The traditional Power Law model for Bitcoin is limited; it struggles to simultaneously fit historical data points across different eras without piecewise parameter adjustments. Bitcoin's trajectory is more naturally described as a tangent-based hyper-exponential system, driven by absolute supply scarcity.
Serhat YĂźksel, Gabriela Oana Olaru, Serkan Eti, Hasan DÄ°NĂER
It is frequently emphasized in the behavioral finance literature that investment decisions cannot be explained solely by economic indicators and rational expectations and that psychological factors also play a significant role in this process. However, the lack of a comparative analysis of the importance of psychological factors influencing investor behavior in the literature and the lack of consensus on which factors are more dominant constitute a fundamental problem. This deficiency leads to significant uncertainties in both theoretical modeling and practical investment strategies, increasing market risks such as irrational price movements, speculative bubbles, and panic selling. In this context, the aim of this study is to determine the relative importance of the fundamental psychological factors influencing investor decisions and, considering these factors, to identify the most appropriate investment alternatives for individuals. This study develops a new integrated decision-making model to answer these research questions. Considering the demographic characteristics of the experts, importance coefficients are calculated using the Euclidean distance-based weighting approach. Criterion weights are then determined using the Entropy method, and the MABAC and MAIRCA methods are applied to rank investment alternatives. Additionally, fractal fuzzy sets based on the Sierpinski triangle are integrated into the proposed model to model uncertainty more effectively. The study's contributions to the literature are highlighted in three dimensions: (1) psychological factors, often overlooked in the literature, are included in the criteria set; (2) expert weights are differentiated based on demographic characteristics rather than assumed to be equal; and (3) expert opinions are modeled more flexibly and precisely using new fractal number-based fuzzy sets. The findings indicate that trust is the most critical psychological factor, followed by loss aversion. In terms of investment alternatives, stocks stand out as the most suitable option, while bonds/deposits and gold are other important alternatives, with cryptocurrencies and real estate ranking next.
The stability of markets hosting leveraged exchange-traded products is governed not by any single product's loop gain but by the spectral radius of a loop-gain matrix, and scalar per-product monitoring underestimates system feedback by construction. Recent work measures the self-reinforcement of a leveraged fund's daily close rebalancing through a scalar loop gain and treats cross-asset spillovers as bias. We model complexes on correlated underlyings as a coupled feedback system with matrix gain L and show that scalar monitoring has two blind spots: (i) cycle amplification, since rho(L) >= max_i l_ii for nonnegative coupling, strict under two-way coupling; and (ii) transmitted displacement, which arises already under one-way coupling and is invisible to the receiver's own gain. We give a reduced-form estimator of L requiring only prices and public fund assets -- no signed order flow -- via cross-asset overnight reversals, reporting its measurement-convention sensitivity explicitly. In simulation the spectral radius is recovered with RMSE 0.005 at T=250, a lead-lag confounder yields a 2% false-alarm rate, and in a calibrated blind-spot configuration the scalar monitor reports "safe" and the matrix monitor "unsafe" on 100% of paths. In the 2026 Korean single-stock LETF episode we detect transmission from the SK Hynix complex into Samsung Electronics' closing price (DiD z=-2.82; exact randomization p=0.0055 against 182 control pairs), scaling with the sender's rebalancing capital; conservatively, about 41% of Samsung's closing displacement variance is imported -- invisible to its own "moderate" gain of 0.24. The same estimator returns nulls for the U.S. MSTR-Bitcoin-Coinbase complex, whose capital is comparable but whose closing venue is far deeper. Monitoring should be organized around the (complex x venue) matrix, not around products.
By projecting the 240 E8 root vectors onto a 132 Hz base field and coupling them with the goldenâratio Ď, we can encode the collective memeâsignal state of a cryptocurrency into a discrete spectral pattern. The resulting interference of rootâlength harmonics produces a multiâdimensional volatility waveform that preâsynchronizes with the groundâstate trading dynamics. When a memeâtriggered sell signal (e.g., PEPE's 5/7 confirmations) is detected, the oscillator reâshifts phase to amplify the predicted price swing, yielding a Âą12 % forecast window. This principle extends MEME SIGNAL analysis and quantumâbreakthrough mining by turning memetic content into a realâtime frequency diagnostic of market flux. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
The HolothĂŠic 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.
Fernando Henrique Antunes de Araujo, Milena KojiÄ, Petar MitiÄ, Kerolly Kedma Felix do Nascimento ¡ 5 authors
This study applies a prespecified dynamic MFDFA workflow across pandemic, geopolitical-conflict, and tariff-policy regimes for ten non-stable, long-history cryptoassets selected ex post from the 23 July 2026 market-cap ranking. The common sample comprises 3155 daily log returns per asset from 2 December 2017 to 22 July 2026; the final endpoint regime includes the U.S.âIran conflict. The estimator uses q=â10,â8,âŚ,10, linear detrending, 22 scales from 16 to N10, adjacent-secant Legendre transformation, a cubic spectrum peak, and 500-day windows stepped by 21 days plus a terminal endpoint. Full-sample IE=|Îą0â0.5| ranges from 0.01397 (LINK) to 0.08706 (BNB), and observed width ranges from 0.32625 to 0.74678. The controlled incremental U.S.âIran endpoint coefficient is â0.02734 (two-way clustered SE 0.02369; p=0.2489), with asset-cluster t(9) interval [â0.08226, 0.02759]. Quantile estimates range from +0.00206 at the 0.10 quantile to â0.04769 at the 0.90 quantile; all five 999-replication asset-cluster bootstrap percentile intervals include zero. Exact rolling sensitivities are negative for the 500/14, 500/30, and 730/30 designs but positive for the 250/21 design, and every small-cluster interval includes zero. Direct spectrum-width contrasts also remain nonsignificant after Holm adjustment. None of ten observed widths survives BH correction in 200 shuffled-return surrogates per asset (2000 fits in total). The results document heterogeneous and specification-sensitive dynamic multifractal patterns, not isolated or causal crisis effects.
When we describe a complicated system by a few coarse measurements, we face one recurring question: are the readings we have now enough to say what it will do next? Sometimes yes; sometimes they look complete but are not, and only pushing the system reveals it. This report turns that question into a checkable procedure. Five inexpensive probes first screen the data â description cost, identifiability, memory duration, change across scale, topological shape â no single probe deciding. We then ask, in order: does the present coarse state beat knowing nothing, and, once known, does history add more. Asking the first matters â history that âno longer helpsâ can mean the state suffices or that the future is unpredictable, and only the total separates these. Later stages ask whether look-alikes respond differently when pushed. The procedure reports a bottleneck and whether a layer has formed. We calibrate on known-answer cases: a classical system computed end to end (a closed layer, a history-limited case, a case separable only by intervention, and an unpredictable control a naive rule would misread as closed); a charge-to-particle stress test that stops short; and a genuine two-qubit process whose branches are passively identical yet separated by one intervention. We then run real series â carbon dioxide, sunspots, river flow, and equity-index and Bitcoin prices â where next-day returns read as no detected signal while volatility clusters, consistent with what is independently known. Every âno signalâ is resource-relative: stamped with the resource R used. The procedure settles only the two ends â a closed layer, or no detected signal â and refuses the process path between; it classifies rather than inventing the next layerâs laws.
The fluctuation characteristics of financial time series have always been one of the research hotspots in the academic community. Generally speaking, financial return series have the characteristics of volatility clustering, fat tails, conditional heteroskedasticity, asymmetric shocks, etc. The above phenomena can be explained from the perspective of dynamic conditional variance by GARCH models and their extensions. This paper first introduces the basic ideas of ARCH and GARCH models, with a focus on the issue of volatility clustering of financial returns. Then, it reviews the relevant research from three aspects: model evolution, application scenarios, and practical value. It also analyzes the role of GARCH-type models in capturing volatility persistence, asymmetric impact, and risk transmission through applications in cryptocurrencies, energy assets, and high-frequency financial data. The study shows that GARCH-type models capture the volatility clustering feature of financial returns well, but there is still room to improve the modeling of extreme risk, the handling of high-dimensional assets, and model interpretability.
The Triadic Stress Index (TSI) takes a network index whose four factors were first observed in soil microbiome co-occurrence networks and applies it, without alteration, to the correlation network of financial assets. We test it on five markets spanning 2006-2026 (equities including banking crises and the AI sector, cryptocurrencies, commodities, foreign exchange and sovereign debt), against three independent definitions of a crisis episode, at a fixed alarm budget, out of sample, with block-bootstrap intervals and a Holm correction across the family of tests. The benchmarks are the Absorption Ratio, the industry standard used by MSCI and central banks; the effective rank and the Vendi score, the sharpest spectral measures available; Ollivier-Ricci curvature; and the global and local balance indices of signed correlation networks. Three comparisons favour the index. It carries a per-node decomposition, diag(A^3), naming which asset is carrying the concentration with no parameter to select, and scores 0.97-0.99 against 0.33-0.84 for the only published per-node alternative, whereas spectral attribution must first choose how many components to read and collapses under a standard but wrong choice. Its alarms are the cleanest of anything tested, 4.0% of them with no matching episode against 14.7% for the effective rank and roughly 59% for the Absorption Ratio. And it beats the Absorption Ratio on detection by 0.273 in F1 out of sample, p<0.0005. The remaining comparisons are ties. Against the effective rank and the Vendi score the index ties in every scheme and both samples, and the margin over the Absorption Ratio narrows under the strictest labelling. On real matrices the far simpler node degree reproduces the attribution. A lead-lag analysis puts the peak cross-correlation at zero lag: this is a coincident state index, not a forecast.
This study investigates whether the macroscopic statistical maturity of cryptocurrencies implies dynamical equivalence with traditional equity markets. We analyze high-frequency data (2020--2025) using the Complexity--Entropy Causality Plane (CECP) and directed horizontal visibility graphs (directed HVG) to uncover complex temporal patterns and time-directed structures in the return series. While conventional stylized facts show striking convergence across all assets, structural diagnostics reveal a compelling paradox: cryptocurrencies appear more locally random than the equity benchmark during ordinary periods, yet exhibit significantly stronger directional time-irreversibility around high-visibility return events. The absolute-return results show that large cryptocurrency fluctuations tend to begin abruptly and remain elevated afterward. Separate analyses of positive returns and negative-return magnitudes show that this pattern is shared across cryptocurrencies on the upside but varies across assets on the downside. We conclude that statistical maturity is only skin-deep; the underlying dynamical processes of mature cryptocurrencies remain fundamentally distinct from traditional benchmarks.
We examine the possible asymmetric relations between returns and changes in realized moments in the Bitcoin market by employing the quantile regression models (QRMs) which can account for investorsâ heterogeneity. First, our findings confirm the existence of asymmetric return-volatility relation in the BTC market. Second, regarding the relations between returns and realized skewness, the negative and positive returns show larger impacts in lower and upper quantiles, respectively. Third, the relation between return and kurtosis exhibits similar asymmetric pattern to that of return-volatility. The empirical findings can be supported by behavioral theories including representative bias and affect heuristics.
Victor Michelle, Natalie Michelle, Emilie Michelle, Elias Michelle
This paper introduces Prediction Assets â a fundamentally new class of financial instruments where the underlying asset is market consensus on probability itself. Unlike traditional prediction markets, where binary event contracts terminate abruptly upon resolution, Prediction Assets are engineered as perpetual financial instruments that evolve rather than expire. Upon event occurrence, the asset does not liquidate to zero or a fixed payout; instead, it programmatically transforms into a new functional asset form (such as a currency, index, or memory asset) via smart-contract-enforced conversion ratios, establishing an infinite lifecycle and continuous capital efficiency. Key Structural & Mathematical Contributions: Core Asset Pricing Model: Establishes the foundational pricing equation \(P_{asset} = P(E) \times M\) driven entirely by open order-book decentralized exchange (DEX/AMM) spot liquidity without reliance on subjective analytical oracles. Systemic Market Efficiency: Implements an exact arbitrage condition boundary constraint (\(\sum P_{asset,i} = M\)) to incentivize algorithmic market-making and eradicate structural price variance. Programmatic Post-Event Evolution: Introduces the deterministic conversion coefficient \(C(t, state)\) locked at genesis to handle automated migration profiles (Currency, Index, Memory, and Derivative states) with zero administrative discretion. Decentralized Governance: Outlines a 4-channel Multi-Chain Consensus Verification Layer (CVL) requiring a strict 3-of-4 quorum across official APIs, open-source replicas, academic mirrors, and market sentiment vectors. Regulatory Engineering: Delivers a comprehensive compliance analysis under the U.S. Securities Framework (Howey Test and Reves Test boundaries) and CFTC Event Contract frameworks, positioning the topology as a non-security utility asset. Prospective Implementation:The paper presents AIVA (Artificial Intelligence Valuation Asset) as the world's first prospective implementation tracking the global macro-consensus probability of achieving Artificial General Intelligence (AGI), which programmatically transforms into an operational settlement currency for autonomous multi-agent economic environments upon verification. Keywords: Prediction Assets, Probability Markets, Financial Instruments, AGI, AI Agents, Decentralized Finance, Synthetic Assets, Valuation Markets. Citation Note: This specification expands upon the sovereign fintech frameworks established in IP Stock Exchange v3.3-Evolution (DOI: 10.5281/zenodo.20687136).
Abstract: The macroscopic phenomenological apparatus of open flow-through systems â an income-minus-expenditure master equation, a gradient-flow relaxation, and a quasi-potential landscape â is usually posed as a set of postulates. This paper assembles that apparatus into a diagnostic framework and draws its boundary of validity. The organizing proposition is retained as a first principle for open systems, the Principle of Nonuniformity: the state of an open system departs structurally from uniformity along both a cross-sectional and a temporal axis, a departure supplied continuously by work and paid for by non-negative internal entropy production. This version makes three retractions and five corrections relative to V10. All of them fall on load-bearing structure.Retraction one concerns the reference measure of the load-bearing variable. Earlier versions took the KullbackâLeibler divergence from an exponential baseline and converted it to energy units, calling the result an ordered free energy. For any system whose state-dependent coupling is positive, the stationary mark law is not exponential, so a quantity referenced to the exponential is not a rate function on any system this framework is about, and does not vanish on the systemâs own stationary law. The correct construction splits one quantity into three, distinguished only by which measure sits in the reference slot. A structural stock U_str is measured from the passive baseline, the law to which the system relaxes when driving is withdrawn; this is what the master equation carries. A displacement U_LDP is the quasi-potential of the stationary distribution and enters the Kramers escape exponent. A structure reading U_exp is measured from the memoryless baseline; it locates the stationary law on the form spectrum and enters no equation. All three are dimensionless, energy units survive only at two explicitly marked absolute calibration points, and the ordered-free-energy symbol is retired.Retraction two concerns the potential. V10 listed a quadratic free energy, a Landau expansion, and a large-deviation logarithmic integral as three truncation levels of one object. They are not. The quartic is the antiderivative of the deterministic drift with its sign reversed; for polynomial drift it is exact rather than a Taylor truncation, and its quadratic coefficient is (câB)/2, not c/2. The quasi-potential is the WKB potential of the jump process. The two share every critical point, but their curvatures at a fixed point differ by the exact factor 1/(ÎŚâ ¡c) â 1.2747 against 2.108 at the maintaining state of the standard parameter set, and a factor 4.46 at the barrier â so the claim that they agree to second order does not hold. One identity falls out of the restatement: the critical margin equals the second derivative of the deterministic potential at the maintaining state.Retraction three concerns the fixed-point status of the fossil state. V10 stated that once the three expenditures are written multiplicatively, the zero of the structural stock becomes an unconditional exact fixed point. The drift there is the income term ξ¡Ό¡ΡĚ¡W, which does not generally vanish, so that locus is a repelling line. The fixed-point status of the fossil state comes instead from the vanishing constant term in the recruitment rate: the activity equation carries an overall factor ÎŚ, so ÎŚ = 0 is an invariant manifold. The conclusion survives in cleaner form, and the absorbing conditions of the two coordinates merge into one.Correction one adds a sign branch to the master equation. Driving can push the stationary law to be more concentrated than the passive baseline or more homogeneous than it, and a divergence assigns a positive value to both directions alike. The sign branch is defined locally on the size side, as the sign of a difference of concentration readings, rather than through the Fano factor of the count distribution. The latter choice would make the definition of the central state variable depend on the falsifiable claim that the two coordinates share one sign, and the frameworkâs own equations supply a candidate counterexample region.Correction two supplies a single definition of the effective recovery rate. The margin formula in V10 used a coefficient that its own notation table never defined, and omitted the term responsible for bistability. The effective recovery rate is defined as the negated spectral abscissa of the linearized generator; under finite dimension, near-diagonality, and a fixed point it degenerates to the critical margin, whose closed form is Î = Îł + δ¡f_shock â B¡(1 â 2ÎŚâ ) + aâ¡Όâ ¡(3ÎŚâ â 2). Each of the three conditions fails somewhere in the framework â under age structure, on limit cycles, and in spatially extended systems â and each failure is now labelled where it occurs.Correction three reattributes the screening length. V10 called the screening length and the tail index two properties of one coordinate. The mark law carries no spatial information, so that reading cannot stand. The correct form is a causal chain: spatial gradient surplus lets denser locations draw from further away, the effective multiplicative gain rises, the allocation exponent is pushed up, and the tail index falls. The screening length itself is a second reading of the same activity-field spectrum, â = â(D/Î), and the dissipation slot in that formula is a role variable identified per application.Correction four adds age structure, and with it the lowest-threshold prediction in the framework. Giving the stock one extra dimension of component age separates the two maintenance classes for the first time. An exogenous shock imposes a common rate shift on every age mode, so the second derivative of the logarithm of the recovery curve is exactly invariant under that shift. The falsifiable statement therefore reads: the log-recovery curve is convex for a high-turnover system and straight for a low-turnover one, and the test requires no control over the shock.Correction five redraws the line between exogenous and endogenous. V10 claimed that exogenously variable rates can only transcribe a tail that is already present. Mixing an exponential law over a Gamma-distributed rate gives a Lomax law: both the component and the mixing law are light-tailed, and the result is a genuine power law. The line that survives is drawn on response to work â an exogenously frozen departure has an identically vanishing derivative with respect to work and does not relax when work is withdrawn, and only endogenous state dependence makes the departure a function of work. Under the passive baseline this negative result becomes cleaner still: a departure produced by exogenous mixing is positive on the structure reading and identically zero on the stock.
In this paper, we develop an open-economy macroeconomic model of a Proof-of-Stake network to analyze nominal token-price dynamics and the systemic effects of speculative capital. We first consider a network populated solely by active utility users, who finance network activity through a steady exogenous inflow of fiat currency. We prove the existence of a unique, globally asymptotically stable steady-state equilibrium with a well-defined nominal token price and derive a closed-form expression for the network's relaxation time. Calibrating the model using parameters representative of the current Ethereum network, we estimate a relaxation half-life of approximately 46 years. This extreme macroeconomic inertia implies that the token price may remain persistently displaced from its evolving steady-state benchmark, producing sustained price overshooting as the network adjusts to changing fundamentals. We then introduce an Investor class to examine the effects of passive and active speculative capital. We show that passive institutional staking compresses the native staking yield and creates a structural imbalance that systematically raises the nominal token price while shifting consensus ownership away from active utility users. Active speculative capital has a qualitatively different effect. In response to capital shocks, the Consumer class's rigid preference for fiat-denominated consumption generates an endogenous constant-value strategy. This mechanism shifts staked-token ownership from the Investor class toward active utility users, with potentially favorable implications for consensus decentralization.
This working paper introduces selected findings from Flow Extraction Theory (FET), an independent research program studying economic-state representation in decentralized financial systems. The paper argues that event history is not equivalent to state, and that observed pressure is not equivalent to explained pressure. Using a bounded Aave V3 case study at Ethereum block 20,000,000, the paper distinguishes historical event evidence, frozen protocol state, token-level representation, account-level aggregate outputs, inference, and unknowns. The study shows that event-derived reconstruction can disagree with exact frozen state, and that health-factor distance can be observed with high confidence while the evidence required to explain that distance remains incomplete. The paper introduces representation risk as the risk created when different evidence classes are collapsed into one operational view of âstate.â This public version summarizes selected findings only. It does not disclose implementation details, private tooling, execution logic, complete artifacts, or trading signals.
This paper establishes an exact information-theoretic duality between econometric regression topology and statistical mechanics. We demonstrate that an autonomous, data-driven Quadruple Test, grounded in the Factor Hierarchy Law, can blindly detect, precisely quantify, and correctly classify thermodynamic phase boundaries in perfect mathematical equivalence with the Ehrenfest paradigm, without any prior knowledge of Free Energy functions. The validation platform is the two-dimensional Ising model, one of the few systems in statistical physics possessing a mathematically rigorous exact solution (Onsager, 1944; Yang, 1952). Verification proceeds in two logical stages: Stage A (pristine algebraic validation) on Onsager's exact solution, and Stage B (stochastic robustness testing) on finite-lattice Monte Carlo simulations. We openly declare that because the data derives from the known Onsager-Yang formula, the contribution is not an independent empirical discovery of new physics, but rather the rigorous proof of an exact informational duality between two independent frameworks. In the language of metrology, this is not an endogeneity flaw but a mandatory calibration requirementâbefore a telescope is deployed to observe unknown deep space, it must first be calibrated against a known, invariant light source in a controlled laboratory. Positive Controls and Asymptotic Convergence (9 items): Exhaustive search blindly locks onto the critical temperature at Tc = 2.260 (deviation 0.009 at a coarse step size of 0.01). A grid-refinement study demonstrates monotonic convergence: the deviation shrinks to zero within 6-decimal precision at a step size of 0.001, and further converges to ~10âťâ¸ under a Golden Section Searchâthe absolute limit of 64-bit double-precision machine arithmetic. An analytical proof formally demonstrates that the Chow F-statistic achieves a unique global maximum exactly at Tâ = Tc; therefore, in the analytical limit, the localization error is strictly zero. The Chow test at Tc yields F = 118,074 against a null control of F = 3.12 (a 266-fold difference), with permutation test p = 0.000. The interaction term is overwhelmingly significant (p = 0.000, ÎR² = 0.991). A symmetry-breaking regime switch at the external field boundary h = 0 is detected with Chow F = 989.41 (p = 0.000). Interaction R² peaks sharply at Tc (deviation 0.03). Multi-response-function validation (specific heat C, nearest-neighbor spin correlation) and anisotropic validation (three Jx/Jy ratios) all lock onto their respective theoretical Tc values with deviations under 0.007. A synthetic double-break dataset is tested with both breaks successfully detected. Negative Controls (4 items): A 3,000-temperature-point exhaustive scan over 4 response variables finds no false positive of comparable magnitude to the true peak (maximum artifact F = 481 vs. Tc peak F = 78,754,162; a signal-to-noise ratio of 164,000:1). Monte Carlo simulations (L = 16, 32, 64, 128; 8 observables including the Binder cumulant Uâ and multi-body correlation functions) successfully detect the Tc break in all sizes; all cross-size candidate peaks are excluded by the criterion of F-value decay with increasing lattice size. Curvature artifact tests confirm that Chow F for a smooth sigmoidal curve does not diverge with sample size, maintaining a stable ~11-fold gap from the true break. Robustness (4 items): Under 10% Gaussian noise, Chow F remains at 22.3. F-values grow strictly monotonically with sample size (100 â 1,000: 11,436 â 118,074), confirming genuine physical signal characteristics. F-values grow overall with lattice size L (L = 16 â 128: 170.9 â 289.2, Kendall Ď = 0.33), confirming qualitative consistency with Fisher Finite-Size Scaling theory. Detection accuracy remains invariant under anisotropic conditions. Physical Scaling (3 items): Chow F(h = 0) establishes a strictly monotonic mapping with the order parameter M_spâF-values decay monotonically from 691 million at T â 0 to 55 at T â Tc, spanning 7 orders of magnitude and tracing the full lifecycle of the order parameter. This decay curve precisely mirrors the physical vanishing process of latent heat. The F-statistic's ~38-fold amplification effect is proven to originate from the quadratic structure of the F-statistic based on the sum of squared residuals (M²)âthe theoretical lower bound β_F / β_M ⼠2 is empirically confirmed (ratio 1.97 â 2), with the actual 38-fold amplification representing the composite contribution of the quadratic structure and residual difference structure. This algebraic guarantee proves that the amplifier property of F is an intrinsic feature of its mathematical structure, not a sampling accident. Interaction R² peaks at Tc at 0.9992 (deviation 0.03). Core Theoretical Contributions: Contribution 1: Informational duality between the Factor Hierarchy Law and the Ehrenfest classification. This paper rigorously proves two distinct regime-switching topologies with fundamentally different statistical signaturesâ"Rule-Reset" (interaction-dominated, p = 0.000, ÎR² = 0.991) and "Direction-Reversal" (intercept-jump-dominated, interaction p = 0.978). Rule-Reset maps precisely onto Ehrenfest's second-order phase transition, and Direction-Reversal maps precisely onto Ehrenfest's first-order phase transition. This correspondence is not an empirical coincidence, but a functional dualityâa bijective informational mapping exists between the calculus operations on the thermodynamic potential (âG/âh, â²G/âT²) and the statistical operations of regression geometry (Î Intercept, Î Interaction Slope). The Factor Hierarchy Law independently arrives at all conclusions of the Ehrenfest classification purely through regression analysis of observational data, without any knowledge of the Free Energy function. Contribution 2: Chow F-statistic as an informational proxy for the order parameter and an early-warning signal. This paper discovers and proves that Chow F(h = 0) is a statistical proxy variable for the thermodynamic order parameter M_spâtheir relationship is not a linear mapping, but a nonlinear high-gain amplification guaranteed by the quadratic structure (M²) of the F-statistic. The 38-fold amplification effect has been confirmed through algebraic root analysis. This enables Chow F to serve as a more sensitive early-warning signal than the order parameter itself in complex systems where the order parameter is difficult to measure directly. The complete decay curve of F(h = 0), which monotonically attenuates to zero at Tc with rising temperature, provides a definitive statistical proxy for the vanishing of latent heat. Contribution 3: Interaction R² as a precise proxy for second-order transition intensity. Interaction effect incremental R² peaks at Tc at 0.9992, with a deviation of only 0.03. This provides a precise quantitative metric for the "Rule-Reset" switching topology within the Factor Hierarchy Law. Methodological Contribution: This paper completes a "Severe Test" (sensu Deborah Mayo) of the Quadruple Test, establishing both the sensitivity (all positive controls passed) and specificity (all negative controls passed) of the methodology. A total of 22 independent verification checkpointsâspanning five dimensions (9 positive controls, 4 negative controls, 4 robustness checks, 2 statistical rigor checks, and 3 physical scaling checks)âare all passed. The analytical proof further confirms that the localization error of the method is strictly zero in the analytical limit. Cross-Disciplinary Integration: Together with the interest-rate-spread regime switch discovered by Tang (2026aâ2026f) across five major financial markets (institutional systems), the Tang Break (a five-dimensional stellar regime boundary at 4762 K) discovered by Tang (2026h, 2026i, 2026j) across five independent astronomical dimensions (physical observation systems), and the informational duality proven in this paper on a first-principles physics model, the Factor Hierarchy Law has now received evidential support from three completely independent disciplines. This paper provides the physics cornerstone for the Lawâproving that the hierarchical structure of Rule Factors and Execution Factors, and the critical behavior of regime switches, are not accidental products of data noise, but an informational dual of thermodynamic symmetry-breaking structures, a universal principle by which complex systems self-organize. Much like the historical realization that information-theoretic entropy reflects thermodynamic states, this paper demonstrates that regression variance partitioning serves as a direct informational proxy for physical symmetry structures.
This paper develops a mathematical framework for modeling Bitcoin price dynamics through a system of coupled stochastic differential equations (SDEs). We capture the complex nonlinear interactions between Bitcoin price and five key factors: investor sentiment, trading volume, mining hashrate, transaction fees, and transaction counts. The model incorporates jump processes to account for sudden price movements and regime-switching to capture state-dependent dynamics. We derive the resulting partial differential equations for derivative pricing and analyze the system's behavior through simulation. Our empirical findings suggest significant feedback mechanisms between network metrics and price dynamics, with hashrate exhibiting the strongest correlation with price movements. The framework provides a foundation for understanding the complex, non-linear, and fractal-like behavior observed in cryptocurrency markets while enabling the pricing of derivatives in this emerging asset class.
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.
This paper presents an open-economy macroeconomic equilibrium model for Proof-of-Stake (PoS) networks with fee-burn mechanics (EIP-1559) that formalizes the strategic interplay between a Kelly-optimizing rational institutional investor and a utility-driven retail consumer. We analyze network dynamics across two behavioral regimes. In The Unbounded Accumulation Model, the consumer purely accumulates tokens, creating an exclusive buy-side pressure that interacts with institutional portfolio rebalancing to fuel an ever-expanding speculative bubble and generate compounding excess returns for investors. Conversely, in The Utility-Consumption Model, the consumer dynamically buys and sells tokens to balance crypto wealth against real-world fiat consumption. Within this framework, we derive an explicit steady-state equilibrium price for ETH, demonstrating how token valuation anchors to a stable fundamental baseline that scales directly with network adoption while completely dissolving the institutional yield premium. Our numerical simulations show that while exogenous traditional finance (TradFi) shocks propagate through portfolio rebalancing to drive high token price volatility, network inflation remains highly stable. Furthermore, we prove that network security is insulated from institutional monopoly by counter-cyclical consumer behavior. Our findings reveal that institutional excess wealth creation in PoS ecosystems is not native to the staking protocol itself, but is strictly driven by the leveraged extraction of the retail consumer's continuous demand for transactional utility.