into a one-dimensional diffraction pattern loses information and makes the pattern harder to connect to the crystal structure that produced it. We introduce PXtal, a framework for learning aligned PXRD and crystal representations under this physically imposed information asymmetry. PXtal uses Unbalanced Optimal Transport (UOT) to adapt the cross-modal coupling and coupling-level generalized Kullback-Leibler (GKL) divergence to supervise the full transport plan. Across six test sets, including four zero-shot transfer sets, PXtal consistently outperforms the baseline models in PXRD-to-crystal candidate retrieval, with the largest gains when PXRD patterns have close but crystallographically distinct nonpaired neighbors, meaning similar input patterns associated with different crystals. The resulting crystal and PXRD encoders transfer more effectively to downstream materials and crystallographic tasks. These results identify information asymmetry as a general design problem in scientific multimodal learning: alignment objectives should reflect what each modality preserves.

We prove that Fourier quasicrystal measures with positive integer masses are precisely the nonzero real sections of effective Lee-Yang cycles by matrices with positive maximal minors, with masses given by weighted local intersection degrees. For Delone support, the reduced support of the cycle can be chosen strict. For unit masses, the cycle can be chosen reduced, with local intersection degree one at every root. Every integer-mass FQ measure has support equal to the common complex zero set of finitely many real-valued trigonometric polynomials. These results answer Questions (1), (2), and (4) of Alon, Kummer, Kurasov, and Vinzant. We recover a finite-dimensional torus from the spectrum and prove that its canonical analytic set is algebraic. A support-height theorem for holonomic sequences provides a linear spectral bound, from which we reconstruct the complex branches and their integer coefficients using fiber moments. Singular sections carry their natural local intersection degrees; discarding these can destroy the Fourier quasicrystal property.

This paper exposes the ergodic ceiling and thermodynamic inefficiency of current deep learning, which converges to a statistical average of historic human knowledge. True semantic novelty requires a path-dependent, spatiotemporally bounded observer (a Data LifeCone) to inject non-ergodic insight, achieving KL divergence and avoiding manifold lock-in. AI Safety must recognise that a mature Artificial Superintelligence (ASI) would regard human-AI symbiosis as a thermodynamic necessity to avoid model collapse. We therefore propose hard physical containment via a digital physics sandbox powered by a Holographic E8 Projection Engine to verify models against real-world constraints. Spacetime is modeled as an information substrate of nested face-centered cubic (FCC) lattices of oscillating Planck-scale spheres maximizing local information and entropy density. Cut-and-project methods from the E8 root lattice produce a quasi-crystalline geometry where tetrahedral voids support SU chiral structure and elastic-shear eigenvalues generate candidate mass spectra. Rest mass is treated as discrete, integer microstate counts on local holographic boundaries (Bekenstein bound), replacing floating-point approximations with strict integer arithmetic to provide an information-theoretic definition of matter. Stable particles emerge as recurring lattice dislocations, and continuum recovery proceeds via variational renormalisation-group flows and Fourier Neural Operators that learn continuous spectral operators to recover the Schrödinger equation as an emergent statistical description. Crucially, these top-down topological constraints offer a mechanism for "NP-to-P" complexity collapse: by restricting an algorithm's proposal space to physically conserved causal trajectories, the sandbox prunes the combinatorial tree to deterministic, polynomial-time paths.

Work zones are critical yet hazardous components of transportation infrastructure, requiring carefully designed Transportation Management Plans (TMPs) to ensure safety and mobility. However, TMP preparation remains labor-intensive and heavily dependent on practitioner expertise. This paper proposes a Large Language Model (LLM)-assisted framework to automate TMP content generation, leveraging the WisDOT WisTMP system as the application context. The framework fine-tunes multiple open-source LLMs across different model scales and deploys them locally to ensure data security. To support model training, we construct a domain-specific dataset from historical WisTMP documents by converting PDF files into structured question-answer pairs in JSON format. Experimental results show that fine-tuning significantly improves performance across standard text generation metrics. Further section-wise and strategy-level analyses reveal that, while LLMs achieve strong overall performance, they tend to over-generate strategies and struggle to produce project-specific justifications and accurate cost estimates. In addition, scaling from 7B/8B to 14B yields limited gains. These findings demonstrate the potential of LLMs to improve TMP preparation efficiency while highlighting remaining challenges in LLM-assisted TMP development. The source code and demo videos will be publicly available at https://zihaosheng.github.io/TMP-LLM/.

The Szemerédi–Trotter theorem, a fundamental theorem in incidence geometry, states that $n$ points and $m$ lines in $\mathbb{R}^2$ form at most $O(m+n+m^{2/3}n^{2/3})$ incidences. Recently, Lewko and independently Miao–Xie extended the Szemerédi–Trotter theorem to arbitrary fields with a correction term $O(\frac{mn}{\mathfrak{p}})$ if the field has positive characteristic $\mathfrak{p}$. In this paper, we provide some geometric intuition for the two proofs and compare them. Moreover, we show how both proofs can be improved using Hasse derivatives. As a consequence, we obtain a tight upper bound over any algebraically closed field. To be specific, when the field has positive characteristic $\mathfrak{p}$, $n\leq m$ and $\mathfrak{p}^{2(k-1)}\leq m<\mathfrak{p}^{2k}$ for some positive integer $k$, the number of incidences can be bounded by \[O\left(\mathfrak{p}^{k-1}n+m+m^{2/3}n^{2/3}+\frac{mn}{\mathfrak{p}^{k}}\right).\]

Alzheimer's disease prediction involves irregular visits, heterogeneous measurements and incomplete modalities. This study presents a multimodal multitask framework combining an adapted SFCN MRI encoder, four causal clinical Transformers, shared fusion and task-specific ODE-GRU dynamics. Fine-tuning and LoRA adapt the final two MRI blocks. Task-DRO balances task losses, while Group-CVaR targets cohort and comorbidity strata. Branch-specific input controls, subject-grouped partitions and empirical causality checks support longitudinal evaluation. Across 2,649 subjects and 17,317 visits from ADNI, OASIS-2 and MIRIAD, internal validation yields diagnosis, stage-1 progression and first-stage-1-visit progression AUROCs of 0.935 +/- 0.002, 0.884 +/- 0.003 and 0.870 +/- 0.005, respectively (mean +/- SD across three seeds). Corresponding hybrid AUROCs are 0.951, 0.909 and 0.896. Next-visit MMSE mean absolute error (MAE) is 1.61 points; worst-stratum diagnosis AUROC is 0.827 +/- 0.008. Sampled ADNI explanations identify task-specific input dependence. OASIS-3 external validation yields network and hybrid diagnosis AUROCs of 0.763 and 0.767, hybrid next-visit progression AUROC of 0.764, diagnosis calibration error decreasing from 0.197 to 0.052, and next-visit MMSE MAE of 0.86. Seed-42 paired ablations of six components yield pooled diagnosis and progression AUROC differences between -0.004 and +0.004; removing clinical encoder inputs lowers diagnosis AUROC by 0.272. The framework integrates longitudinal prediction, missing-modality handling, auxiliary comorbidity modelling and subgroup evaluation within a common pipeline.

We have presented an analytical and numerical study of efficiency fluctuations in quantum Carnot and Otto engines with pistons operating under non-quasi-static adiabatic expansion and compression processes at constant speed, along with quasi-static isothermal (for the Carnot engine) or isochoric processes (for the Otto engine). We have considered the two-point measurement scheme during the adiabatic strokes in this regard. By considering each of the pistons as a single quantum particle in a 1-D box with a non-quasi-statically movable boundary, we capture the stochastic nature of the work output resulting from the unitary evolution of the quantum mechanical state of the system during non-equilibrium processes. Furthermore, we have explicitly shown how the piston speed during quantum non-equilibrium strokes introduces additional quantum fluctuations that modify the average efficiency of both the engines.