This preprint develops a unified thermodynamic and game-theoretic framework for the analysis of monetary systems, with particular focus on Bitcoin as a proof-of-work-based digital monetary architecture. The work combines concepts from thermodynamics, information theory, game theory, monetary economics, and econophysics to investigate how monetary systems may be understood as coordination systems operating under informational, institutional, and physical constraints. The manuscript introduces a distinction between monetary entropy, associated with uncertainty in monetary issuance, layered claims, and purchasing-power instability, and physical entropy generated through irreversible energy dissipation in proof-of-work systems. Building on this distinction, the concept of monetary temperature is proposed and operationalized through purchasing-power volatility and related coordination variables. Within this framework, Bitcoin is interpreted as a thermodynamically enforced Nash-equilibrium system in which strategic stability is constrained through irreversible physical cost. Comparative analysis of Bitcoin, gold, and fiat monetary systems suggests that monetary architectures can be understood as evolving entropy-management architectures adapted to different technological and civilizational conditions. Finally, the paper proposes an evolutionary interpretation of monetary history in which monetary systems function as mechanisms for stabilizing large-scale human cooperation under increasing informational complexity. Monetary evolution is interpreted as a cooling process in which declining volatility corresponds to increasing coordination maturity and stabilization across expanding economic networks. Keywords: Bitcoin, thermodynamics, Nash equilibrium, monetary entropy, entropy-management architectures, proof-of-work, econophysics, monetary systems, monetary temperature, game theory.
ABSTRACT This paper examines the relationship between skewness and kurtosis in Bitcoin spot and futures markets using highâfrequency data. We document a strong convex skewnessâkurtosis relationship consistent with theoretical moment restrictions. Trading activity is positively associated with realized kurtosis, particularly in futures markets, though sensitive to specification and driven by extremeâreturn episodes. Allowing the relationship to evolve over time reveals substantial curvature variation, indicating stateâdependent higherâmoment dynamics. The close coâmovement of results across markets suggests patterns reflect broad marketâwide conditions. The empirical framework is reducedâform and results should be interpreted as conditional associations rather than causal effects.
Maximal Extractable Value (MEV) in decentralized finance (DeFi) enables searchers to profit from transaction ordering and arbitrage opportunities across Automated Market Makers (AMMs). Among MEV strategies, atomic triangular arbitrage is widely deployed due to its deterministic execution within a single transaction. However, executing profitable arbitrage under realistic constraints, such as limited wallet balance, pool liquidity, gas costs, and blockchain latency, remains a challenging optimization problem. In this work, we formulate atomic triangular arbitrage as a constrained optimization problem that jointly selects an ordered three-pool path and trade amount to maximize net profit. To solve this non-convex problem, we propose a Deep Reinforcement Learning approach based on Proximal Policy Optimization (PPO). Experimental results show that while exhaustive grid search attains the highest returns, it requires a significantly high amount of inference time, making it infeasible for on-chain execution. In contrast, the proposed PPO agent achieves millisecond-level inference latency while generating consistent positive profit. These findings highlight a fundamental speedâprofit trade-off in MEV extraction and demonstrate that PPO provides an effective and practical solution for atomic triangular arbitrage in DeFi.
Jeong-Hyuck Park, Chanhee Park, Claudio J. Tessone, Yu Zhang
Digitalisation transforms money from distinguishable physical objects into fungible informational units. A recent theoretical framework predicts that such indistinguishable wealth obeys bosonic occupancy statistics, leading to geometric ownership distributions and enhanced inequality. Using Bitcoin blockchain data, we test this prediction on 63 UTXO denominations across 72 monthly snapshots (2018--2023). A one-parameter geometric model describes the ownership distributions, reproducing both mean holdings and their temporal evolution; Jensen--Shannon divergence values lie below $0.08$ in $99.74\%$ of cases. The inferred inverse-temperature parameter satisfies the analytic mean--temperature relation to better than $0.1\%$ in every sample -- a self-consistency test that two-parameter alternatives cannot pass -- and remains within a narrow band across eight orders of magnitude in denomination and over six years. Bitcoin UTXO ownership statistics are therefore consistent with bosonic occupancy laws, suggesting that the informational nature of electronic money may act as a structural driver of inequality in digital economies.
The Landauer principle motivates the definition of economic temperature as the monetary price of processing a bit irreversibly. No empirical test of this definition exists in transparent fee markets. This paper fills that gap using daily Bitcoin and Ethereum data, constructing canonical thermodynamic state variables and evaluating five diagnostic layers: state variable behavior, Maxwell-type integrability, Carnot-style efficiency bounds, nonlinear regime separation, and structural break sensitivity to protocol events. Bitcoin's log-temperature behaves as a persistent mean-reverting process with an AR(1) coefficient of 0.97 and a half-life of 21 days; Ethereum is highly persistent, with weaker formal evidence of stationarity than Bitcoin. Maxwell integrability is frequency-dependent: Bitcoin passes all four relations at monthly frequency, whereas Ethereum passes two of four. Carnot-style evidence is the strongest: realized fee extraction efficiency stays well below the implied bound, with daily compliance exceeding 97% on both chains. Structural breaks around Bitcoin ordinals, EIP-1559, the merge, and Shanghai confirm that protocol changes reorganize the temperature relation. The thermodynamic framework provides structure that standard fee market analysis does not, including a first principles efficiency bound and a state space coherence test. The findings provide partial, frequency-dependent, and chain-specific empirical support for a Landauer-based thermodynamic description of blockspace markets.
This paper introduces a heterogeneous macroeconomic model of a Proof-of-Stake (PoS) network to analyze the long-term centralizing effects of external traditional finance (TradFi) yields. We model a continuum of rational actors divided into two distinct classes: investors, who optimize portfolios between staking and external variance-dominated investments, and consumers, who balance staking yields against the transactional utility of holding liquid assets. By employing a quasi-linear utility function to model consumer behavior, we derive a cubic polynomial that strictly defines the unique macroeconomic equilibrium of the coupled network. The model demonstrates that, at scale, external macroeconomic factors force the complete institutional capture of the PoS consensus layer. Because investors have access to external risk premiums, their wealth compounds exponentially, leading to massive capital inflows that crush the protocol's internal staking yield to effectively zero. We show that as the yield is crushed, consumer wealth becomes strictly upper-bounded. Ultimately, consumers are forced to cease staking entirely and hold all remaining wealth in liquid form to satisfy their transactional constraints.
ThemeThe convergence of Artificial Intelligence (AI), Quantitative Finance, and Blockchain technologies is reshaping how capital is analyzed, deployed, and optimized across both traditional and decentralized markets.
Automated Market Makers (AMMs), as a core infrastructure of decentralized finance (DeFi), uniquely drive on-chain asset pricing through a deterministic reserve ratio mechanism. Unlike traditional markets, AMM price dynamics is triggered largely by on-chain events (e.g., swap) that change the reserve ratio, rather than by continuous responses to off-chain information. This makes event-level analysis crucial for understanding price formation mechanisms in AMMs. However, existing research generally neglects the micro-structural dynamics at the AMMs level, lacking both a comprehensive dataset covering multiple protocols with fine-grained event classification and an effective framework for event-aware modeling. To fill this gap, we construct a dataset containing 8.9 million on-chain event records from four representative AMMs protocols: Pendle, Uniswap v3, Aave and Morpho, with precise annotations of transaction type and block height timestamps. Furthermore, we propose an Uncertainty Weighted Mean Squared Error (UWM) loss function, which incorporates the block interval regression term into the traditional Temporal Point Process (TPP) objective function by weighting the uncertainty with homoscedasticity. Extensive experiments on eight advanced TPP architectures across four representative DeFi protocols demonstrate that this loss function reduces the time prediction error by an average of 31.17% while maintaining the accuracy of event (transaction) type prediction, establishing a robust benchmark for event-aware prediction in the AMMs ecosystem. This work provides the necessary data foundation and methodological framework for modeling the discreteness and event-driven characteristics of on-chain price discovery. All datasets and source code are publicly available. https://github.com/finbrain-lab-hkustgz/Deep-AMM-Events
A central question of the Ethereum ecosystem is where Maximal Extractable Value (MEV)revenue originates and to what extent it stems from harming unsuspecting users. It is acceptable if MEV arises from arbitrages between centralised and decentralised exchanges (CEX-DEX). Yet theoretical models have significantly underestimated the scale of these arbitrages, while empirical studies have highlighted their importance - though these remain conservative estimates, constrained by numerous debatable heuristic assumptions. Revisiting the theoretical model, we found that CEX-DEX arbitrages require trading volumes on the order of the total activity of major liquidity pools and yield profits comparable to MEV. Most prior AMM models utilised the Black-Scholes (BS) stochastic differential equation (SDE) - i.e., geometric Brownian motion - and assumed continuous price trajectories where asset prices move in small increments only.We argue that BS underestimates arbitrage profits by ignoring price jumps, which are precisely the points at which arbitrage opportunities tend to arise. To address this gap, we present an extended discrete-time AMM model in which the price process is the sum of a diffusive component and stochastic jumps that can have arbitrary noise distributions. Although mathematically more involved this framework allows us to employ a general discrete-time SDE and compute the stationary probability distribution via function iteration with geometric convergence. We further prove that the resulting mispricing process is an ergodic Markov chain. We implement our model in C++, collect spot prices and AMM exchange data from the Ethereum blockchain and fit the model parameters to the observed prices. The estimates derived from our model closely match empirical observations and provide a natural theoretical explanation for several fundamental questions in the blockchain ecosystem.
Version: v1.6.4 (June 2026) Major additions in this version: phased migration protocol with cryptographic quarantine (Section 6.4.4), sensitivity boundaries delineating the statistical decoupling threshold up to mu = 1.9% (Section 6.7), and integration of recent empirical MEV findings (Mancino & Rezzoli, 2025). Abstract Contemporary blockchain architectures face a critical impasse defined herein as the "Tetra-Lemma"âa four-dimensional optimization problem encompassing decentralization, security, scalability, and thermodynamic sustainability. Legacy Proof-of-Work networks confront diminishing security budgets due to the exhaustion of block subsidies, while Proof-of-Stake systems inherently risk oligarchic centralization. This paper establishes a Unified Monetary-Supply Framework that resolves these structural conflicts by synthesizing the deterministic Customized Halving schedule with the probabilistic regeneration logic of the Proof of Rinne (PoR). We demonstrate that by enforcing a "Thermodynamic Statute of Limitations" on dormant assets, the protocol functions as a Non-Equilibrium Thermodynamic Engine. This architecture transforms entropic asset attritionâtraditionally viewed as systemic lossâinto a regenerative security budget. The remainder of the abstract, covering the SDE and Fokker-Planck validation, the ZKP owner recovery model, and the resulting equilibrium, is in the manuscript. Data & Code AvailabilityThe mathematical models and high-precision stochastic simulations (e.g., Monte Carlo paths, SDE convergence, and Fokker-Planck distributions) presented in this manuscript are fully reproducible. The corresponding Python simulation suite and open-source models are made available at the author's GitHub repository (rincoin-regenerative-simulations) to ensure scientific transparency. Integrity & Provenance This document is anchored to the Bitcoin blockchain via OpenTimestamps. The proof file verification_data_v1.6.4.ots, included in the files below, covers the SHA-256 digest of Tokino_Rincoin_v1.6.4.pdf: 5269207ea7e363e8df312ed50c00afc119b43e6fa5d3c717e6a7d8fc9863147b The archived proof is in its as-submitted form: it commits the digest to the public OpenTimestamps calendars and does not itself embed the Bitcoin attestations. Completing it against those calendars â which both verification paths below do automatically â yields three Bitcoin attestations, the earliest in block 952366. An OpenTimestamps proof carries no wall-clock time of its own â any date reported for it is read from a Bitcoin block header. To verify, upload the PDF and the .ots file to opentimestamps.org, or with a Bitcoin node: ots verify -f Tokino_Rincoin_v1.6.4.pdf verification_data_v1.6.4.ots â the -f flag is required because the proof's filename differs from the document's. The provenance of this document is recorded in a separate signed artifact, the Rincoin Provenance Certificate (10.5281/zenodo.21415730), which binds this whitepaper to the digest above and is the reference for the full anchoring detail. That certificate carries its own OpenPGP signature, Bitcoin anchor, and PAdES signature; this whitepaper itself carries the OpenTimestamps proof only. Zenodo archival gives this record a persistent identifier and an independent retrieval path; it is not itself a cryptographic control. Validation_Scientific_Provenance_v1.6.4.pdf in the files below is an earlier certificate edition, retained as evidence. It is superseded by the record cited above. Correspondence & AffiliationPrimary Author: Tokino, Michiru (æäč æș)Affiliation: Rincoin Core Research Academic Inquiries: edu@aevust.org Community Governance: @aevustus (Discord) / @aevust (X/Telegram) Keywords: Rincoin, Proof of Rinne (PoR), regenerative crypto-economics, non-equilibrium thermodynamics, non-equilibrium steady state (NESS), stochastic differential equations (SDE), Fokker-Planck equation, recirculation incentive mechanism, macroeconomic homeostasis, Nash equilibrium, cryptographic vault, zero-knowledge proofs (ZKP), modular blockchain architecture, account abstraction, blockchain tetra-lemma, MEV mitigation, sandwich attack resistance, sensitivity analysis, statistical decoupling threshold, phased migration protocol
Employing a time-varying multifractal approach, we highlight the influence of political narratives and speculative expectations surrounding the second presidency of Trump on Bitcoin efficiency. Bitcoin exhibits persistent dynamics, deviating from the ideal efficiency benchmark. During the anticipation of Trumpâs victory, Bitcoin returns became more predictable (less efficient) due to narrative-driven speculation and arbitrage, whereas during his presidency, efficiency increased, reflecting institutional adoption and favorable regulations. In recent months, Bitcoin has regained its natural balance, with efficiency converging to levels observed in non-speculative periods. Thus, U.S. political narratives function as mechanisms of speculative market arbitration, distorting efficiency while favoring decentralized assets.
Decentralized finance (DeFi) systems currently rely on static parameters and reactive mechanisms that fail to adapt to rapidly changing market conditions. These limitations contribute to systemic inefficiencies including yield instability, capital fragmentation, and the extraction of value through adversarial mechanisms such as maximal extractable value (MEV). This paper introduces The Aeon Protocol, a control-theoretic framework for adaptive financial infrastructure. The protocol models decentralized liquidity management as a closed-loop control system in which economic variables are continuously monitored, predicted, and regulated through feedback mechanisms derived from classical control theory. The Aeon architecture integrates four primary system layers: âą KENDRA â predictive forecasting and regime detection from on-chain data streamsâą NOEMA â model predictive control for economic orchestrationâą AURA â ethical routing layer that captures and redistributes MEV through sealed-bid auctionsâą LEIA â liquidity management engine governing protocol-owned liquidity across decentralized markets At the core of the system is a PID-controlled adaptive yield mechanism designed to regulate total value locked (TVL) and stabilize protocol yield within bounded ranges. A complementary Burn-and-Mint Equilibrium (BME) mechanism dynamically adjusts token supply to maintain long-term economic balance. A central implication of the Aeon architecture is the emergence of a self-reinforcing liquidity ecosystem. By integrating predictive forecasting, control optimization, and ethical MEV capture into a closed-loop economic system, the protocol continuously identifies inefficiencies in decentralized markets and redirects the associated value back into the protocolâs liquidity layer. This process transforms otherwise extractive market dynamics into a productive feedback cycle, where captured value is redistributed through liquidity provisioning, treasury reserves, and reflection mechanisms. Empirical simulations and historical replay experiments demonstrate that this feedback architecture materially increases capital utilization across the system. In controlled Monte Carlo simulations spanning 10,000 market scenarios, the protocol achieved improvements of 50â180% in capital efficiency, while redirecting approximately 68% of extractable value to protocol participants rather than external arbitrage actors. These results suggest that adaptive control systems can convert structural market inefficiencies into a persistent source of liquidity and yield generation, enabling decentralized financial networks to operate as self-regulating economic environments rather than static rule-based infrastructures. Formal analysis establishes asymptotic stability conditions for the controller using the RouthâHurwitz criterion and Lyapunov stability methods, providing theoretical guarantees that the system converges toward equilibrium under defined parameter constraints. Collectively, the results demonstrate that control-theoretic economic architectures can provide a principled foundation for designing stable, transparent, and adaptive decentralized financial infrastructure. The Aeon Protocol represents a broader research direction toward autonomous economic systems, where financial networks operate as self-regulating feedback environments capable of maintaining equilibrium under dynamic market conditions.
Samet GĂŒnay, Kata VĂĄradi, NĂłra Felföldi-SzƱcs
Abstract This study examines bubble dynamics in the S&P 500 Index and Bitcoin, with particular emphasis on the role of gold as a proxy for market-wide stress. We apply the GSADF bubble test, time-varying Granger causality, and multifractal detrended fluctuation analysis to both original and gold-filtered price series. The results reveal a pronounced asymmetry between equity and cryptocurrency markets. Bitcoin exhibits statistically significant and persistent bubble behavior in both raw and filtered data, accompanied by multifractal persistence consistent with self-reinforcing speculative dynamics. In contrast, the S&P 500 shows no consistent evidence of sustained bubble behavior, and its multifractal properties remain aligned with short memory and rapid information absorption. The causality analysis indicates a stable, state-dependent predictive relationship from gold to equity prices, suggesting sensitivity to global risk sentiment, while no comparable persistent linkage is observed for Bitcoin. Overall, the findings suggest that equity price dynamics remain connected to market-wide stress conditions, whereas Bitcoinâs behavior appears to be driven primarily by asset-specific speculative forces.
The stability of global financial markets is increasingly threatened by rapid liquidity cascades, manifesting empirically as instantaneous "Flash Crashes." Current quantitative risk models, such as Value-at-Risk (VaR) and the Efficient Market Hypothesis (EMH), assume continuous liquidity and treat extreme volatility as probabilistic statistical anomalies based on historical distributions. These models fundamentally lack a deterministic, geometric boundary for limit-order book coherence. This paper introduces a strict topo-dynamical framework for financial network scaling. By modeling the market structure as a spatial competition between the geometric propagation of liquidity and localized volatility shocks, we derive a universal square-root geometric invariant (âmarket). We provide an intuitive translation of this threshold, explicitly dissect the failure of VaR during the May 2010 Flash Crash, and map the invariant across both traditional equities and Decentralized Finance (DeFi) Automated Market Makers (AMMs). Finally, we present a hardware-aware (FPGA) blueprint for Active Liquidity Throttling (ALT), acknowledging systemic implementation risks and regulatory hurdles.
FUNDAMENTAL LAW OF REALITY: TERNARY SYNTHESIS OF MATHEMATICS, PHYSICS, AND HISTORY Version 11.0 (Complete Synthesis with Structural Proof of Fermat's Last Theorem) This paper presents an algorithmic system discovered by the author during many years of analyzing price movements in financial markets. Four software modules written in MQL4 revealed a universal ternary hierarchical structure possessing Zâ-symmetry. From the code analysis, the fundamental group Zâ Ă Zâ, generating 9 basic relations, and the formula for the number of intersection points in the hierarchy, P = N â 2K, were derived. The discovered structure has proven to be universal across various fields of knowledge: Mathematics: Zâ Ă Zâ is isomorphic to a subgroup of SU(3) and the nilpotent ring â[x,y]/(xÂł, yÂł); the system's fractal dimension is D = log 3 / log 2 â 1.585. Number Theory: The synchronization parameter Ï = 0 at the non-trivial zeros of the Riemann zeta function is equivalent to the Riemann Hypothesis, numerically confirmed on 4153 zeros (100% match). Physics: Zâ Ă Zâ â SU(3) describes the color symmetry of Quantum Chromodynamics; the 9 compactification moduli of string theory correspond to the 9 system relations; the Ï = 0 state is interpreted as a transition to 11-dimensional M-Theory. History: Using an inverse problem method on 251 key dates, the reference points Tâ = â5502, Tâ = â5501, Tâ = â5500 were determined. The formula D = Tâ + 3k + s describes all key historical events. Four epochal points (â5502, â3315, â1128, 1059) mark shifts in civilizational cycles. Verification on over 12,000 dates and a blind test of 20 dates yielded 100% accuracy. Markets: On BRENT oil data (1998â2026), 4 convergence points (2005, 2011, 2018, 2025) were found with an 81-month interval, corresponding to the historical epochal points. Geopolitics: 20 key events of 2025 correspond 100% to the model's predictions for zones s=0,1,2. Fermat's Last Theorem: A structural explanation is derived through the formula P = N - 2K: for n > 2, the hierarchy depth K â„ 2 leads to a critical shortage of intersection points for synchronizing three independent circuits (x, y, z). A physical analogy is drawn with quark confinement in quantum chromodynamics. The cumulative statistical significance of all confirmations is p < 10â»âčÂłâ”, which excludes random coincidence. The system is fractally invariant and works identically at any time scale (from minute charts to millennia). The source code (4 MQL4 modules + Python implementation) is available upon request for non-commercial research under the CC BY-NC-ND 4.0 license. Keywords: ternary hierarchy, Zâ Ă Zâ, intersection points, Riemann Hypothesis, Fermat's Last Theorem, SU(3), string theory, M-theory, historical periodization, fractals, algorithmic realism, power law distribution, confinement.
With distributed financial microservices, the DualWrite problem frequently results in data discrepancy between payment gateways and in-house ledgers. Conventional reconciliation schemes are based on high-latency batch reconciliation or hard-coded rules, and cannot identify Soft Drifts, small corruptions in the data (e.g. 3% deviation) that resemble normal variance. The paper suggests a real-time reconciliation model that combines an Apache Kafka streaming high-throughput system and an Unsupervised Isolation Forest anomaly detector. The experimental outcomes have shown that although the application of static rules resulted in a Recall rate of only 52.1% (it does not detect soft drifts), the offered AI model attained 100% Recall in all types of drifts. Moreover, the system had a consistent latency of 3.76 ms which was found to be viable in high-frequency trading settings where low-latency and data integrity are of utmost importance.
The rapid growth of cryptocurrency markets has created new challenges in understanding and predicting the structural dynamics of digital asset prices. Bitcoin, as the most traded blockchain-based currency, exhibits extreme volatility, nonlinear patterns, and complex regime shifts that traditional financial models cannot adequately capture. This study proposes a hybrid analytical framework that integrates K Means clustering with the Hidden Markov Model to identify and model multiple market regimes in Bitcoin time series data. The Bitcoin dataset used in this research contains minute-level records that were preprocessed to extract key indicators, namely logarithmic returns and rolling volatility, which represent the short-term dynamics of market behavior. The K Means algorithm was first employed to segment the data into three distinct clusters that correspond to bullish, bearish, and sideways regimes, followed by the application of the Hidden Markov Model to estimate probabilistic transitions between these regimes over time. The results reveal that the hybrid K Means and Hidden Markov Model approach achieves superior performance compared to a standalone model, as indicated by a higher log likelihood and a lower Bayesian Information Criterion value. The transition probability matrix shows that bullish and bearish regimes are highly persistent, while the sideways regime acts as a transitional buffer that connects both market extremes. The empirical findings confirm that Bitcoin prices evolve through persistent and probabilistically determined regimes rather than random fluctuations. The proposed framework provides a more comprehensive understanding of cryptocurrency market dynamics and offers practical value for investors, risk analysts, and policymakers in designing adaptive trading and risk management strategies within blockchain-based financial ecosystems.