February 2026

Unlike geometry, spheres in topology have been seen as topological invariants, where their structures are defined as topological spaces. Forgetting the exact notion of geometry, and the impossibility of embedding one into another, homotopy theory relates how a sphere of one dimension can wrap around, or map into, a sphere of another dimension. This paper revisits the classical theory of homotopy groups of spheres, providing a detailed exploration of their computation and structure. We place special emphasis on […]

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Modern insurance organizations have adopted artificial intelligence in narrow, task-specific roles, resulting in fragmented systems that optimize isolated functions without fundamentally reshaping the underwriting and claims lifecycle. This “incrementalism” yields a human-default, sequential process plagued by structural bottlenecks, inconsistent risk evaluation, and limited transparency. This paper introduces NEXUS (Next-Generation Executive Underwriting and Settlement Intelligence), a framework to re-architect insurance as an AI-native system. NEXUS transitions AI from a peripheral tool to the primary orchestrator of end-to-end processes, conceptualizing […]

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Support matrix machine (SMM) is an emerging classification framework that directly handles matrix-structured observations, thereby avoiding the spatial correlations destroyed by vectorization. However, most existing SMM variants rely on convex or nonconvex surrogate loss functions, which may lead to high sensitivity to noise. To address this issue, we propose a novel Heaviside low-rank SMM model called HL-SMM, which leverages the Heaviside loss instead of the common hinge or ramp losses for robustness. Moreover, the low-rank constraint is adopted […]

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Developments in the machine learning voting domain have shown both promising results and risks. Trained models perform well on ballot classification tasks (> 99% accuracy) but are at risk from adversarial example attacks that cause misclassifications. In this paper, we analyze an attacker who seeks to deploy adversarial examples against machine learning ballot classifiers to compromise a U.S. election. We first derive a probabilistic framework for determining the number of adversarial example ballots that must be printed to […]

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This paper presents, in a unified form and with explicit logical justification, a chain of original results on the internal structure of perfect powers and their connection with Fermat’s Last Theorem (FLT). Starting from the historical formula of Nicomachus of Gerasa (c. 100 AD) for the cumulative sum of cubes, S_3 (n)=T_n^2, and applying the backward finite-difference operator ∇ —formalised by Taylor (1715) and systematised by Boole (1860)— the Anderson Identity (2026) is derived: n^3=n^2/4 [(n+1)^2-(n-1)^2 ]=T_n^2-T_(n-1)^2. This […]

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This paper introduces a Morse code transmission system utilizing an ESP32 microcontroller and displaying the decoded message via a Telegram bot in real-time. In contrast to the traditional Morse code inputting methods, which are normally based on a single button with timing distinction between dot and dash, the suggested design utilizes two special buttons for dot and dash, respectively, and another button for sending the entire message. This method simplifies the input of users, minimizes timing errors, and […]

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Hi everyone, I’m a research student working independently on a project, and I recently finished a paper with results that I believe are solid and meaningful. I’m still new to the academic publishing process, though, and I’d really appreciate some guidance. I learned that for posting on arXiv you sometimes need an endorsement, but since I did this work solo, I’m not sure how to move forward or who to approach. What are the usual steps for someone […]

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This paper presents the application of a micro unmanned aerial vehicle (UAV) that acts as a pollination agent in a controlled environment simulating greenhouse conditions. The micro-UAV system was integrated with a convolutional neural network (CNN) for autonomous flower detection and navigation. The ResNet-18 CNN architecture is was utilized onboard to perform real-time binary classification to accurately distinguish flowers from non-flower objects. The fusion of this deep-learning-based detection with precise micro-UAV navigation enables efficient identification and approaches to […]

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In the U.S. digital economy, small and medium-sized businesses (SMBs) and creators in remote regions face structural disadvantages in access to integrated advertising and incentive platforms, largely due to accelerating privacy regulations and the fragmentation of cross channel datasets. This paper proposes a unified federated and differentially private measurement framework that integrates Topics/Protected Audience, Attribution Reporting, and SKAdNetwork, aiming to achieve privacy-preserving incentive optimization and cross-channel effectiveness measurement for web and mobile environments. The framework prioritizes compliant data […]

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