Abstract: We present a classical theoretical framework in which combinatorial optimization emerges from nonlinear relaxation of coupled real-valued phase fields governed by a global Lyapunov energy functional. Each computational element (CF-bit) evolves in a bistable periodic potential while pairwise interactions encode problem-specific couplings, enabling gradient-descent minimization of QUBO and Ising objective functions. The key contribution is an explicit global energy functional from which all dynamics are derived, guaranteeing monotonic energy descent under damping. This distinguishes the approach from existing oscillator-based Ising machines where no closed-form Lyapunov functional exists. Numerical simulations on instances up to 20 bits demonstrate deterministic phase-locking convergence, with optional transient noise improving exploration of rugged landscapes. While limited in scale and not overcoming NP-hardness, this work provides a conceptual framework showing how discrete optimization can emerge from continuous classical dynamics with mathematically transparent energy structure.

Abstract: The structure of the direct electrical current in a conductor is discussed neither in the educa-tional nor scientific literature. This problem is directly related to the boundary condition for thenormal component of current density. The generally accepted approach to this problem requiresmore careful consideration. The following article is devoted to the analysis of the direct current dis-tribution in a conductor. In this paper, we consider two mutually exclusive approaches to explainthe structure of direct current in a conductor.

Abstract: This article presents the systematization of results from the project "Communicative Interdisciplinarity" through the introduction of a system of 14 elective courses on the interdisciplinary class in Mathematics-Physics teacher training. It is demonstrated that the essential transformation of professional performance requires reconceptualizing the class not as an isolated outcome, but as an integrated organic totality. The experience, analyzed through a "complex model of systematization," revealed patterns of self-similarity and recursivity in the instructional design, foreshadowing its subsequent theoretical formalization as a fractal and neuronal system. This systematization constitutes the indispensable empirical and methodological basis that underpins the development of integrated theoretical frameworks for education.

Abstract: Does structure and parameter determine function in complex coupled oscillator systems? Conventional theory of synchronization stability is built upon this premise, relying crucially on knowledge of network topology and system parameters. We challenge this view by discovering a universal synchronization stability boundary defined solely by the states of oscillators, which is independent of configuration (encompasses both the interaction topology and oscillator parameters). Through exhaustive validation in two disparate test systems and rigorous mathematical proof, we demonstrate that this boundary is rooted in physical reality, not in any specific model. Furthermore, a novel type of spontaneous synchronization, a non-equilibrium critical phenomenon, has also been discovered near this boundary and likewise exhibits configuration-independence. These findings challenge the structural basis of the synchronization stability boundary (a key function) on complex networks. They demonstrate that the loss of synchronization stability is governed by an intrinsic, configuration-independent critical condition. Consequently, our work challenges the theoretical foundation of the “from configuration to function” principle for predicting collective behaviors in complex systems.

Abstract: We study a variety of stochastic contact processes --directly related to models of rumor and disease spreading-- from the viewpoint of their constants of motion, either exact or approximated. Much as in deterministic systems, constants of motion in stochastic dynamics make it possible to reduce the number of relevant variables, confining the set of accessible states, and thus facilitating their analytical treatment. For processes of rumor propagation based on the Maki-Thompson model, we show how to construct exact constants of motion as linear combinations of conserved quantities in each elementary contact event, and how they relate to the constants of motion of the corresponding mean-field equations, which are obtained as the continuous-time, large-size limit of the stochastic process. For SIR epidemic models, both in homogeneous systems and on heterogeneous networks, we find that a similar procedure produces approximate constants of motion, whose average value is preserved along the evolution. We also give examples of exact and approximate constants of motion built as nonlinear combinations of the relevant variables, whose expressions are suggested by their mean-field counterparts.

Abstract: The challenging goal of equipping HF radars with a target classification ability has been pursued for many years, yet no satisfactory system-level methodology has been reported. This shortcoming severely limits the utility of radar information as, without knowing the nature of detected objects, there is little prospect of understanding the situation and tailoring a suitable response. In this paper, we present a framework within which a comprehensive approach to target characterization can be formulated. We proceed to explore a wide range of physical mechanisms whereby target information is impressed on HF radar echoes, illustrated with real data. The paper concludes with a commentary on the difficulty of integrating target classification, recognition and identification procedures with other radar tasks and resource management.

Abstract: Newton published his mechanics in the form of an axiomatic system just as the Euclidean geometry. The Newton’s three laws are three axioms, from which, together with the necessary definitions of physical concepts and propositions, all contents of classical mechanics can be derived. Non-Euclidean geometries tell us that one of the axioms in an axiomatic system may take different forms. Modified axioms can lead to new axiomatic systems that are logically rigorous and self-consistent. The fifth axiom in the Euclidian geometry was modified to be two other different form, and consequently, two non-Euclidean geometries were developed. We think that Newton’s second law can be modified. The second law can be simply stated as: force is the cause of acceleration. It can be modified as: force is the cause of deceleration. This results in a new axiomatic system called new classical mechanics. This paper presents the fundamental formulas of the new classical mechanics. The most distinctive feature of the new mechanics is that the direction of momentum is opposite to that of velocity, and the kinetic energy is negative, i.e., a negative sign is attached to usual positive kinetic energy (PKE). Therefore, the new classical mechanics can be called negative kinetic energy (NKE) one, while the existing classical mechanics can be called PKE one. These two parts can be collectively referred to as a whole classical mechanics, which includes both PKE and NKE parts. The formulas of these two parts have symmetry with respect to positive and negative kinetic energy. The PKE classical mechanics describes the motion of macroscopic matter that we can observe, while the NKE classical mechanics describes the motion of macroscopic matter that we cannot observe, i.e., the motion of dark matter. Our universe has symmetry with respect to PKE and NKE, which is also the symmetry with respect to matter and dark matter. The basic equations of quantum mechanics describing the motion of micro-particles also have symmetry with respect to PKW and NKE, which has been elaborated in the author’s previous work. The theory presented in this paper describe the motion of macroscopic NKE matter.

Abstract: The Discrete Extramental Clock Law proposes that objective time in chaotic systems emerges discretely from statistically significant ordinal conjunctions across multiple trajectories, modulated by a universal gating function g(τs)g(τs​) rooted in Kendall's rank correlation and Feigenbaum universality. This study provides numerical evidence for the ontological hierarchy: high local chaotic activity (e.g., positive Lyapunov exponents) does not advance objective time; only global ordinal coherence (high ∣τs∣∣τs​∣) generates effective temporal ticks. Using coupled logistic maps, the Lorenz attractor, fractional-order extensions, and empirical \textit{Aedes aegypti} population data, we demonstrate negative correlation between local variance/Lyapunov activity and the rate of emergent time advance, fractal inheritance in tntn​ (Dtn≈1.98Dtn​​≈1.98), and robust noise tolerance. These results challenge the universality of Newtonian time in chaotic regimes, supporting emergent discreteness even in classical chaos.

Abstract: Absolute Newtonian time—as a continuous, universal parameter external to physical reality—contradicts the emergent, discrete temporal structure observed in chaotic systems. This paper provides numerical validation for the hypothesis that objective time emerges discretely from ordinal patterns rather than being imposed a priori. The Discrete Extramental Clock Law, defined by tn+1 = tn +∆t·g(τs) with universal gating g(τs) rooted in Kendall’s τ variance thresholds and Feigenbaum scaling, is tested across classical and non-classical chaotic attractors. Extensive simulations reveal empirical support for three core predictions: fractal inheritance in emergent time tn (Dtn ≈ 1.98 from D ≈ 2.06), trimodal stochastic dynamics in g(τs) with high variance (σ2 ≈ 0.85) and autocorrelation (ρ1 ≈ 0.85), and ∼ 50% variance reduction in weakly coupled networks, yielding smoother collective temporality. These results demonstrate time as a fractal-stochastic emergent phenomenon, providing quantitative evidence against Newtonian absolutism and supporting Polo’s transcendental view of extramental persistence. The findings bridge physics and metaphysics, offering empirical tools for modeling synchronization in biological collectives and human agency in critical regimes, where local retrocausality enables kairos—opportune moments—from chaotic physis.

Abstract: Gait and postural symmetry are essential indicators of neuromotor development and rehabilitation. This brief report presents a single-case pilot study evaluating the feasibility of combined baropodometric and stabilometric analyses in healthy pediatric subjects. A male child (8 years old) underwent static and dynamic plantar pressure tests and stabilometric assessments under eyes-open and eyes-closed conditions using a FreeMed® system. The results revealed mild asymmetry in plantar load (51% left vs. 49% right) and posterior loading tendency (62% rearfoot). Dynamic assessment indicated a longer stance duration on the left and higher propulsion forces on the right. Stabilometric analysis showed increased sway and a Romberg index >2.0 under visual deprivation, suggesting strong visual dependence for balance control. These findings demonstrate the sensitivity and feasibility of integrating baropodometric and stabilometric tools for detecting functional asymmetries, even in healthy children. This preliminary evidence supports their potential use in early screening, rehabilitation monitoring, and preventive assessment. Furthermore, the integrated approach contributes to advances in understanding gait symmetry and knee-related kinematic balance strategies during pediatric development.

Abstract: Laboratory experiments and observations of natural phenomena conducted in this research series indicates the presence of a thermally dependent component of gravitational interaction, influencing matter at both microscopic and macroscopic scales. Presented herein are investigations of properties of gravitational interactions among gas molecules through a thermodynamic approach applying a two-molecule force model. Unlike conventional treatments that consider gravity as a single attractive force, the experimental interpretation in this work proposes that the net gravitational effect may arise from two components: a attractive force and a temperature-dependent repulsive force.By applying established thermodynamic data for gases, the model yielded results that: (1) support the existence of both attractive and repulsive gravitational components among gas molecules,(2) indicate both forces follow an inverse-cube dependence on the intermolecular distance, and(3) show the repulsive component varies linearly with absolute temperature, indicating a connection between thermal energy and fundamental force behavior. The magnitudes of the proposed gravitational repulsion and attraction components are calculated to be significantly larger than the classical gravitational force between molecules, suggesting that the observed weak gravitational interaction may be the small resultant of two much stronger opposing forces. This introduces the possibility that controlled manipulation of these force components could lead to new physical insights and technological applications.

Abstract: Emergent properties are properties of a whole that cannot be reduced to the properties of its parts. Properties of a system can be defined as relations between a particular input given to a system and its corresponding output. From this perspective, whole systems formed by coupling component systems have properties different from the properties of their components. Wholes tend to arise spontaneously through a process of self-organization, in which components randomly interact until they settle in a stable configuration that in general cannot be predicted from the properties of the components. That configuration constrains the relations between the components, thus defining emergent “laws” that downwardly cause the further behavior of the components. Thus, emergent wholes and their properties arise in a simple and natural manner.

Abstract: Financial time series often show periods where market index values or asset prices increase or decrease monotonically.These events are known as price runs, uninterrupted trends, or simply runs. By identifying such runs in the daily DJIA and IPC indices from 01/02/1990 to 10/17/2025, we construct their associated returns, to obtain a non-arbitrary sample of multi-scale returns, we named trend returns (TReturns). The time scale for each multi-scale return is determined by the exponentially distributed duration of its respective run. We empirically reveal that the distribution of these coarse-grained returns show interesting statistical properties: the central region displays an exponential decay, likely resulting from the exponential trend duration, while the tails follow a power-law decay. This combination of exponential central behavior and asymptotic power-law decay has also been observed in other complex systems; and our findings provide an additional evidence of its natural emergence. We also explore the informational aspects of multi-scale returns using three measures: Shannon entropy, permutation entropy and compression-based complexity. We find that Shannon entropy increases with coarse-graining, indicating a wider range of values; permutation entropy drops sharply, revealing underlying temporal patterns and compression ratios improve, reflecting suppresed randomness. Overall, these findings suggest that constructing TReturns filters out microscopic noise, reveals structureded temporal patterns, and provides a complementary and clear view of market behavior.

Abstract: This technical note presents the complete mathematical derivation of the discrete extramental clock law introduced across Padilla-Villanueva’s 2025 preprints. The evolution rule \( t_{n+1} = t_n + Δt · g(τ_s) \) and its universal gating function \( g(τ_s) \) are derived step-by-step from Kendall’s rank correlation theory, empirical bifurcation thresholds, and Feigenbaum universality — without free parameters.

Abstract: This technical note isolates and formally presents the discrete-time model first introduced across Padilla-Villanueva’s 2025 preprints. Real (extramental) time in complex chaotic systems is shown to be an emergent succession of statistically significant ordinal conjunctions of trajectories, governed by a universal gating function of systemic tau ($\tau_s$). The model yields three qualitatively distinct temporal regimes — monotonic forward, fractional/critical, and locally retrograde — without violating global causality or the fractal dimension of the underlying attractor. All foundational definitions and empirical validations of $\tau_s$ are available in prior works [1–3].

Abstract: This technical note formally defines and characterizes the chaotic range in Systemic Tau (τₛ), corresponding to the intermediate volatility zone where |τₛ| < 0.41. Previously implicit in validations across ecological, physical, and fractional-order chaotic systems, this regime represents the region of maximal dynamical volatility during active bifurcations. Grounded in Kendall’s tau ordinal correlations and Feigenbaum universality (δ ≈ 4.669, α ≈ 2.502), the chaotic range exhibits weakened ordinal agreement, extreme sensitivity to initial conditions, and robust noise tolerance (up to 15%). Simulations confirm τₛ ≈ 0.036 in fully developed chaos beyond the Feigenbaum point, with variance constrained by σ² ≤ 1/N. By explicitly delineating the boundaries at ±0.41, this note strengthens the predictive capacity of τₛ for early detection of critical transitions. Applications span ecology, climate modeling, artificial intelligence, financial systems, physical attractors, cardiology, materials engineering, social network resilience, and strategic forecasting under uncertainty.

Abstract: Throughout the history of scientific discovery, the question of could a machine be able to find the laws of nature directly from observed data without relying on any prior information has been unimaginable until the emergence of modern-day computing and Artificial Intelligence. We develop a framework as an operator operation, evaluation, and optimization for a decision-machine to conduct scientific discovery: both nature’s “behavior” and the decision-machine’s “actions” are modeled with a formalized system under Hilbert Space; three inductive rules are utilized to evaluate the decision-machine’s performance; and the evolutionary algorithm is applied to optimize the best way to reconstruct the historical data and effectively predict its future. A simulated random dataset is used to show that the decision-machine is able to reasonably reconstruct the experimental data and effectively predict the future. Crucially, our developed framework is a versatile and experimentally feasible tool for conducting scientific discovery by machine that has broad implications for forecasting, AI for science, and fundamental scientific discovery of the natural and social sciences.

Abstract: The Ahuraic Framework (AF) is a comprehensive, multilayered theoretical system designed to model phenomena across scales, from subatomic particles to biological and cosmic structures. It is founded on the Ahuric Core and Fundamental Axiomatic Components, which enable mathematical derivation of space, fields, particles, laws, and algorithms. This study applies the AF to the problem of biological homochirality, specifically the exclusive selection of L-amino acids and D-sugars in living systems. While conventional explanations often treat homochirality as a stochastic outcome, the AF interprets it as a necessary consequence of hierarchical principles such as Minimum Information–Energy Action, Dynamic Compatibility, and Active Transformation. The transition from a racemic mixture to a stable homochiral configuration emerges structurally through interactions with the Ahuric Directive Field and attainment of the Organizational Threshold. Dynamical equations and mechanisms such as chiral locking are used to establish an analytical connection between symmetry breaking in fundamental physics, including weak interactions, and its stabilization in molecular biology. The model also outlines potential pathways for experimental validation. Overall, the Ahuraic Framework offers a unified approach to understanding the origin of order, the emergence of symmetry breaking, and development of life, providing a consistent mathematical and conceptual bridge between physical laws and biological phenomena.

Abstract: This article explores the origin of time and the universe through the integrated lenses of modern cosmology, alternative quantum theories, and the Kalam Cosmological Argument. It challenges the notion of a temporally infinite cosmos and critiques materialist interpretations that deny a beginning to time. Drawing from classical Islamic philosophy—particularly Al-Ghazali’s arguments on creation ex nihilo and Divine Will—the paper incorporates contemporary insights from quantum cosmology, such as the Hartle-Hawking no-boundary proposal, loop quantum cosmology, and philosophical developments in the Kalam argument. It argues that time is a contingent feature of the universe, emerging with creation, and not an eternal backdrop. The discussion highlights the epistemological limits of physics in addressing metaphysical origins and underscores the necessity of philosophical and theological perspectives in cosmological discourse.

Abstract: Accurate forecasting of local weather patterns is essential for climate resilience and sustainable planning. This study analysed 35 years (1990--2025) of hourly temperature and precipitation data from Thohoyandou, South Africa, to assess the effects of climate change and improve anomaly prediction. Exploratory analysis and BEAST decomposition revealed accelerated warming trends of 0.025 °C per year in temperature anomalies, and irregular rainfall patterns dominated by extreme events rather than systematic changes. Two machine learning models, Artificial Neural Networks (ANN) and Long Short-Term Memory (LSTM) networks, were evaluated for anomaly forecasting, with feature selection guided by LASSO regression. For temperature, the LSTM model outperformed the ANN, achieving RMSE = 0.678, MAE = 0.466, and MASE = 0.520, compared to RMSE = 0.738, MAE = 0.524, and MASE = 0.585 for the ANN, with improvements confirmed by the Diebold--Mariano test. For precipitation, both models performed similarly, with the LSTM slightly better (RMSE = 0.432, MAE = 0.112, MASE = 1.897). These results highlight the LSTM model’s superior ability to capture temperature anomalies and the continued challenges of modelling rainfall, providing evidence-based insights to support agricultural planning, water management, and climate adaptation in Southern Africa.