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Maria Carannante, Oday Masoudi, Alessandro Mazzoccoli
No abstract is available for this record.
Andrew Stewart Caldin
By projecting the 240 E8 root vectors onto a 132 Hz base field and coupling them with the golden‑ratio φ, we can encode the collective meme‑signal state of a cryptocurrency into a discrete spectral pattern. The resulting interference of root‑length harmonics produces a multi‑dimensional volatility waveform that pre‑synchronizes with the ground‑state trading dynamics. When a meme‑triggered sell signal (e.g., PEPE's 5/7 confirmations) is detected, the oscillator re‑shifts phase to amplify the predicted price swing, yielding a ±12 % forecast window. This principle extends MEME SIGNAL analysis and quantum‑breakthrough mining by turning memetic content into a real‑time frequency diagnostic of market flux. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Aurélie Assouline
The Holothéic Method is both a mathematical operator and a formalism for extracting predictive information from the second derivative of transition structures in complex fields. Applied here across ten distinct fields simultaneously cryptocurrency markets, geopolitical dynamics, AI adoption, foreign exchange, energy, real estate, and artificial general intelligence the operator identifies ratchet locks: configurations in which a transition has become structurally irreversible. Each prediction is time-stamped, falsifiable, and publicly verifiable within defined deadlines ranging from 72 hours to 12 months. The underlying mechanics are proprietary. This publication establishes intellectual priority as of August 21, 2026, 04:12 CET.
Salim Lahmiri, Stelios Bekiros
Background: Lyapunov exponent has been used in many science and engineering problems to quantify chaos in systems and understand their nonlinear dynamics. In financial engineering and forecasting, evaluation of chaos in financial data helps determine whether the data are predictable and if profits can be generated. The purpose of this study is to examine presence of chaos in cryptocurrency markets. Methods: To examine chaos, Lyapunov exponent is computed from a set of 50 cryptocurrencies and statistical one-sided and two-sided Student-t tests are performed to check if on average the computed Lyapunov exponents are equal, less, or larger than zero. Results: The statistical results reveal strong evidence that prices, returns, and trading volume changes are all chaotic; hence, they show nonlinear and deterministic characteristics. Conclusions: Prices, returns, and trading volume changes in cryptocurrencies could be predicted in the short run; for instance, on a daily basis. In this regard, active traders and investors may implement predictive systems to generate daily profits.
Insu Choi
No abstract is available for this record.
Krzysztof Numpsa
We propose a revolutionary shift in the utility of Non-Fungible Tokens (NFTs), transitioning from static digital assets to "Dynamic Logic Seeds" (DLS). By leveraging the Coherence Tensor () and fractal memory architectures, these assets act as frequency-based keys that trigger recursive computational expansions. Through a dual-blockchain system (Low-Frequency/High-Frequency), we demonstrate a method for preserving infinite logical versions across spacetime fluctuations at the Planck scale.
Ahmed M. Hala
This research establishes a formal topological framework for managing non- stationary market assets in portfolios by synthesizing high-dimensional chaotic dy- namics with industrial quality control and cryptographic verification. We introduce the Hala Operator as a state-dependent regulator capable of inducing Successive Controlled Collapse (SCC)—a process that maps continuous chaotic flows onto discrete, stable fixed-point constellations. By utilizing Taguchi Design of Experiments (DoE) for off-market robustness and Zero-Knowledge SNARKs for execution privacy, we provide a mathematically rigorous solution to the "Newtonian Trap" of market unpredictability. Formal proofs of global stability, dimension collapse via divergence analysis, and the uniqueness of the discrete constellation are presented.
Faruk Temel, Osman TUĞAY
No abstract is available for this record.
Stanisław Drożdż, Paweł Jarosz, Jarosław Kwapień, Maria Skupień · 5 authors
Correlations in complex systems are often obscured by nonstationarity, long-range memory, and heavy-tailed fluctuations, which limit the usefulness of traditional covariance-based analyses. To address these challenges, we construct scale- and fluctuation-dependent correlation matrices using the multifractal detrended cross-correlation coefficient ρr that selectively emphasizes fluctuations of different amplitudes. We examine the spectral properties of these detrended correlation matrices and compare them to the spectral properties of the matrices calculated in the same way from synthetic Gaussian and q-Gaussian signals. Our results show that detrending, heavy tails, and the fluctuation-order parameter r jointly produce spectra, which substantially depart from the random case even under the absence of cross-correlations in time series. Applying this framework to one-minute returns of 140 major cryptocurrencies from 2021 to 2024 reveals robust collective modes, including a dominant market factor and several sectoral components whose strength depends on the analyzed scale and fluctuation order. After filtering out the market mode, the empirical eigenvalue bulk aligns closely with the limit of random detrended cross-correlations, enabling clear identification of structurally significant outliers. Overall, the study provides a refined spectral baseline for detrended cross-correlations and offers a promising tool for distinguishing genuine interdependencies from noise in complex, nonstationary, heavy-tailed systems.
Vening, Edwin Jean-Paul
10.5281/zenodo.17605813 chaos structure complexity sequences / test files / public domain Chaos Complexity Domain Sequencing"Maximum Entropy Equilibrium"sha384sum OUTFN_BASE-OUTFN_VER-OUTFN_VERMIN-20221230191340.OUTFN_EXT.1069cbf8cebedf73040848960d915d728f8ebce64de339e57c03984b9b125065571ee73cba2fbe8324d57770631f22d3c27download Value Char Occurrences Fraction 0 4000000106 0.500000 1 3999999894 0.500000Total: 8000000000 1.000000Entropy = 1.000000 bits per bit.Optimum compression would reduce the sizeof this 8000000000 bit file by 0 percent.Chi square distribution for 8000000000 samples is 0.00, and randomlywould exceed this value 99.81 percent of the times.Arithmetic mean value of data bits is 0.5000 (0.5 = random).Monte Carlo value for Pi is 3.141394237 (error 0.01 percent).Serial correlation coefficient is 0.000013 (totally uncorrelated = 0.0).sha384sum OUTFN_BASE-OUTFN_VER-OUTFN_VERMIN-20230103155948.OUTFN_EXT.107d6275873f72a0edc7585db17bba50cdfb4a5097f3f50ac7b69eaa85ae8ec95975fb187579a5b05ff0c69ca71378fe71d download Value Char Occurrences Fraction 0 4000000107 0.500000 1 3999999893 0.500000Total: 8000000000 1.000000Entropy = 1.000000 bits per bit.Optimum compression would reduce the sizeof this 8000000000 bit file by 0 percent.Chi square distribution for 8000000000 samples is 0.00, and randomlywould exceed this value 99.81 percent of the times.Arithmetic mean value of data bits is 0.5000 (0.5 = random).Monte Carlo value for Pi is 3.141257485 (error 0.01 percent).Serial correlation coefficient is 0.000004 (totally uncorrelated = 0.0). DATA MORGANA COMMUNICATIONS AUTHOR/ EDWIN J. VENINGEDITOR EDWIN J. VENINGCORRESPONDENCE ADMIN@DATAMORGANA.NETWEBSITE SPAWN HTTPS://WWW.DATAMORGANA.NETRELEASED DD 20230525 [ YYYYMMDD ]EDIT REV.DD 20231208 over 20230726REF <symbolic base> See addendum:- binary ambiguity is expectedIntroduction in Dutch : page 2 20230726 crt0 Addendum: The test vectors presented here stem from the design of a custom generator, originally intended to outperform competitors in various categories of "randomness" generation. The goal was to achieve chaotic streams that exceeded the capabilities of other contenders, without relying on traditional methods for balancing distribution qualities. The resulting system incorporates parametric high-gain, maximum entropy equilibrium functions and methods, with output files available for download from this page. These files are derived from this work and should be used with caution. Historical Context: In 2019, a proposal was made to enhance the cryptographic subsystem of operating systems through a novel approach. This concept involved hardening the system with a new cryptographic processing "idea" of operation(s), integrated within a fresh confidence model. This idea was presented as the open-source project: /dev/entropy, a Unix non-blocking character device designed for non-disclosed ZKP (Zero-Knowledge Proof) seasonal or projected transactions/operations. The goal was to bootstrap system entropy pools using unique host identification, confidence constraints, and host signature processing in its own ZKP design (a system verifier capsule). /dev/entropy was intended to serve as the system entropy pool, which would be well-documented and securely stored. The author and programmer asserted that chaining cryptographic functions could weaken their security, leading to a proposal for entropy pools that would re-seed cryptographic functions in the host stack using non-linear, complexity-driven methods. These operations were intentionally designed to be opaque to prevent exposure, aiming to mitigate known mechanical noise attack vectors and thwart binary dissection. The processing would involve a novel use of "RAM" or "held latent memory." The project concluded in 2019 but remains a significant influence on the development of unique event processing and symbolic information transformations. As for the test vectors, no claims are made regarding their randomness or indexing properties. Envisioned Applications for the Methods and Functions: High-speed calibration of scientific instruments High-gain precision, offering persistent increases in resolution for guidance systems, telemetry, and high-availability scheduling (real-time systems) Persistence of identification tokens, tokenizing information by range, sequence hinting (*), as suggested in the ZKP paper ZKP 'circuitry' / 'gadgets' with enhanced properties, allowing for directional confidence balancing and omni-directional jumps, encoding with unique event processing such as spacetime locality encoding Real-time processing improvements, introducing new priority-type scheduling and domain sequencing (correlated context, with no known limits or recursion results) Application of "lossy" parity and "hashing" in new contexts, utilizing range hinting or the development of a symbolic encoded sequence that persists in noisy systems. The ratio is under testing. Expected hardware development: Domain sequencing through event processors with hardened/optical circuitry and one-way functions These methods aim to serve as a critical infrastructure carrier post-quantum Cryptography (PQC), offering potential solutions for complex network topologies and signal semantics for future interstellar applications. This approach leverages spatial and referential qualities without sudden collapse, adding the Temporal Domain Cryptography from 2015 as part of the ongoing evolution. DISCLAIMER: The contents of these vectors may contain the densest information to date, with an inherent carbon footprint that requires careful handling. Due to the dense nature of this data, it may cause local mechanical friction and, in extreme cases, could lead to combustion. As with any significant discovery, proceed with caution. Note: This is not the recommended practice in the narrowing binary domain of information. For reference: CACert Random Number Results — "No Entropy Here" home https://www.datamorgana.net
Tetsuya Takaishi
The finite sample effect on the Hurst exponent (HE) of realized volatility time series is examined using Bitcoin data. This study finds that the HE decreases as the sampling period $Δ$ increases and a simple finite sample ansatz closely fits the HE data. We obtain values of the HE as $Δ\rightarrow 0$, which are smaller than 1/2, indicating rough volatility. The relative error is found to be $1\%$ for the widely used five-minute realized volatility. Performing a multifractal analysis, we find the multifractality in the realized volatility time series, smaller than that of the price-return time series.
P.R.L. Alves
No abstract is available for this record.
Mir Feiz Fallah, Rezvan Pourmansouri, Bahador Ahmadpour
No abstract is available for this record.
Ismail A Mageed
This work introduces my second entropy measure, Ismail’s second entropy, namely $(H_{1}^{q})$ is a novel generalization to Shannonian entropy with a visionary link to both long- and short-range interactions, (LRIs), (SRIs) respectively. The fractal dimension of $H_{1}^{q}$ is identified in this paper. Following this, some potential fractal applications to ChatGPT, Distributed Ledger Technologies(DLTs), and Image Processing are highlighted. The paper ends with closing remarks combined with some challenging open problems and the next phase of research.
Anurag Dutta, Liton Chandra Voumik, A. Ramamoorthy, Samrat Ray · 5 authors
Cryptocurrencies are in high demand now due to their volatile and untraceable nature. Bitcoin, Ethereum, and Dogecoin are just a few examples. This research seeks to identify deception and probable fraud in Ethereum transactional processes. We have developed this capability via ChaosNet, an Artificial Neural Network constructed using Generalized Luröth Series maps. Chaos has been objectively discovered in the brain at many spatiotemporal scales. Several synthetic neuronal simulations, including the Hindmarsh–Rose model, possess chaos, and individual brain neurons are known to display chaotic bursting phenomena. Although chaos is included in several Artificial Neural Networks (ANNs), for instance, in Recursively Generating Neural Networks, no ANNs exist for classical tasks entirely made up of chaoticity. ChaosNet uses the chaotic GLS neurons’ property of topological transitivity to perform classification problems on pools of data with cutting-edge performance, lowering the necessary training sample count. This synthetic neural network can perform categorization tasks by gathering a definite amount of training data. ChaosNet utilizes some of the best traits of networks composed of biological neurons, which derive from the strong chaotic activity of individual neurons, to solve complex classification tasks on par with or better than standard Artificial Neural Networks. It has been shown to require much fewer training samples. This ability of ChaosNet has been well exploited for the objective of our research. Further, in this article, ChaosNet has been integrated with several well-known ML algorithms to cater to the purposes of this study. The results obtained are better than the generic results.
Pavlos I. Zitis, Shinji Kakinaka, Ken Umeno, M. P. Hanias · 6 authors
This article investigates the dynamical complexity and fractal characteristics changes of the Bitcoin/US dollar (BTC/USD) and Euro/US dollar (EUR/USD) returns in the period before and after the outbreak of the COVID-19 pandemic. More specifically, we applied the asymmetric multifractal detrended fluctuation analysis (A-MF-DFA) method to investigate the temporal evolution of the asymmetric multifractal spectrum parameters. In addition, we examined the temporal evolution of Fuzzy entropy, non-extensive Tsallis entropy, Shannon entropy, and Fisher information. Our research was motivated to contribute to the comprehension of the pandemic's impact and the possible changes it caused in two currencies that play a key role in the modern financial system. Our results revealed that for the overall trend both before and after the outbreak of the pandemic, the BTC/USD returns exhibited persistent behavior while the EUR/USD returns exhibited anti-persistent behavior. Additionally, after the outbreak of COVID-19, there was an increase in the degree of multifractality, a dominance of large fluctuations, as well as a sharp decrease of the complexity (i.e., increase of the order and information content and decrease of randomness) of both BTC/USD and EUR/USD returns. The World Health Organization (WHO) announcement, in which COVID-19 was declared a global pandemic, appears to have had a significant impact on the sudden change in complexity. Our findings can help both investors and risk managers, as well as policymakers, to formulate a comprehensive response to the occurrence of such external events.
Baki ÜNAL
Cryptocurrencies are new kinds of electronic currencies based on communication technologies. These currencies have attracted the attention of investors. However, cryptocurrencies are very volatile and unpredictable. For investors, it is very difficult to make investment decisions in cryptocurrency market. Therefore, revealing changes in the dynamics of cryptocurrencies are valuable for investors. Bitcoin is the most popular and representative cryptocurrency in cryptocurrency market. In this study how dynamical properties of Bitcoin changed through time is analyzed with recurrence quantification analysis (RQA). RQA is a pattern recognition-based time series analysis method that reveals dynamics of the time series by calculating some metrics called RQA measures. This method has been successfully applied to nonlinear, nonstationary, short and chaotic time series and does not assume a statistical model. RQA can reveal important properties of time series data such as determinism, laminarity, stability, randomness, regularity and complexity. By using sliding window RQA we show that in 2021 RQA measures for Bitcoin prices collapse and Bitcoin becomes more unpredictable, more random, more unstable, more irregular and less complex. Therefore, dynamics and stability of the Bitcoin prices significantly changed in 2021.
Tao Yin, Yiming Wang
This paper mainly studies the market nonlinearity and the prediction model based on the intrinsic generation mechanism (chaos) of Bitcoin’s daily return’s volatility from June 27, 2013 to November 7, 2019 with an econophysics perspective, so as to avoid the forecasting model misspecification. Firstly, this paper studies the multifractal and chaotic nonlinear characteristics of Bitcoin volatility by using multifractal detrended fluctuation analysis (MFDFA) and largest Lyapunov exponent (LLE) methods. Then, from the perspective of nonlinearity, the measured values of multifractal and chaos show that the volatility of Bitcoin has short-term predictability. The study of chaos and multifractal dynamics in nonlinear systems is very important in terms of their predictability. The chaos signals may have short-term predictability, while multifractals and self-similarity can increase the likelihood of accurately predicting future sequences of these signals. Finally, we constructed a number of chaotic artificial neural network models to forecast the Bitcoin return’s volatility avoiding the model misspecification. The results show that chaotic artificial neural network models have good prediction effect by comparing these models with the existing Artificial Neural Network (ANN) models. This is because the chaotic artificial neural network models can extract hidden patterns and accurately model time series from potential signals, while the benchmark ANN models are based on Gaussian kernel local approximation of non-stationary signals, so they cannot approach the global model with chaotic characteristics. At the same time, the multifractal parameters are further mined to obtain more market information to guide financial practice. These above findings matter for investors (especially for investors in quantitative trading) as well as effective supervision of financial institutions by government.
Yan Yan, Wei Shao, Jian Wang
In this paper, we explored the price-volume cross-correlation asymmetric multifractal properties of some cryptocurrencies using multifractal asymmetric detrended cross-correlation analysis (MF-ADCCA). Bitcoin, Ethereum, Tether, Binance Coin, Cardano, and Dogecoin are examples of cryptocurrencies. The empirical results reveal that the price-volume cross-correlations of all six cryptocurrencies display anti-persistent, multifractal, and asymmetric features, although the degree of these characteristics differs depending on the cryptocurrencies and market trends. Specifically, the anti-persistence multifractal of the price-volume cross-correlation is significantly stronger in the upward market than in the downward market for Bitcoin and Ethereum; for the remaining four cryptocurrencies, the opposite result is obtained. Furthermore, Dogecoin price-volume cross-correlation exhibits the most marked anti-persistence and the most significant asymmetric multifractality among the six cryptocurrencies analyzed.
Cristiana Vaz, Rui Pascoal, Hélder Sebastião
Since its launch in 2009, bitcoin has thrived, attracting the attention of investors, regulators, academia, and the public in general. Its price dynamics, characterized by extreme volatility, severe jumps, and impressive long-term appreciation, suggest that bitcoin is a new digital asset. This study presents a comprehensive overview of the fractality of bitcoin in a high-frequency framework, namely by applying Multifractal Detrended Fluctuation Analysis (MF-DFA) and a Multifractal Regime Detecting Method (MRDM) to Bitstamp 1 min bitcoin returns from January 2013 to July 2020. The results suggest that bitcoin is multifractal, with smaller and larger fluctuations being persistent and anti-persistent, respectively. Multifractality comes from significant long-range correlations, which cast some doubts on the informational efficiency at this frequency, but mainly comes from fat-tails, which highlights the significant risks undertaken by investors in this market. Our most important result is that the degree and richness of multifractality is time-varying and increased after 2017, when volumes and prices experienced an explosive behaviour. This complexity puts into perspective the duality of bitcoin: while it is characterized by long-run attractiveness and increasing valuation, it also has a high short-run instability. Hence, this study provides some empirical evidence supporting the relationship between these two observable features.
Łukasz Pietrych, Julio E. Sandubete, Lorenzo Escot
No abstract is available for this record.
Sérgio Adriani David, Claudio Marcio Cassela Inacio, Rafael Amorim Belo Nunes, J. A. Tenreiro Machado
Introduction: Cryptocurrencies have been attracting the attention from media, investors, regulators and academia during the last years. In spite of some scepticism in the financial area, cryptocurrencies are a relevant subject of academic research. Objectives: In this paper, several tools are adopted as an instrument that can help market agents and investors to more clearly assess the cryptocurrencies price dynamics and, thus, guide investment decisions more assertively while mitigating risks. Methods: We consider three methods, namely the Auto-Regressive Integrated Moving Average (ARIMA), Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) and Detrended Fluctuation Analysis, and three indices given by the Hurst and Lyapunov exponents or the Fractal Dimension. This information allows assessing the behaviour of the time series, such as their persistence, randomness, predictability and chaoticity. Results: The results suggest that, except for the Bitcoin, the other cryptocurrencies exhibit the characteristic of mean reverting, showing a lower predictability when compared to the Bitcoin. The results for the Bitcoin also indicate a persistent behavior that is related to the long memory effect. Conclusions: The ARFIMA reveals better predictive performance than the ARIMA for all cryptocurrencies. Indeed, the obtained residual values for the ARFIMA are smaller for the auto and partial auto correlations functions, as well as for confidence intervals.
Şahin Telli, Hongzhuan Chen
No abstract is available for this record.
Luiz Almeida Sampaio Filho
The behavior of the foreign exchange and cryptocurrency markets was studied from the perspective of the theory of dynamical systems. Using the phase space reconstruction procedure under the validity of Takens' theorem (1981). The presence of serial dependence was investigated through the BDS test, the property of sensitivity to initial conditions through the Lyapunov maximum exponent and the distinction between deterministic and stochastic signals observing the behavior of the E2(d) function in Cao's method (1997). Evaluating 17 exchange rate log-return series, evidence of serial dependence, possibly non-linear, was found in 11 of them. As for sensitivity to initial conditions, no series has shown conclusive results on such a property. All series presented evidence that they follow processes of a random nature and non-Gaussian increments, in the same way as the cryptocurrency log-return series. Of the 10 series of cryptocurrencies, the IID hypothesis was rejected for 8 of them, and none presented a conclusive result regarding a positive Lyapunov exponent. As a conclusion, no consistent characteristics of chaotic dynamics were found for the foreign exchange and digital currency markets in the analyzed period.