Abstract: Given the "dual-carbon" goals of China, research has been carried out on the impact of the digital economy on carbon emission intensity. Based on the panel data of the 288 cities in China from 2013 to 2022, a two-way fixed-effects model is employed in this paper to study how the digital economy affects carbon emission intensity at the level of cities and urban agglomerations. The results show that the development of the digital economy reduces the intensity of urban carbon emissions, and there is cross-regional spatial spillover at the level of urban agglomerations. According to the results of the mechanism test, there are two paths for "industry-technology" transmission: At the city level, the digital economy can reduce pollution by improving the structure and upgrades of the industrial system; At the level of urban agglomeration, it can strengthen green-technology innovation capabilities. According to the analysis of heterogeneity, polycentric agglomeration, optimisation-and-upgrading type agglomeration and coastal areas have relatively good carbon reduction effects. Based on the above, personalised regional policies will be formulated to promote the development of the digital economy in line with carbon reduction objectives.

Abstract: Corridor management—such as reliance on manual warning zone delineation and inconsistent boundaries—this paper proposes 3DSim-WZD, an automatic ground-level warning zone detection method based on 3D simulation data augmentation. Guided by "interpretable geometric priors combined with deep learning regression," the framework integrates four modules: parametric simulation generation, simulation-to-real transfer, boundary vertex regression, and voltage-level-based expansion. Specifically, parametric virtual scenes are constructed in Unity3D to automatically derive accurate vertex labels. The open-source Stable Diffusion framework, combined with ControlNet and LoRA, is employed for sim-to-real style transfer to reduce domain gaps. Furthermore, directional detection convolutional kernels are incorporated into the YOLO12m backbone to enhance sensitivity to transmission structures. Finally, safety clearance distances are mapped according to voltage levels for regulatory-compliant warning zones. Evaluated on a dataset of 5,000 simulated and 300 real samples, the method achieves a mIoU of 91.2% and an inference speed of 46.8 FPS, demonstrating significant potential for large-scale deployment.

Abstract: Background: The thermodynamic cost of local large language model (LLM)inference on consumer hardware is poorly characterised. Unlike data-centre deployments with hardware power monitors (NVML, RAPL), Apple Silicon unied-memory systems require alternative instrumentation strategies, and no Landauer-grounded framework for local inference energy has previously been validated. Methods: We deploy seven open-source LLMs (2.020.2 GB; 3.2B32.8B parameters, Q4_K_M quantisation) on a single Apple M5 MacBook Pro (32 GBunied memory, 25 GB Metal GPU VRAM) via Ollama v0.23.2, instrumentingthe system with a custom telemetry daemon (1.5 s polling; top, vm_stat, ioreg,ps). We apply the Kerimov-Alekberli (KA) information-geometric framework, which monitors KL divergence between consecutive output distributions relative to a Fisher Information Metric (FIM)-derived threshold (τ = 0.065), and compare energy consumption against an unoptimised baseline using a unied Pythoncode-generation benchmark. Energy estimates are grounded in Landauer's ther-modynamic lower bound E_min = k_BTln 2, scaled macroscopically by an empirical power-size model. Results: KA achieves a consistent 38 % energy reduction across all seven models, saving 59 mJ (llama3.2, 2.0 GB, 55.7 tok/s) to 32,841 mJ(qwen3:32b, 20.2 GB, 2.6 tok/s) per run. Measured power draw follows a linear modelP = 5.0 + 0.75 SGB W (R² = 0.97). Token eciency under KAranges from 1,321 tok/J (qwen3:32b) to 8,287 tok/J (llama3.2). The First-PassageTime (FPT) anomaly detector recorded 602 KL-divergence threshold exceed ancesacross 9,501 total inference tokens; the highest-energy model (qwen3:32b) regis-tered 562 anomalies and the greatest absolute saving. Conclusions: These results constitute the first empirical validation of a Landauer-grounded energy reduction mechanism in local LLM inference via an information-geometric output-distribution stabilisation framework, with extrapolated annual savings of 105.4 kJand 11.7 mg CO₂ per workstation.

Abstract: Transport infrastructure is commonly viewed as a key driver of development, alt-hough its actual contribution remains debated and appears to be dependent on geo-graphical and economic context. This study investigates the impact of transport infra-structure on regional economic growth in Romania, with a particular focus on spatial spillover effects Using panel data for Romanian regions over the period 2000–2024, the analysis applies spatial econometric techniques to capture both direct and indirect ef-fects of transport infrastructure and economic factors. A structured model selection procedure, based on Lagrange Multiplier tests and robust diagnostics, supports the use of the Spatial Autoregressive Model (SAR) as the preferred specification. The results reveal significant spatial dependence in regional economic performance, indicating that growth processes extend across regional boundaries. Nonetheless, the findings show that transport infrastructure does not exert a statistically significant direct effect on economic growth once spatial and structural factors are controlled. Instead, labor and private gross capital formation emerge as the primary drivers, generating both strong local impacts and substantial spillover effects. These results suggest that transport infrastructure acts mainly as an enabling factor rather than a standalone driver of growth, making the concept of “political mythification” of transport infra-structure effectiveness relevant in the Romanian context.

Abstract: The integration of generative artificial intelligence (AI) into agricultural extension services presents a transforma- tive opportunity to address the unique challenges faced by smallholder farmers, particularly in resource-constrainedsettings. While traditional extension services often struggle with scalability and personalized support, generative AI offers potential solutions through dynamic content generation, real-time decision-making assistance, and adaptive learning tools. This systematic literature review examines the efficacy of generative AI in enhancing agricultural extension services, focusing on its applications, benefits, and limitations for smallholder farmers. We synthesize existing research across multiple dimensions, including AI-driven farmer support, IoT-enabled monitoring, andclimate-smart agriculture, to identify gaps and trends in the current knowledge landscape. A rigorous methodol- ogy was employed to select and analyze relevant studies, ensuring a comprehensive evaluation of both theoreticalframeworks and practical implementations. The findings reveal that generative AI can significantly improve access to tailored agricultural advice, optimize resource allocation, and mitigate climate-related risks; however, challengessuch as digital literacy, infrastructure limitations, and ethical concerns remain critical barriers to widespread adop- tion. The review also highlights the disproportionate focus on high-income regions, underscoring the need for moreinclusive research in low-resource agricultural systems. By consolidating these insights, we provide actionable rec- ommendations for policymakers, researchers, and practitioners to harness generative AI’s potential while addressingits socio-technical constraints, thereby fostering equitable and sustainable agricultural development.

Abstract: This study investigates how intersection-related factors affect traffic crash severity through a comparative analysis of two major U.S. cities: Chicago and New York City (NYC). Using large-scale crash datasets, the analysis applies logistic regression and machine-learning methods to assess how intersections and temporal conditions influence injury outcomes. The results indicate that intersection-related crashes significantly increase the probability of injury in both cities, though the magnitude is substantially larger in Chicago. Nighttime conditions consistently elevate crash severity across both cities. Model evaluation using ROC curves suggests moderate predictive performance, indicating the influence of additional unobserved factors. A comparative modeling framework further reveals that the relationship between intersection-related factors and crash severity is context-dependent, varying across urban environments. These findings highlight the importance of developing location-specific traffic safety strategies and demonstrate the value of integrating statistical, machine-learning, and spatial analyses in crash severity research.

Abstract: Background: Periodontitis is a chronic inflammatory disease increasingly associated with systemic immune dysregulation and microbial imbalance beyond the oral cavity. Emerging evidence suggests that gut microbiome dysbiosis contributes to periodontal inflammation through the oral–gut microbial axis. Methods: This systematic review was conducted according to PRISMA guidelines using the PECOS framework. A comprehensive literature search was performed across PubMed, Embase, Scopus, Web of Science, Cochrane Library, CINAHL, and Google Scholar databases to identify studies evaluating the association between gut microbiota and periodontitis, including microbiome alterations, inflammatory pathways, and microbiome-modulating interventions. Results: The included studies demonstrated that patients with periodontitis frequently exhibit reduced gut microbial diversity, enrichment of pro-inflammatory taxa, impaired intestinal barrier function, and elevated inflammatory mediators including C-reactive protein, interleukin-6, and tumor necrosis factor-alpha. Several studies identified translocation of periodontal pathogens such as Porphyromonas gingivalis and Fusobacterium nucleatum to the gastrointestinal tract, supporting the existence of an oral–gut axis. Probiotics, prebiotics, synbiotics, and periodontal therapy showed potential benefits in improving periodontal parameters and restoring microbial homeostasis. Conclusions: Current evidence supports a significant relationship between gut microbiome dysbiosis and periodontitis through immune, inflammatory, and metabolic mechanisms. However, heterogeneity among studies and limited longitudinal evidence warrant further standardized clinical and mechanistic investigations to establish causality and optimize microbiome-targeted therapeutic strategies in periodontal disease.

Abstract: Sleep disorders affect a substantial proportion of hospitalized patients yet remain among the most systematically underdiagnosed conditions in acute care medicine, with up to 80% of moderate-to-severe cases carrying no formal diagnosis at the time of admission. At the same time, frailty—a state of heightened physiological vulnerability arising from cumulative multi-system biological decline—is present in 40–80% of inpatients and shares deep, bidirectional neurobiological pathways with sleep pathology through shared mechanisms of circadian dysregulation, hypothalamic-pituitary-adrenal axis activation, and chronic low-grade inflammation. Despite this convergence, no study has integrated validated, administratively computable frailty phenotyping with a machine learning framework specifically designed to predict inpatient sleep disorder diagnosis at the point of hospital admission. To address this gap, we developed and evaluated a suite of five binary classification models—XGBoost, Random Forest, LightGBM, CatBoost, and Decision Tree—using 9,682 balanced hospitalization episodes from the MIMIC-IV (version 2.2) database. The predictor set comprised 23 admission-time structured features across three domains: frailty and comorbidity burden, including the Hospital Frailty Risk Score (HFRS) derived from ICD-10 codes, the Elixhauser comorbidity index, prior admission history, and six binary disease flags (obesity, hypertension, type 2 diabetes, heart failure, COPD, and depression/anxiety); physiological and laboratory biomarkers from the first 24 hours of care, including minimum SpO₂, heart rate variability, hemoglobin, creatinine, albumin, and arterial blood gas parameters; and sociodemographic and administrative variables encompassing age, sex, ethnicity, insurance type, and admission acuity. Two binary outcomes were modeled independently: any sleep disorder diagnosis (ICD-10: G47.x) and insomnia specifically (ICD-10: G47.00). Model performance was assessed through five-fold stratified cross-validation and bootstrap confidence intervals (n = 1,000 iterations), with predictor importance quantified using SHapley Additive exPlanations (SHAP). XGBoost achieved the strongest aggregate performance across all evaluation metrics, attaining an area under the receiver operating characteristic curve (AUC) of 0.871 (95% CI: 0.856–0.887), accuracy of 79.6%, F1-score of 0.820, and sensitivity of 94.9%, correctly identifying 903 of 952 true positive cases in the held-out test set; all gradient boosting frameworks substantially outperformed the Decision Tree baseline (AUC 0.836). SHAP analysis identified the HFRS and Elixhauser index as the two dominant predictors, followed by depression/anxiety, obesity, hypertension, and minimum SpO₂—a pattern that is mechanistically consistent with established pathophysiological literature on frailty-associated sleep pathology. The well-calibrated probability outputs of the XGBoost model make it directly suitable for integration into clinical decision support systems, offering a deployable, interpretable screening tool for inpatient sleep disorder identification that requires no dedicated instrumentation beyond routine admission data.

Abstract: The paper seeks to find the direct and indirect association amongst capital structure and firm value among all the nonfinancial firms listed in PSX from (2014-2019). Secondary panel data was used to conduct analysis. Structural equation modelling technique in Stata was used to estimate the direct effects. MedSEM, a special package for Stata, was used to estimate the indirect effects. Results showed that capital structure had no direct effect on value of the firm, but financial distress mediated the association amongst capital structure and value of the firm. Substantial indirect effect clearly manifests the existence of indirect nature of association amongst capital structure and value of the firm.

Abstract: Atmospheric icing is one of the most critical meteorological hazards for unmanned aerial vehicles (UAV), whose operation under adverse conditions—high latitudes, elevated altitudes, long-endurance missions without pilot intervention—particularly exposes them to ice accumulation on aerodynamic surfaces and propellers. Unlike manned aviation, where this phenomenon has been extensively studied and regulated, a significant knowledge gap exists in the UAV domain that limits the development of effective protection systems adapted to energy constraints. This article provides an integrated review of atmospheric ice formation mechanisms, their specific effects on UAV propellers, and the two most promising mitigation approaches: electrothermal modelling for the optimisation of electric heating systems, and the development of functional surface materials, including superhydrophobic coatings (SHC), composites with conductive nanofillers (graphene, carbon nanotubes), and piezoelectric actuators. The analysis demonstrates that hybrid systems combining passive and active strategies managed by intelligent control represent the most viable solution for extending UAV operational envelopes under known icing conditions, with a potential reduction in anti-icing energy consumption exceeding 40% compared to conventional continuous heating. Key research gaps are identified, and a prioritised future research agenda is proposed to support the development of certifiable anti-icing systems for rotary-wing UAV platforms.

Abstract: Zn₂SnO₄ is a promising anode for lithium-ion batteries owing to its high theoretical capacity, yet its pratical utilization is severely limited by sluggish reaction kinetics, large volume expansion, and unstable electrode/electrolyte interfaces. Here, we intro-duce a dimensionality-reduction strategy that simultaneously boosts capacity and cy-cling stability. Through surfactant-directed crystal growth, acid-etching reconstruction, and hydrothermal carbon coating, compact Zn₂SnO₄ octahedra are controllably trans-formed into sheet-assembled structures and finally into a core–shell composite with a continuous carbon layer (C@M-Zn₂SnO₄ (H⁺)). The continuous structural evolution shortens Li⁺ diffusion paths, buffers mechanical stress, and stabilizes the sol-id-electrolyte interphase without altering the intrinisic lithium-storage mechanism of Zn₂SnO₄. As a result, the optimized C@M-Zn₂SnO₄ (H⁺) electrode delivers a reversible capacity of 650 mAh g⁻¹ after activation and retains 620 mAh g⁻¹ after 600 cycles at 200 mA g⁻¹, with Coulombic efficiency approaching 100% throughout. This work demon-strates that dimensionality-reduction-assisted structural engineering is an effective strategy for developing high-capacity, long-cycle-life anode materials.

Abstract: In the philosophy of language, Frege’s (1892) distinction between sense and reference provides a foundational framework for identity statements. Geach’s (1967) relative identity breaks out of the framework of absolute identity and opens another perspective for us. Putnam’s (1975) “Twin Earth” thought experiment, with its striking insight, pushes externalism to the extreme, successfully challenging the internalist model of meaning and setting the basic agenda for decades of subsequent debate on the problem of reference determination. However, despite the inspirational value of these groundbreaking works, a noteworthy phenomenon is that the debates they triggered—such as discussions around core cases like the Ship of Theseus and identical particles—seem to have reached a certain impasse. This paper argues that this impasse may not stem from the depth of the problems themselves, but precisely from a deep, unexamined presupposition shared by these otherwise highly persuasive theories: namely, that there exists a single, decisive category (whether microscopic physical structure or historical causality) capable of once and for all answering the question of identity. Instead of continuing to seek a better single answer under this presupposition, a more productive approach may be to reflect on the presupposition itself. To this end, we attempt to analyze the problem from a different angle. Interestingly, this angle shows that the aforementioned seemingly opposed excellent theories can actually all be understood as special cases of this theory under different categories; the difficulties they encounter become inevitable precisely when they attempt to make assertions across categories. Therefore, this paper is not intended to negate previous work, but to clarify the valid scope of its application, thereby providing a new path to resolve a series of philosophical difficulties arising from category mistakes.

Abstract: The El Duende ‘one-canvas’ model was developed as an arts-based practice for supervision in art therapy training. Responding to changes in institutional teaching structures, this case review reflects on its use in experiential training groups on one UK-based course, with the aim of developing understanding and theoretical insights that may inform future teaching practice. Eight training group facilitators retrospectively reviewed their experience of the model as applied in five experiential training groups over a three-month period. Data were analysed thematically through an iterative, collaborative, and reflexive process and four core themes were identified. Results are discussed with links made to Donald Winnicott’s ideas of creative destructiveness, use of the object, transitional space, and the holding environment. While limited in scope, results indicate that, through sustained cycles of repetition and return, the ‘one-canvas’ model served to hold intense transformational processes within a condensed timeframe, offering trainees a valuable experiential learning experience. The study builds on established research in the field, expanding previous applications of the model including theoretical understanding, and supporting innovation and reflection in art therapy education. Future research may consider further adaptations to the model, student perspectives, and its influence on personal and professional development.

Abstract: We address the paradoxical transformation of a classical-mechanical particle motion when the space and time scales of observation pass down the uncertainty principle threshold. This is analyzed in the language of classical statistical mechanics, considering specifically many-particle systems inhomogeneous along one spatial direction. We employ the density functional formalism in its square-gradient form and find: i) The macroscopic solution is analogous to the classical trajectory of a particle under a potential of force given by (minus) the free energy density. Whereas, ii) fluctuations around the solution in (i) are equal to the quantum-mechanical wave functions of a particle under a potential given by the curvature of the free energy density. We illustrate this situation with three textbook examples: A particle in a box, the harmonic oscillator, and the hydrogen atom. We show that their time-independent Schrödinger equation wave functions describe, respectively, the fluctuations of a fluid interface, of critical point fluctuations, and of a confined ideal gas. At large scales sharp probability distributions make fluctuations irrelevant, the vanishing of the first variation yields the macroscopically observable statistical-mechanical non-uniformity, equivalent to the classical particle trajectory. But at sufficiently small scales, with necessarily very few particles, distributions appear much wider, fluctuations dominate, and one obtains the Schrödinger equation (for the microscopic potential).

Abstract: Background: COVID-19 manifested with a wide range of clinical symptoms, including asymptomatic or mild illness and life-threatening respiratory failure. We hypothesized that elevated predictors during intensive care unit (ICU) stays would independently predict mortality and the subsequent development of post-COVID-19 condition (PCC). Methods: In this retrospective cohort study, we evaluated the clinical and laboratory determinants of mortality using hospital records in severe COVID-19 patients in conjunction with their PCC in survivors by self-reported survey. This research was conducted at XX University Hospital, and adult patients with laboratory-confirmed SARS-CoV-2 infection by RT-PCR assay who required ICU admission for respiratory failure or hemodynamic instability were included. Biomarkers were monitored throughout ICU stay to evaluate dynamic changes and their association with mortality. Survivors were followed from ICU discharge to assess readmissions, vaccination status, and post-COVID-19 condition, including fatigue, sleep disturbance, physical exhaustion, concentration problems, and memory impairment. Post-ICU mortality and hospitalization due to cardiovascular, respiratory, neurological, or other complications were recorded. Results: A total of 273 critically ill patients were included, of whom 112 survived and 161 died during ICU stay. Non-survivors were older and had lower mean arterial pressure. Intubation was more frequent among non-survivors, and APACHE II scores were significantly higher in this group. Hospitalizations due to cardiovascular, respiratory, and neurological complications were particularly associated with increased hazard of death (HRs ≥2, p-values < 0.05). Patients who died after ICU discharge (31.5%) had higher rates of fatigue, physical exhaustion, and memory impairment, suggesting a strong correlation between biomarker derangements during ICU stay and PCC. Conclusions: The present study was specifically designed to address this critical gap by evaluating whether biomarker trajectories during ICU follow-up not only predict in-hospital mortality but also serve as early determinants of Post-COVID status in survivors.

Abstract: The increasing accumulation of nano-/microplastics (NMPs) in agricultural soils has become an emerging environmental concern, posing risks to soil health, crop productivity, and food safety. Due to their persistence and small size, NMPs can disrupt soil structure, alter microbial communities, and facilitate the transport and uptake of contaminants by plants. In this context, biochar has attracted significant attention as a climate-smart soil amendment capable of improving soil quality while mitigating emerging pollutants. This review explores the potential role of biochar, including modified biochar, as a sustainable strategy for enhancing soil health and reducing the risks associated with NMPs contamination in agricultural systems. The unique physicochemical properties of biochar—such as its high surface area, porous structure, and abundant functional groups—enable interactions with plastic particles and associated contaminants through adsorption, aggregation, and immobilization processes. These interactions can reduce mobility, bioavailability, and plant uptake of NMPs in soil. In addition, biochar contributes to soil fertility improvement by enhancing nutrient retention, increasing water holding capacity, improving soil structure, and stimulating beneficial microbial activity. Biochar application also plays an important role in climate change mitigation by stabilizing carbon in soils and reducing greenhouse gas emissions from agricultural systems. Although biochar is considered a promising material for sustainability, some types of biochar may have adverse effects in saline–alkaline soils due to their high pH and salinity, particularly when produced at high pyrolysis temperatures. Overall, integrating biochar or modified biochar into sustainable agricultural practices offers multiple co-benefits, including soil restoration, pollutant mitigation, improved soil health, and enhanced climate resilience. This review synthesizes recent advances in understanding the mechanisms by which biochar influences NMPs behavior in soil–plant systems and highlights current knowledge gaps and future research directions needed to support its effective application in sustainable agriculture.

Abstract: Background/Objectives: The present study aimed to examine the relationship between Dark Triad personality traits (narcissism, psychopathy, and machiavellianism) and conspiratorial thinking. Additionally, it sought to investigate whether perceived social support acts as a mediator in this relationship, potentially serving as a protective factor against the adoption of conspiracy beliefs. Methods: The sample consisted of 620 participants (N = 620), including 523 women and 97 men, aged 18 to 69 (M = 35.74; SD = 11.36). Data were collected through an online survey using the Generic Conspiracist Beliefs Scale (GCBS), the Dirty Dozen Scale, and the Multidimensional Scale of Perceived Social Support (MSPSS). Results: Statistical analyses using Pearson’s correlation coefficient did not indicate a statistically significant co-occurrence between conspiratorial thinking and Dark Triad personality traits. Furthermore, the mediation models did not show significant values for mediating effects, suggesting that perceived social support—including its dimensions of support from a significant person, family, and friends—did not alter the relationship between personality traits and conspiracy thinking in this sample. Conclusions: The findings contradict several earlier reports, contributing to the ongoing debate regarding the dispositional roots of conspiracy beliefs. The results suggest that conspiratorial ideation may not be rooted in stable aversive personality traits, but instead may be driven by specific neurocognitive processes such as uncertainty processing and threat reactivity, aligning with current brain-based models of belief evaluation. Future research should integrate neuroscientific perspectives with social psychology to develop more comprehensive models of conspiratorial ideation.

Abstract: For the first time, a race survey of Puccinia graminis f. sp. tritici (Pgt) population was conducted on Triticum durum in the Altai region of Western Siberia, Russia. A total of 34 single pustule isolates with different virulence phenotypes were identified on durum wheat (Triticum durum) in 2025 and compared with Pgt from bread wheat (Triticum aestivum). The UPGMA-based clustering separated Pgt isolates into two distinct groups, suggesting the host-driven differentiation that was further proven using tools of population genetics. The pathogen isolates from durum showed a wider range of virulence complexity, higher variability, and greater average singularity. Virulence frequencies of Pgt on T. durum and T. aestivum differed markedly for Sr6, Sr7b, Sr9e, Sr17+13 and several other genes, while Sr24 and Sr31 remained effective independently of the pathogen origin. Two races, PKCSF and NFMSF, were detected on both the hosts, indicating a shared pathogen gene pool between bread and durum wheat. Even assuming host-specific divergence of Pgt in the Altai region, there is a need in deployment of the same resistance genes into both T. aestivum and T. durum cultivars to prevent an outbreak of stem rust in an event of favorable conditions for inoculum exchange between crops.

Abstract: Shannon entropy and Kolmogorov complexity describe complementary facets of information. We revisit Q2 from 27 Open Problems in Kolmogorov Complexity: whether all linear information inequalities including non‑Shannon‑type ones admit $\mathcal{O}(1)$-precision analogues for prefix‑free Kolmogorov complexity. We answer in the affirmative via two independent arguments. First, a contradiction proof leverages the uncomputability of $K$ to show that genuine algorithmic dependencies underlying non‑Shannon‑type constraints cannot incur length‑dependent overheads. Second, a coding‑theoretic construction treats the copy lemma as a bounded‑overhead coding mechanism and couples prefix‑free coding (Kraft's inequality) with typicality (Shannon-McMillan-Breiman) to establish $\mathcal{O}(1)$ precision; we illustrate the method on the Zhang-Yeung (ZY98) inequality and extend to all known non‑Shannon‑type inequalities derived through a finite number of copy operations. These results clarify the structural bridge between Shannon‑type linear inequalities and their Kolmogorov counterparts, and formalize artificial independence as the algorithmic analogue of copying in entropy proofs. Collectively, they indicate that the apparent discrepancy between statistical and algorithmic information manifests only as constant‑order effects under prefix complexity, thereby resolving a fundamental question about the relationship between statistical and algorithmic information structure.

Abstract: We give a constructive high-dimensional escape sequence for the equation (∆ − x ·∇)u = u associated with the symmetric Ornstein–Uhlenbeck operator in Gaussian space. Let (a_i)_i≥1 be a positive square summable sequence and let B_n = {x ∈ Rⁿ : ∑ⁿ_i=1 a_i² x_i² < 1}. We construct functions u_n that are continuous on Rⁿ, smooth on both sides of ∂B_n, solve the positive spectral equation away from ∂B_n, and have finite Gaussian H¹ energy. The construction uses a single real harmonic polynomial, Re(x1 +ix2)^m_n with m_n = ⌊n^1/8⌋, multiplied by the finite-energy Tricomi branch of the separated radial Ornstein–Uhlenbeck equation and then extended into B_n by the weighted Dirichlet principle. The exterior energy has a lower bound of order (2π)^n/2n^−1/2(2m_n/e)^m_n, whereas the interior minimizing energy is bounded by (2π)^n/2n^CC_a^m_n. Hence the ratio of total Gaussian H¹ energy to the energy inside B_n tends to infinity. The proof is written with all non-standard notation defined explicitly, and two examples, including an ℓ¹-small sequence with ∑_i a_i < 1, are included as checks of the hypotheses.