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 paper presents the fundamental formulas of a new classical mechanics that is symmetrical to the present classical mechanics. Non-Euclidean geometries tell us that one of the postulates in an axiomatic system may take different forms. Modified postulates can lead to new axiomatic systems. The classical mechanics is an axiomatic systems and the Newton’s three laws are three postulates. From the three laws, together with the necessary definitions of physical concepts and propositions, all contents of classical mechanics can be derived. Newton’s second law can be simply stated as: force is the cause of acceleration. The author thinks that it can be modified as: force is the cause of deceleration. This results in a new axiomatic system called 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 the PKE. Therefore, the new classical mechanics can be called negative kinetic energy (NKE) one, while the existing classical mechanics can be called PKE (PKE) one. These two parts can be collectively referred to as a while 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: 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: Synchronization is a fundamental phenomenon in complex systems, with conventional theory positing that its stability crucially depends on network topology and system parameters. However, these information often incomplete in real world scenarios. Here, we derive a elegant boundary equation for synchronous stability and report a new type of spontaneous synchronization near the boundary. Simulation experiments and mathematical proofs demonstrate that both the boundary and spontaneous synchronization are independent of the network. These results challenge the structural foundation of synchronization on complex networks. The framework establishes that the emergence of synchronization phenomena originates from fundamental principles transcending network. This work offers a novel unified perspective on synchronization phenomena in diverse fields.

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.

Abstract: This article examines the simulation hypothesis through a formal epistemic and axiomatic lens, assessing whether it can constitute a coherent and testable account of cosmological reality. After outlining the conceptual claim that our universe might be a high-level computational construct, the paper develops a minimal axiomatic framework for a “simulation matrix” and evaluates its logical status. It is shown that the hypothesis is internally consistent yet inherently incomplete, in the Gödelian sense that no observer embedded within the simulated domain can obtain evidential access to the ontological ground of its implementation. Even when strengthened with empirical commitments intended to render it testable, the hypothesis remains ontologically underdetermined: detectable implementation is not equivalent to demonstrable provenance. Accordingly, the simulation hypothesis, far from being a cosmological thesis, functions as a limit-case of self-referential epistemology — a modern restatement of the logical horizon beyond which no system can verify the reality of its own foundations.

Abstract:

Despite athletes initiating sprints from dynamic starts during gameplay, sprint performance is traditionally measured from a static position. This article aimed to determine whether static start or “pickup” acceleration are related or relatively independent motor qualities by assessing their relationship and examining how athletes’ rank order changes between static and pickup conditions. Thirty-one male athletes (20.3 ± 5.3 years) completed two 30 m sprints from a static start and two 30 m pickup accelerations following 20 m paced entries at 1.5 and 3.0 m/s, regulated by an LED system. Peak acceleration (a_max) was measured via a horizontal linear position encoder (1080 Sprint). The shared variance between a_max from the static and pickup starts was R² =11.6-39.6%, indicating, for the most part, a great amount of unexplained variance. The shared variance between pickup acceleration entry velocities was R² = 16.8%. Visual analysis of an individualized rank order table confirmed that, for the most part, the fastest static start athletes differed from the fastest pickup athletes. In summary, static and pickup acceleration seem relatively distinct motor abilities, most likely requiring a paradigm shift in strength and conditioning practice in terms of acceleration assessment and development.

Abstract: The aim of this study is to quantify the impact of increased surface solar radiation on climate warming in Central Europe from 1915-2024 and to re-examine the relationship between CO2 concentrations and global CO2 emissions. A statistical model with proxies for short-wave and long-wave radiation (sunshine duration SSD and CO2 concentration) as independent variables and surface air temperature as the dependent variable was tested for validity and significance, and the results were presented for six long-term measuring stations in Central Europe. A lifetime concept was evaluated for CO2 concentration and contrasted with the concept of accumulated CO2 emissions. The statistical model fulfilled all tests (error probability, normal distribution of the residuals, autocorrelation, statistical power, multicollinearity) and showed that the increase in SSD in the entire year accounts for around 20% of the warming over the last 100 years, in the summer half-year (April-September) and summer (June-August) it is around 30%. The increase in CO2 concentration accounts for the remainder portion of warming of 70-80%. Studies and models neglecting the influence of the increase in surface solar radiation are overestimating the influence of GHG on warming. The development of CO2 concentrations from industrialization until today can be mapped very well with a lifetime of 58 years. Therefore, reducing annual CO2 emissions by around half would stabilize CO2 concentrations.

Abstract: The interaction of an ultra-short, high-power laser pulse with a solid target, in the so-called Target Normal Sheath Acceleration (TNSA) configuration, produces particles in the MeV range. Fast electrons can escape from the target after the interaction, inducing electrostatic fields on the order of TV/m close to the target surface. These fields accelerate MeV protons and heavy ions at the rear of the target, allowing them to escape. The complete process is difficult to probe, as it occurs on the sub-ps timescale. At the INFN-LNF SPARC_LAB test facility, single-shot diagnostics such as the Electro-Optical Sampling (EOS) are being developed and tested for time-resolved direct measurements of the produced electrons and associated longitudinal electric fields. Electrons are the core of the process, and their properties determine the following production of positive charge particles and electromagnetic radiation. Different target geometries and materials are being investigated to analyze the enhancement of fast electron emission and the correlation with positive charge production. Simultaneous observations of electron and proton beams have been performed using two diagnostic lines, the EOS for electrons and a time-of-flight (TOF) detector for protons. This work provides an overview of the previous experiments performed at SPARC_LAB dedicated to the TNSA characterization.

Abstract: We present a unified geometric framework for the full Lorentz group, based on a bounded angle parametrization of spacetime transformations within a hyper-spherical geometry. By mapping the unbounded hyperbolic angle φ to a bounded angle β using the Gudermannian function, hyperbolic, causal, and Euclidean three-spheres are brought together into a single structure: hyper-spacetime. This structure unifies the Euclidean R⁴ and Minkowski R^1,3 domains, incorporates discrete symmetries in a continuous way, and removes discontinuities at the lightlike boundary. Each three-sphere carries a natural spinor set, encoding symmetry, and acting as eigen-spinors of corresponding observables. These reproduce the Dirac spectrum while confining singular behavior to a scalar factor. The bounded angle parametrization therefore provides a continuous, closed representation of the full Lorentz group and a transparent geometric basis for spacetime symmetry.

Abstract: Artificial neural networks (ANNs) are powerful models inspired by the structure and function of the human brain. They are widely used for tasks such as classification, prediction, and model recognition. This study examines the stability of fractional-order neural networks with neuronal conditions, dynamic behavior, synchronization, and delays of time

Abstract: This study investigates the extension of fractional anti-synchronization to coupled physical systems, employing Systemic Tau (tau_s) as a stability metric, building upon its validation in ecological chaos derived from Aedes aegypti population dynamics. By applying tau_s to the fractional-order Lorenz system, the analysis incorporates Caputo fractional derivatives, an event-based time model, and perturbations with 10-15% noise. Through iterative parameter adjustments, a master-slave configuration achieves tau_s < -0.41, aligning with ecological bifurcation thresholds. The results highlight robust anti-synchronization under noisy conditions, suggesting potential applications in chaos control, turbulence modeling, and secure communications.

Abstract: This paper develops a unified mathematical framework that connects invariant structures across physics, biology, and consciousness using the language of category theory and topos theory. We begin with classical invariants from physics, such as those arising from Noether’s theorem, and systematically construct parallel notions in genomics and neural perception. Tangent perceptual spaces (TPS), introduced as foundational geometric structures for conscious experience, are modeled within projective and Hilbert space frameworks, with consciousness localized as a delta-function-like point in these spaces. Topos theory is employed to explore internal logics of different ontological domains, allowing us to generalize classical Boolean logics into intuitionistic or modal settings relevant for subjective experience. We define monoidal categories to represent bifunctorial tensor structures in Lagrangian physics, genetic recombination, and integrated perceptual architectures. Consciousness emerges as a fixed-point functor over categorical structures, where computation, sensory input, and quantum dynamics converge. The paper also analyzes the potential for conscious quantum computation, arguing that under sufficiently complex entanglement entropy, decoherence resistance, and perceptual functoriality, artificial agents may support qualia. Ethical, cognitive, and philosophical consequences are derived using sheaf-theoretic constructions and logical internalizations of subjective states. Our model ultimately suggests that life, mind, and physics can be mathematically unified through a hierarchy of category-theoretic functors, monads, and topoi, with invariant-preserving transformations acting as the bridge across ontological strata.

Abstract: In two preprints posted in September 2025, Johel Padilla-Villanueva introduces Systemic Tau (\(\tau_s\)), a universal metric derived from ordinal correlations and fractal self-organization, designed to assess stability and emergent order in chaotic systems. The foundational preprint, "Unveiling Systemic Tau: Redefining the Fabric of Time, Stability, and Emergent Order Across Complex Chaotic Systems in the Age of Interdisciplinary Discovery," redefines time as discrete event-based conjunctions guided by Feigenbaum constants, illustrating \(\tau_s\)'s applicability across ecology, artificial intelligence (AI), climate modeling, financial markets, and physical attractors. The companion preprint, "Validation of Anti-Synchronization in Chaotic Systems Using Systemic Tau from Padilla-Villanueva (2025)," confirms \(\tau_s\)'s effectiveness in detecting divergent anti-phase dynamics (\(\tau_s < 0\)) using empirical data from Aedes aegypti mosquito populations in Puerto Rico and logistic map simulations with fractional extensions. Rooted in Padilla-Villanueva's 2022 doctoral dissertation and supported by meteorological datasets, this synthesis consolidates their theoretical foundations, methodologies, results, and potential applications, presenting \(\tau_s\) as a pivotal tool for interdisciplinary chaos research with implications for public health (e.g., dengue forecasting) and AI robustness, while identifying areas for further refinement and validation.

Abstract: This study investigates anti-synchronization in chaotic systems, building on frameworks by Pecora and Carroll [1] and Mainieri and Rehacek [2], validated through 2022 doctoral fieldwork in Puerto Rico’s Caño Martín Peña [3]. Anti-synchronization, characterized by divergent dynamics, is quantified using Systemic Tau (τ_s) as defined in Padilla-Villanueva (2025) [4], revealing hidden patterns in fluctuating Aedes aegypti populations amidst complexity.The analysis utilizes a discrete event-based time model, as established in Padilla-Villanueva (2025) [4], guided by Feigenbaum constants (δ ≈ 4.669, α ≈ 2.502) [5], to highlight anti-synchronization during bifurcations, marked by a threshold Ε ≈ 0.41, linked to mosquito population shifts during precipitation events (e.g., weeks 20-30, 2018, with τ_s = -0.469 ± 0.280, and weeks 45-50 with τ_s = -0.733 ± 0.200 from NOAA PRCP.cum data [3]). Empirical data from 104-week trap counts (S1-S5) show anti-synchronization, with S1 declining 20% and S3 rising 15% at a 9.4 mm PRCP.cum peak (2017-12-29), yielding τ_s = -0.469 ± 0.280 (p = 0.064, t = -2.89, p = 0.02). Simulations beyond the Feigenbaum point (r ≈ 3.57) and fractional extensions (α = 0.8 to 1.0) with 10-15% noise tolerance further confirm divergent patterns, suggesting applications in ecological stability and chaos management.

Abstract: Humanity is at a critical juncture in its evolution, marked by unprecedented technological advancements and the pursuit of higher civilization statuses as defined by the Kardashev scale. This study provides a comprehensive exploration of humanity’s potential progression towards achieving Type I and Type II civilizations, characterized by planetary- and stellar-scale energy utilization, respectively. Building upon Kardashev's framework, we propose refinements that integrate key parameters including energy consumption, information processing, construction mass, and population dynamics. By leveraging machine learning techniques, we analyze global energy data to simulate humanity’s energy future, with emphasis on the exponential growth of renewable and nuclear energy sources, and incorporate stellar classifications and insolation flux data from the Planetary Habitability Laboratory to establish energy utilization benchmarks for habitable exoplanets orbiting G-, K-, and M-type stars. Our simulations suggest that humanity could plausibly achieve Type I status by ~2271 CE, enabled by planetary-scale energy harnessing, advanced computational infrastructure, and sustainable population management, while under optimistic assumptions about technological progress and resource utilization, Type II civilization status might emerge between 3200–3500 CE. This projection, however, remains highly contingent on breakthroughs in stellar-scale infrastructures—such as Dyson swarms or Matrioshka Brains—and the sustained integration of interplanetary societies. To more effectively track these trajectories, we introduce a modified Kardashev metric—the Civilization Development Index (CDI)—which balances contributions from energy, information, construction, and population scales, and demonstrate its robustness under varying assumptions. Overall, this study offers a novel, interdisciplinary framework for understanding humanity’s long-term trajectory as a multiplanetary civilization, while emphasizing both the promise and uncertainty of forecasting our progression toward stellar-scale futures. Such recognizable existential risks—often described as potential “Great Filters”—could delay, divert, or even prevent this pathway of continued progression, underscoring the urgency of addressing global sustainability and resilience today.