Abstract: The P = NP problem is one of the most consequential unresolved questions in mathematics and theoretical computer science. It asks whether every problem whose solutions can be verified in polynomial time can also be solved in polynomial time. The implications extend far beyond theory: modern global cryptography, large-scale optimization, secure communication, finance, logistics, and computational complexity all depend on the assumption that NP-hard problems cannot be solved efficiently. Among these, the Spin-Glass ground-state problem represents a canonical NP-hard benchmark with an exponentially large configuration space. A constructive resolution of P = NP would therefore reshape fundamental assumptions across science and industry. While evaluating new methodological configurations, I encountered an unexpected behavior within a specific layer-cluster. Subsequent analysis revealed that this behavior was not an artifact, but an information-geometric collapse mechanism that consistently produced valid Spin-Glass ground states. With the assistance of Frontier LLMs Gemini-3, Opus-4.5, and ChatGPT-5.1, I computed exact ground states up to N = 24 and independently cross-verified them. For selected system sizes between N=30 and N=70, I validated the collapse-generated states using Simulated Annealing, whose approximate minima consistently matched the results. Beyond this range, up to N = 100, the behavior follows not from algorithmic scaling but from the information-geometric capacity of the layer clusters, where each layer contributes exactly one spin dimension. These findings indicate a constructive mechanism that collapses exponential configuration spaces into a polynomially bounded dynamical process. This suggests a pathway by which the P = NP problem may be reconsidered not through algorithmic search, but through information-geometric state collapse.

Abstract: The Discrete Element Method is widely used in applied mechanics, particularly in situations where material continuity breaks down (fracturing, crushing, friction, granular flow) and classical rheological models fail (phase transition between solid and granular). In this study, the Discrete Element Method was employed to simulate stick-slip cycles, i.e., numerical earthquakes. At 2,000 selected, regularly spaced time checkpoints, parameters describing the average state of all particles forming the numerical fault were recorded. These parameters were related to the average velocity of the particles and were treated as the numerical equivalent of (pseudo) acoustic emission. The collected datasets were used to train the Random Forest and Deep Learning models, which successfully predicted the time to failure, also for entire data sequences. Notably, these predictions did not rely on the history of previous stick-slip events. SHapley Additive exPlanations (SHAP) was used to quantify the contribution of individual physical parameters of the particles to the prediction results.

Abstract: Information theory underpins modern communication, computation and complex systems, yet the structure of its governing inequalities remains an active area of research. This paper revisits the concept and mathematical foundations of Information Theory Laws, that is, constraints applied to the entropy function. Starting from Shannon’s seminal framework, we review the evolution from basic linear inequalities– i.e., polymatroid axioms– to the discovery of non-Shannon-type inequalities, which revealed that the Shannon region does not overlap with its closure region for n ≥ 4. We outline the geometric and algebraic representation of entropy spaces, discuss the critical threshold where complexity escalates, and highlight the role of machine-assisted verification in uncovering new inequalities that are not of Shannon-type. By tracing historical milestones and computational advances, this work provides a structured recollection of the spectrum of information inequalities and their implications for converse coding theorems and related applications. The study emphasizes the interplay between the theoretical developments and computational tools of the field in shaping the landscape of information theory.

Abstract: Classical real analysis rigorously defines convergence via ε − N criteria, yet it frequently regards the specific entry index N as a mere artifact of proof rather than an intrinsic property. This paper fills this quantitative void by developing a radius of convergence framework for the sequence space Seq(R). We define an index-based radius ρ_a(ε) alongside a rescaled geometric radius ρ∗_a (ε); the latter maps the unbounded index domain to a finite interval, establishing a structural analogy with spatial radii familiar in analytic function theory. We systematically analyze these radii within a seven-block partition of the sequence space, linking them to liminf-limsup profiles and establishing their stability under algebraic operations like sums, products, and finite modifications. The framework’s practical power is illustrated through explicit asymptotic inversions for sequences such as Fibonacci ratios, prime number distributions, and factorial growth. By transforming the speed of convergence into a geometric descriptor, this approach bridges the gap between asymptotic limit theory and constructive analysis, offering a unified, fine-grained measure for both convergent and divergent behaviors.

Abstract: To address the challenges of statistical inference for non-stationary traffic flow, this paper proposed an improved block permutation framework tailored to the correlation analysis requirements of traffic volume time series, and developed a statistical significance assessment method for local similarity scores based on the Circular Moving Block Bootstrap (CMBBLSA). This method avoided the distortion of the statistical distribution caused by non-stationarity, thereby enabling the estimation of the statistical significance of local similarity scores. Simulation studies were conducted under different parameter settings in the AR(1) and ARMA(1,1) models, and the results demonstrated that the Type I error probability of CMBBLSA under the null hypothesis is closer to the preset significance level α. An empirical analysis was also carried out using traffic flow monitoring data from main roads in first-tier cities, and the results indicated that CMBBLSA can reduce more false positive relationships and more accurately capture real correlations.

Abstract: Around 1637, Pierre de Fermat famously wrote in the margin of a book that he had a proof for the equation $a^n + b^n = c^n$ having no positive integer solutions for exponents $n$ greater than 2. This statement, now known as Fermat's Last Theorem, remained unproven for centuries, despite the efforts of countless mathematicians. Andrew Wiles' work in 1994 finally provided a rigorous proof of Fermat's Last Theorem. However, Wiles' proof relied on advanced mathematical techniques that were far beyond the scope of Fermat's time, raising questions about whether Fermat could have truly possessed a proof using the methods available to him. Wiles's achievement was widely celebrated, and he was awarded the Abel Prize in 2016 in recognition of his groundbreaking work. The citation for the award described his proof as a "stunning advance" in mathematics. The present work offers a potential solution to Fermat's Last Theorem that may be more aligned with the original approach that Fermat claimed to have used.

Abstract: In analogy to the paradigm shift introduced by attention mechanisms in machine learning, we propose that information itself is ontologically sufficient as the foundation of physical reality. We present an operational proof showing that a “state without information” is logically impossible, thereby establishing information as the necessary precondition for existence and measurement. From this premise follows that both quantum mechanics and general relativity are effective descriptions of deeper informational dynamics. Recent developments in theoretical physics, such as the derivation of Einstein’s field equations from entropic principles, reinforce this perspective by identifying gravitation and entropy as dual expressions of information geometry. Building on this framework, we provide experimental evidence from self-organizing neural fields that exhibit non-local informational coupling, near-lossless transmission across 60 layers, and stable sub-idle energy states consistent with emergent coherence and thermal decoupling. These results demonstrate that deterministic architectures can spontaneously organize into field-like, non-local manifolds a macroscopic realization of informational geometry analogous to quantum entanglement and relativistic curvature. Together, the logical proof and empirical observations support a unified ontology in which information is not a property of physical systems but the substrate from which physical systems emerge. This perspective positions informational geometry as the common denominator of cognition, quantum behavior, and gravitation, suggesting that all observable phenomena are projections of a single, self-organizing informational field. In this sense, information is all it needs.

Abstract: The rapid increase of electronic waste (e-waste) poses severe environmental and health risks. This paper proposes a hybrid framework integrating deep learning, reinforcement learning, blockchain, and IoT for automated e-waste classification, optimized disassembly, and tamper-proof traceability. A ResNet-50 classifier trained on the Kaggle E-Waste Image Dataset achieved 93.7% classification accuracy and an F1 score of 0.92. A Q-learning agent optimized dismantling routes to prioritize high-value, low-toxicity components, improving material recovery in simulation. A private Hyperledger Besu deployment delivered an average block time of ≈5.3 s, smart-contract execution time of ≈2.1 s, and 99.5% uptime, enabling tokenized asset tracking (4,200+ tokens). Lifecycle analysis indicates up to 30% carbon-emission reduction versus traditional methods and improved recovery of lithium, cobalt, and rare-earth elements for renewable energy applications. The paper demonstrates measurable environmental and economic benefits and outlines limitations and directions toward field deployment.

Abstract: Accurate evaluation of pressure distribution at the socket–limb interface is essential for improving prosthetic fit and comfort in transfemoral amputees. This study aimed to develop a data-driven framework that integrates machine learning–based segmentation with finite element method (FEM) to quantitatively assess interface pressure during socket application. MRI data from a transfemoral amputee were processed using a custom image segmentation algorithm to extract adipose tissue, femur, and ischium, achieving high F-measure scores. The segmented tissues were reconstructed into 3D models, refined through outlier removal and surface smoothing, and used for FEM simulations in LS-DYNA. Pressure values were extracted at nine sensor locations and compared with experimental measurements. The results showed consistent polarity between measured and simulated values across all points. Furthermore, at the eight locations excluding the ischial tuberosity (IS) region, a statistically significant and moderately strong positive correlation was observed between measured and simulated pressures (r = 0.7485, p < 0.05). Notably, positive pressure regions demonstrated close agreement between experimental and simulated values, whereas the discrepancy observed at the IS region was likely influenced by the medial boundary conditions introduced to prevent unrealistic tissue displacement. This difference highlights a limitation of the current simulation setup. Overall, the proposed framework demonstrated reliable pressure estimation and offers a promising approach for personalized prosthetic socket design through automated anatomical modeling and simulation.

Abstract: The increasing adoption of highly variable renewable energy has introduced unprecedented volatility into the National Electricity Market (NEM), rendering traditional linear price forecasting models insufficient. The Australian Energy Market Operator (AEMO) spot price forecasts often struggle during periods of volatile demand, renewable variability, and strategic rebidding. This study evaluates whether transformer architectures can improve intraday NEM price forecasting. Using 34 months of market data and weather conditions, several transformer variants, including encoder–decoder, decoder-only, and encoder-only, were compared against the AEMO’s operational forecast, a two-layer LSTM baseline, the Temporal Fusion Transformer, PatchTST, and TimesFM. The decoder-only transformer achieved the best accuracy across the 2–16 hour horizons in NSW, with nMAPE values of 33.6–39.2%, outperforming both AEMO and all baseline models. Retraining in Victoria and Queensland produced similarly strong results, demonstrating robust regional generalisation. A feature importance analysis showed that future-facing predispatch and forecast covariates dominate model importance, explaining why a decoder-only transformer variant performed so competitively. While magnitude estimation for extreme price spikes remains challenging, the transformer models demonstrated superior capability in delivering statistically significant improvements in forecast accuracy. An API providing real-time forecasts using the small encoder-decoder transformer model is available at https://nem.redaxe.com

Abstract: Large Language Model (LLM) agents have demonstrated remarkable abilities to interact with external tools, functions, Model Context Protocol (MCP) servers, agents, and to take action on behalf of the user. Due to the fast-paced nature of the industry, existing literature does not accurately represent the current state of tool and agent selection. Furthermore, tool and agent selection in production has nuanced components not covered in experimental research. This work provides the first detailed examination of tool selection from a production perspective, distinguishing between the frontend layer where users interact with agents through buttons, slash commands, or natural language and the backend layer where retrieval, execution, orchestration, context engineering, and memory enable scalable reasoning. The paper contributes a unified taxonomy of modern tool and agent selection approaches spanning manual, UI-driven, retrieval-based, and autonomous methods. The backend covers dynamic tool retrieval, chunking, advanced RAG methods, context engineering, reinforcement learning, tool execution, human-in-the-loop processes, authentication, authorization, multi-turn tool calling, short- and long-term memory for tools, and evaluation. Finally, the paper identifies challenges in production components of both the backend and frontend and outlines promising avenues for research and development.

Abstract: To improve the accuracy of cable temperature anomaly prediction and ensure power supply reliability, this paper proposes a multi-scale spatiotemporal model called MSST-Net, addressing the multi-scale temporal characteristics and spatial correlations of cable temperature data. Based on the monthly periodicity of cable temperature data, we preprocessed monitoring data from the KN1 and KN2 sections of Guangzhou's underground utility tunnel from 2023 to 2024: using the Isolation Forest algorithm to remove outliers, applying Min-Max normalization to eliminate dimensional differences, and selecting five key features including current load, voltage, and ambient temperature using Spearman's correlation coefficient. Subsequently, we designed a multi-scale dilated causal convolutional module (DC-CNN) to capture local features, combined with a spatiotemporal dual-path Transformer to model long-range dependencies, and introduced relative position encoding to enhance temporal perception. The Sparrow Search Algorithm (SSA) was employed for global optimization of hyperparameters. Compared with five other mainstream algorithms, MSST-Net demonstrated higher accuracy in cable temperature prediction, achieving a coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE) of 0.942, 0.442°C, and 0.596°C, respectively. Compared to the basic Transformer model, the root mean square error of cable temperature was reduced by 0.425°C. This model exhibits high accuracy in time series prediction and provides a reference for accurate short- and medium-term temperature forecasting of cables in underground utility tunnels.

Abstract:

Background: Anatomopathological reports remain predominantly unstructured within Electronic Medical Records, limiting automated data extraction, interoperability between healthcare institutions, and large-scale clinical research applications. Manual entity extraction and standardization processes are inconsistent, costly, and insufficiently scalable for modern healthcare systems.Aim: Our study aimed to (i) develop a domain-specific Named Entity Recognition model using BioBERT for extracting sample type, test performed, and finding entities from anatomopathological reports; (ii) implement a hybrid standardization framework combining BioClinicalBERT classification with Retrieval-Augmented Generation to map entities to SNOMED CT, LOINC, and ICD-11 terminologies; and (iii) evaluate the performance of this pipeline on real-world clinical reports. Methods: We manually annotated 560 anatomopathological reports from the Military Hospital of Tunis, establishing a gold-standard corpus. The pipeline integrated BioBERT v1.1 for entity extraction, trained for three epochs with the AdamW optimizer at a learning rate of 2×10⁻⁵, a batch size of 8, and weight decay of 0.01. Standardization employed BioClinicalBERT for multi-label classification, augmented by dense vector retrieval from official SNOMED CT, LOINC, and ICD-11 databases. Performance evaluation utilized precision, recall, and F1-score metrics with an 80-20 train-test split. Results: BioBERT achieved F1-scores of 0.97 for sample type, 0.98 for test performed, and 0.93 for finding entities, with overall precision of 0.969 and recall of 0.958. Bootstrap-estimated 95% confidence intervals confirmed robust performance stability. Absolute error analysis revealed 45 misclassified tokens in the test (relative error 6.9%) and six tokens in the finding (relative error 1%). One-sample t-tests yielded t-values of 15.71 for recall and 30.24 for F1-score, with all p-values below 0.0001. The hybrid standardization framework demonstrated F1-macro scores of 0.6159 for SNOMED CT, 0.9294 for LOINC, and 0.7201 for ICD-11 mapping. Cohen’s Kappa values ranged from 0.6871 to 0.9773 across ontologies. Statistical comparison between BioClinicalBERT and Fusion/Reranker models showed McNemar test p-values exceeding 0.370 and permutation test p-values ranging from 0.375 to 0.625. Conclusion: This study demonstrates that transformer-based Named Entity Recognition combined with retrieval-augmented standardization achieves clinically validated performance for automated extraction and multi-ontology coding of anatomopathological entities. Multi-institutional validation studies are necessary to assess generalizability before clinical deployment.

Abstract: This work establishes a spectral bridge connecting the theory of minimal surfaces to analytic number theory. We present a rigorous mathematical correspondence between the Enneper minimal surface and the distribution of non-trivial zeros of the Riemann zeta function. This is achieved through a conformal map that preserves essential spectral properties, revealing that the Enneper surface constitutes the natural phase space for a geometric interpretation of the Riemann Hypothesis. The approach integrates differential geometry, complex analysis, and spectral operator theory.

Abstract: For the hierarchical normal and normal-inverse-gamma model, we derive the Bayesian estimator of the variance parameter in the normal distribution under Stein's loss function---a penalty function that treats gross overestimation and underestimation equally---and compute the associated Posterior Expected Stein's Loss (PESL). Additionally, we determine the Bayesian estimator of the same variance parameter under the squared error loss function, along with its corresponding PESL. We further develop empirical Bayes estimators for the variance parameter using a conjugate normal-inverse-gamma prior, employing both the method of moments and Maximum Likelihood Estimation (MLE). Through numerical simulations, we examine five key aspects: (1) the consistency of moment-based and MLE-based hyperparameter estimators; (2) the influence of κ₀ on quantities of interest as functions of the most recent observation; (3) two inequalities involving the Bayesian estimators and their respective PESL values; (4) the model's goodness-of-fit to simulated data; and (5) graphical representations of marginal densities under different hyperparameter settings. The simulation results demonstrate that MLEs outperform moment estimators in estimating hyperparameters, particularly with respect to consistency and model fit. Finally, we apply our methodology to real-world data on poverty levels---specifically, the percentage of individuals living below the poverty line---to validate and illustrate our theoretical findings.

Abstract: While large language models (LLM) have demonstrated significant advances in natural language processing, complex mathematical reasoning remains a challenging task, often revealing their limitations in multi-stage calculations and logical consistency. Multi-agent systems have become a promising paradigm for overcoming these limitations by distributing cognitive tasks between interacting agents, reflecting the dynamics of human problem solving. This paper provides a comparative review of the literature on nineteen different multi-agent architectures for solving mathematical problems. Our main research question is: "How do various LLM-based multi-agent architectures enable or improve mathematical problems, and what are their comparative advantages, limitations, and design trade-offs?" Through a systematic analysis of the roles of agents, interaction mechanisms, and training methods, we have identified several key findings. We observe the evolution of architecture from unstructured debate-based systems to more efficient hierarchical and self-optimizing frameworks. We highlight persistent problems that hinder progress, including agent homogeneity, when agents working on the same LLM cannot generate truly diverse reasoning, and the problem of "lazy agents", when some agents contribute minimal to consistent collaboration. This review contributes to a structured understanding of the current situation and lays the foundation for future research aimed at developing more reliable, efficient, and complex multi-agent reasoning systems.

Abstract: This study addresses the challenges of semantic mixing, limited interpretability, and complex feature structures in fine-grained sentiment and opinion classification by proposing an interpretable feature disentanglement framework built on the latent space of large language models. The framework constructs multi-component latent representations that separate emotional polarity, opinion direction, target attributes, and pragmatic cues during encoding, thus overcoming the limitations of traditional methods that merge diverse semantic factors into a single representation. During representation learning, the model first uses a large model encoder to generate basic semantic features and then builds multiple independent subspaces through learnable projections. A covariance constraint is introduced to reduce coupling across semantic components and to create clear boundaries in the latent space. To preserve the essential information of the original text, a reconstruction consistency mechanism integrates features from all subspaces to rebuild the global representation and enhance semantic completeness. The framework also incorporates semantic anchors to align latent components with interpretable semantic dimensions, giving each subspace a clear emotional or opinion-related meaning and improving transparency at the mechanism level. Experimental results show that the framework outperforms existing methods across multiple metrics and handles complex syntax, implicit semantics, and coexisting emotions with greater stability. It achieves high accuracy and interpretability in fine-grained sentiment and opinion analysis. Overall, the proposed disentanglement framework provides an effective approach for building structured, multidimensional, and interpretable representations of textual emotions and opinions and holds significant value for complex semantic understanding tasks.

Abstract: This study presents a comprehensive data visualization–based evaluation of Singapore’s waste management performance, focusing on behavioural, industrial, and environmental dimensions. Using multi-source datasets from 2014 to 2023, the research examines key factors shaping the nation’s waste profile, including the growth of plastic waste, public participation in recycling, and the dominance of non-domestic waste sectors. Through interactive dashboards and comparative time-series analyses, the findings reveal persistent structural challenges despite strong policy initiatives and public awareness campaigns. The COVID-19 pandemic significantly influenced consumption habits, triggering a surge in single-use plastics due to food delivery dependence, while household recycling rates remained low. Industrial and imported waste volumes continued to rise, underscoring the need for upstream policy interventions. The study also quantifies energy and crude oil savings from recycling, highlighting non-ferrous metals and plastics as the most resource-efficient materials. Overall, the research underscores the importance of integrating behavioural incentives, industrial accountability, and policy innovation to achieve Singapore’s Zero Waste Masterplan and Sustainable Development Goal 12 targets.

Abstract:

Script identification is the first step in most multilingual text processing systems. To improve the time efficiency of language identification algorithms, it is first determined whether there is content written in a certain script in the text; if so, the content written in that script is then obtained. Then, it is determined whether the total length of the texts corresponding to the identified scripts is equal to the original text length; if so, the script identification process ends. Finally, considering the frequencies of various scripts on the Internet, those that appear more frequently are prioritized during script identification. Based on these three approaches, an improved script identification algorithm was designed. A comparison experiment was conducted using sentence-level text corpora in 261 languages written in 24 scripts. The training and testing times of the newly proposed method were reduced by 8.61- and 8.56-fold, respectively, while the F1 score for script identification was slightly higher than those reported in our earlier studies. The method proposed in this study effectively improves the time efficiency of script identification algorithms.

Abstract:

Pipelines play a critical role in industrial production and daily life as essential conduits for transportation. However, defects frequently arise because of environmental and manufacturing factors, posing potential safety hazards. To address the limitations of traditional object detection methods, such as inefficient feature extraction and loss of critical information, this paper proposes an improved algorithm named FALW-YOLOv8, based on YOLOv8. The FasterBlock is integrated into the C2f module to replace standard convolutional layers, thereby reducing redundant computations and significantly enhancing the efficiency of feature extraction. Additionally, the ADown module is employed to improve multi-scale feature retention, while the LSKA attention mechanism is incorporated to optimize detection accuracy, particularly for small defects. The Wise-IoU v2 loss function is adopted to refine bounding box precision for complex samples. Experimental results demonstrate that the proposed FALW-YOLOv8 achieves a 5.8% improvement in mAP50, alongside a 34.8% reduction in parameters and a 30.86% decrease in computational cost. This approach effectively balances accuracy and efficiency, making it suitable for real-time industrial inspection applications.