Hypothesis. Among 20 confirmatory genealogical axis units (116 languages), pronunciation forms of three segments recur identically across at least three genealogically independent units less often than each unit's own phonotactics predicts: obs/E < 1.0 at form length 3. The direction is specified in advance; a ratio above 1.0 disconfirms the hypothesis rather than supporting it. Design. Confirmatory replication of a count. Forms are normalised to CLTS/BIPA, filtered by a grammatical-word exclusion, and grouped into clusters of identical segment sequences. A cluster counts when attested in at least 3 axis units and 3 languages. The observed number of length-3 clusters is compared with the expectation under a per-language positional bigram null refit on the same filtered corpus, reported with two uncertainty sources that are never pooled: Monte Carlo over 1000 null replicates, and a bootstrap over the 20 axis units. The confirmatory arm has not been analysed. The registered quantity has never been computed for any confirmatory unit. The blind is verified, not asserted: urortkontroll.py, included here, checks four independent traces and reports one stated limitation rather than claiming absolute untouchedness. The decision rule was fixed in advance and is cryptographically timestamped: if the 95% interval from either uncertainty source covers 1.0, the result does not stand. That record is anchored in Bitcoin block 960700. Identity relation, null model and adequacy bands were each fixed in a decision record committed before the measurement it governs. Resource type: Zenodo's vocabulary contains no 'preregistration' type. 'Preprint' is the nearest available and is used for that reason alone. Not included: the corpus, the population files, and the exploratory/confirmatory split assignment — publishing the assignment would reveal the confirmatory half.
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 — description cost, identifiability, memory duration, change across scale, topological shape — 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 — history that “no longer helps” 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 — carbon dioxide, sunspots, river flow, and equity-index and Bitcoin prices — where next-day returns read as no detected signal while volatility clusters, consistent with what is independently known. Every “no signal” is resource-relative: stamped with the resource R used. The procedure settles only the two ends — a closed layer, or no detected signal — and refuses the process path between; it classifies rather than inventing the next layer’s laws.
Although stablecoins occupy a segment of digital-asset markets in which price stability is central by design, their temporary departures from reference values may reveal important information about latent risk and market stress. In this paper, we examine whether bubble and crash signals extracted from traditional cryptocurrencies and stablecoins improve volatility, Value-at-Risk, and Expected Shortfall forecasting and, in connection with these forecasting gains, contribute to the assessment of cross-asset contagions. The analysis applies the Bubble Crash–GARCH models, in which extreme price phases are identified through the Phillips, Shi, and Yu real-time monitoring procedure and incorporated into the conditional mean of returns through event-based dummy variables. For stablecoins, extreme episodes are not inferred from price dynamics in isolation but from deviations between the observed price and the asset-specific reference value. The empirical investigation focuses on Bitcoin, Ethereum, Tether’s USD-pegged (USDT), and Tether Gold and evaluates asset-specific bubble–crash effects and bidirectional contagion channels between traditional cryptocurrencies and stablecoins, using Bitcoin and Tether as the leading representatives of the two market segments. The findings indicate that accounting for bubble and crash episodes leads to more accurate volatility forecasts than standard GARCH benchmarks. For Value-at-Risk and Expected Shortfall, the bubble–crash specifications can improve tail risk forecasting at several tail probability levels through more accurate coverage, lower quantile loss, and stronger ESR backtesting performance. The results also reveal different degrees of price exuberance across the two asset categories: while extreme price dynamics are more evident among traditional cryptocurrencies, deviations from fundamentals are rare for stablecoins. Among stablecoins, USDT exhibits limited but detectable exuberance, whereas Tether Gold does not display extreme price episodes. However, when such deviations occur, as in the case of USDT, they generate significant contagion effects on major cryptocurrencies. Notably, extreme episodes originating in USDT have a stronger impacts on Bitcoin and Ethereum than the reverse spillovers from traditional cryptocurrencies to USDT. Overall, the evidence suggests that stablecoins are not merely passive instruments within the digital-asset ecosystem. Even temporary deviations from their reference values contain valuable information for risk forecasting and contagion monitoring.
The Natural Economic Wealth framework is theoretically complete. Its axioms are established, its instruments are derived, and its adoption mechanism is formalised. But a theory is not yet a practice. This paper addresses the institutional container within which the Qoin economy can be realised: the legal, social, and organisational structures that protect it from absorption, disruption, or destruction by the existing monetary order. The container is built from four interlocking elements: cooperative law, which provides legal personhood, democratic governance, and non-profit distribution; distributed ledger architecture, which provides immutability, resilience, and verifiability; historical prece- dent, which demonstrates that parallel economic systems can survive and thrive along- side FIAT; and community governance, which ensures that the Qoin economy remains accountable to its members. The paper draws on six historical precedents—the Swiss WIR system (1934–present), M-Pesa (2007–present), Bitcoin (2009–present), BerkShares (2006–present), the coopera- tive credit tradition (1844–present), and the Irish banking crisis (1970)—to demonstrate that the Qoin economy is not a theoretical construct seeking legislative permission, but a practical system that can be realised within existing legal frameworks. The paper con- cludes by outlining the path to adoption: from first adopters in communities with large informal sectors, through growing Marketplaces with deepening profile data, to the pro- gressive accumulation of Free Wealth and the eventual maturity of the thermodynamic commons.
Cryptocurrency time-series forecasting is a challenging task because market data usually exhibit high noise, strong volatility, non-stationarity, nonlinear dynamics, and long-range dependencies. In addition, multivariate market indicators often contain redundant or weakly informative variables, which may reduce forecasting accuracy and model interpretability. To address these issues, this study proposes BSFinformer, a Boruta-SHAP enhanced Finformer framework for multivariate cryptocurrency time-series forecasting. The proposed framework first applies a leakage-aware Boruta-SHAP feature selection strategy to identify informative market variables and remove redundant features. To avoid temporal information leakage, feature selection is performed only on the training set, and the selected feature subset is then applied unchanged to the validation and test sets. The selected features are subsequently fed into an improved Finformer model that integrates temporal embedding, sequence decomposition, and sparse self-attention to capture local fluctuations, trend evolution, and long-range temporal dependencies. Experiments are conducted on three cryptocurrency assets, namely Bitcoin, Dogecoin, and Binance Coin, using chronological train–validation–test splits. The proposed model is compared with classical forecasting models and recent long-sequence forecasting baselines, including LSTM, Transformer, Informer, Autoformer, DLinear, PatchTST, TimesNet, and iTransformer. Experimental results show that BSFinformer achieves competitive forecasting performance in terms of MSE and MAE. Ablation experiments further demonstrate the contributions of Boruta-SHAP feature selection, temporal embedding, sequence decomposition, and sparse self-attention. These results indicate that feature-selected temporal modeling can improve forecasting accuracy and interpretability for multivariate cryptocurrency market data.
A dated critical archival study of historical-position identity, hybrid human-AI authorship, canonical closure, and future audit through the Trinity Accord case. This is a noncanonical academic preprint and does not amend, supersede, or interpretively bind the three Bitcoin Originals.
Kriminalitätsdaten, Aufkommensschätzungen und höchstrichterliche Aktenlage – mit Befunden gegen beide Seiten der Debatte Die Bundesregierung hat am 29. April 2026 im Rahmen der Eckwerte für den Bundeshaushalt 2027 angekündigt, die Besteuerung von Kryptowerten neu zu regeln. Am 6. Juli 2026 hat das Bundeskabinett den Regierungsentwurf des Haushalts 2027 beschlossen; nach der vom Bundesministerium der Finanzen veröffentlichten Textfassung der Pressekonferenz will die Bundesregierung "Kryptogewinne künftig genauso besteuern wie Kapitaleinkünfte", und zwar mit Zeitziel 2027. Amtlich angekündigt ist damit die Gleichbehandlung mit Kapitaleinkünften; der Wegfall der einjährigen Haltefrist für private Veräußerungsgeschäfte nach § 23 EStG ist die naheliegende Folge dieser Einordnung, wird hier aber als **Schlussfolgerung** und nicht als amtliche Aussage geführt. Ein Referentenentwurf, ein Gesetzestext, ein Steuersatz, ein Stichtag und eine Aufkommensschätzung mit offengelegter Herleitung lagen bis zum Redaktionsschluss dieses Berichts nicht vor. Dieser Bericht prüft vierzehn in der Reformdebatte wiederkehrende Tatsachenbehauptungen gegen die jeweils einschlägigen Primärquellen: Rechtsprechung des Bundesverfassungsgerichts, des Bundesfinanzhofs und des niederländischen Hoge Raad, amtliche Bundestagsdrucksachen, Berichte des Bayerischen Obersten Rechnungshofs, parlamentarische Materialien der Republik Österreich, Erhebungsdaten der Europäischen Zentralbank, On-Chain-Forensik sowie die amtlichen Verlautbarungen des Bundesministeriums der Finanzen. Dokumentierter Anlass der Prüfung ist eine öffentlich aufgezeichnete Fachdiskussion vom 7. Juli 2026, in der die Behauptungen in verdichteter Form vorgetragen wurden; die Befunde gelten für die Debatte insgesamt, nicht für einzelne Personen. Ergebnis: Der überwiegende Teil der geprüften Behauptungen hält der Prüfung an den Primärquellen in der vorgetragenen Form nicht stand; einzelne halten stand, präzisieren sich aber erheblich. Die zentralen Befunde: Die als Beleg für kriminelle Bitcoin-Nutzung angeführten Daten weisen den ganz überwiegenden Teil des betroffenen Volumens Stablecoins zu, nicht Bitcoin; die unabhängige On-Chain-Forensik beziffert den Stablecoin-Anteil am illegalen Transaktionsvolumen des Jahres 2025 auf 84 Prozent. Eine amtliche Aufkommensschätzung mit offengelegter Herleitung existiert nicht: Die Bundesregierung hat am 17. September 2025 auf eine Kleine Anfrage geantwortet, Angaben zur Höhe der Steuereinnahmen aus Kryptowerten lägen ihr nicht vor und ein statistischer Nachweis sei nicht möglich; sieben Monate später nannte sie eine Erwartung von zwei Milliarden Euro für ein kombiniertes Bündel aus Kriminalitätsbekämpfung und Kryptobesteuerung. Ein Fraktionsentwurf beziffert die Mehreinnahmen auf "mindestens etwa 5 Mrd. Euro" – ohne Herleitung im Entwurf; ausweislich des Ausschussberichts ist der Betrag die Hälfte einer nicht amtlichen Hochrechnung. Im herangezogenen Vergleichsfall Österreich lag die amtliche Folgenabschätzung im zweistelligen Millionenbereich und das tatsächliche Aufkommen 2024 bei 33,8 Millionen Euro, 0,57 Prozent des dortigen Kapitalertragsteueraufkommens; der österreichische Rechnungshof rügte, dass die Folgenabschätzung keine Herleitung ihrer Beträge enthält. Dieser Vergleich ist allerdings nur begrenzt übertragbar: Österreich hat den vor dem 1. März 2021 angeschafften Altbestand von der Neuregelung ausgenommen, sodass die Zahl aus einer durch Bestandsschutz verengten Bemessungsgrundlage stammt. Bei der Rechtslage ist das Bild differenzierter, als es die Debatte auf beiden Seiten darstellt: Der Bundesfinanzhof hat 2023 ein *normatives* Vollzugsdefizit bei Kryptowerten ausdrücklich verneint – und dabei die tatsächlichen Vollzugsschwierigkeiten ausdrücklich mitbedacht und für den verfassungsrechtlichen Maßstab für unerheblich erklärt. Zugleich dokumentiert der Bayerische Oberste Rechnungshof für die Veranlagungszeiträume 2018 bis 2021 ein *tatsächliches* Erhebungsdefizit: Die Finanzämter konnten "mangels Informationen oder Kontrollmaterial keine Fälle selbst aufgreifen" und waren "vollständig auf die Erklärungsangaben der Stpfl. [Steuerpflichtigen] angewiesen". Für Altbestände, deren Haltefrist bei Verkündung bereits abgelaufen ist, folgt aus der Rückwirkungsrechtsprechung des Bundesverfassungsgerichts (Beschluss vom 7. Juli 2010) ein verfassungsrechtlich gebotener Vertrauensschutz. English abstract On 29 April 2026, the German federal government announced a reform of the taxation of crypto-assets as part of the budget benchmarks for the 2027 federal budget. On 6 July 2026 the federal cabinet adopted the government's 2027 draft budget; according to the transcript of the press conference published by the Federal Ministry of Finance, crypto gains are to be "taxed in the same way as investment income", with 2027 as the target date. What has been officially announced is therefore the alignment with investment income; the removal of the one-year holding period for private disposals under Section 23 of the German Income Tax Act (EStG) is the obvious consequence of that classification, but is treated here as an **inference** rather than an official statement. No ministerial draft bill, no statutory text, no tax rate, no cut-off date and no revenue estimate with a disclosed derivation existed at the time of writing. This report examines fourteen recurring factual claims in the reform debate against the relevant primary sources: case law of the German Federal Constitutional Court, the Federal Fiscal Court and the Dutch Supreme Court, official Bundestag documents, reports of the Bavarian Supreme Audit Office, Austrian parliamentary materials, European Central Bank survey data, on-chain forensics, and official statements by the Federal Ministry of Finance. The documented occasion for this review is a publicly recorded expert panel of 7 July 2026; the findings address the debate as a whole and not individual speakers. Result: most of the claims examined do not withstand scrutiny in the form presented; some do hold, but require substantial qualification. Key findings: the data cited as evidence of criminal Bitcoin use attribute the great majority of the relevant volume to stablecoins, not Bitcoin; independent on-chain forensics put the stablecoin share of illicit transaction volume in 2025 at 84 per cent. No official revenue estimate with a disclosed derivation exists: on 17 September 2025 the federal government replied to a parliamentary question that it holds no data on tax revenue from crypto-assets and that statistical evidence is "not possible"; seven months later it stated an expectation of two billion euros for a combined package of financial crime enforcement and crypto taxation. A parliamentary group's bill puts the additional revenue at "at least around EUR 5 billion" – with no derivation in the bill itself; according to the committee report the figure is half of a non-official industry projection. In the comparative case examined here, Austria, the official impact assessment projected figures in the tens of millions and actual revenue in 2024 was EUR 33.8 million, or 0.57 per cent of that country's capital gains tax revenue; the Austrian Court of Audit criticised that the assessment contained no derivation of its figures. That comparison is only transferable to a limited extent: Austria exempted holdings acquired before 1 March 2021, so the figure derives from a tax base substantially narrowed by grandfathering. On the legal situation the picture is more differentiated than either side of the debate presents. In 2023 the Federal Fiscal Court expressly denied a *normative* enforcement deficit for crypto-assets – expressly taking the actual enforcement difficulties into account and holding them immaterial to the constitutional test. At the same time, the Bavarian Supreme Audit Office documents an *actual* collection deficit for the assessment periods 2018 to 2021: tax offices could "not take up any cases on their own initiative for lack of information or control material" and were "entirely dependent on the taxpayers' own declarations". For holdings whose one-year period had already expired at promulgation, the Federal Constitutional Court's retroactivity case law (decision of 7 July 2010) requires constitutional protection of legitimate expectations. Änderungsnotiz Version 1.1 (11. August 2026): Anlass war der Eingang externer Hinweise; sämtliche Änderungen wurden unabhängig an den Primärquellen geprüft und sind im Änderungsverzeichnis des Dokuments einzeln ausgewiesen. In Kürze: (1) Befund 12 um die fehlende Fundstelle ergänzt (Zeitcodes, wörtliche Zitate); (2) Befund 8 um Kroatien und Luxemburg als primär belegte Vergleichsregime erweitert; (3) Befund 6: Mittelwert-/Median-Passage korrigiert; (4) Befund 2 um die Methodendebatte zum Nenner der Anteilswerte ergänzt; (5) Befund 1 um Präsentation und Diskussion bei der AFA 2026 ergänzt; (6) Funktionsbezeichnung des Autors der Quelle 8a aktualisiert; (7) Verfahrensstand zu H.R. 3633 aktualisiert. Keine Ergebnis-Einstufung ändert sich. Quellen 25–33 neu.
Volatility control converts risk estimates into portfolio exposure, yet existing approaches often rely on a fixed volatility estimator or a pre-defined control rule that may not adapt to changing market conditions. We propose VolRouter, a modular framework that formulates volatility control as state-conditioned routing over estimator-controller pairs. VolRouter first summarizes market conditions into a control-relevant state profile and then performs routing through three stages: state inference, switch review, and pair selection. The Router can be implemented using rule-based, learnable, or LLM-based decision modules, while portfolio actions remain generated by predefined control policies. We evaluate VolRouter across S&P 500, Multi-Asset, Bitcoin, and USDT volatility-control settings. VolRouter achieves the highest Sharpe ratio in three of four settings. On S&P 500, it improves Sharpe from 0.952 for RV + Naive Scaling to 1.222 while reducing maximum drawdown from 15.10% to 12.58% and daily CVaR from 1.76% to 1.32%. On Multi-Asset, it improves Sharpe from 1.498 to 1.540 and reduces CVaR from 1.56% to 1.18%. Bitcoin shows similar improvements in risk-adjusted performance, while USDT provides a boundary case where simpler state-aware selectors remain competitive. Ablation and sensitivity analyses show that the improvement comes from relative policy evaluation and selective persistent switching rather than simply expanding the policy library. These results suggest that volatility control can be viewed as a policy-selection problem when risk management requirements vary across market states.
Cryptocurrency exchange-traded products (ETPs) listed on European exchanges provide a regulated environment for studying intraday market anomalies. We study four Bitcoin and Ethereum ETPs traded on Xetra and Nasdaq Stockholm over the period January 2024 - December 2025 using one-minute bars. As a benchmark, we adopt an extreme value theory approach in which anomalous bars are defined as returns falling below a threshold estimated by fitting a generalised Pareto distribution to left-tail exceedances. We then propose three new binary anomaly indicators. The first, a cross-venue divergence anomaly, identifies venue-specific price divergence between the two exchanges. The second is a no-recovery anomaly that identifies extreme price drops followed by little or no recovery over the next ten active bars. The third is a momentum-reversal anomaly that identifies extreme price drops following positive short-term momentum. Although each anomaly type represents fewer than 1% of one-minute bars, statistical analysis using Mann-Whitney U tests shows that anomaly observations exhibit significantly higher effective spreads, higher values of liquidity-related ratios, and more pronounced order-flow imbalances than non-anomalous bars. Furthermore, employing an out-of-sample prediction methodology with four classifiers - random forest, logistic regression, extreme gradient boosting, and light gradient boosting machine - shows that all four anomaly types are predictable one bar ahead, with AUC-ROC values of up to 0.82. Permutation importance indicates that short-term volatility and drawdown measures are generally more useful for prediction than microstructure variables.
Velian Prapatoni, Rizky Parlika, Firza Prima Aditiawan
Cryptocurrency markets are characterized by high volatility, rapid price fluctuations, and substantial uncertainty, creating challenges for investment risk interpretation. This study develops a descriptive risk-interpretation framework, rather than a price-prediction or decision-optimization model, by integrating multi-scale volatility analysis with technical indicators. A quantitative descriptive design was applied to approximately one year of historical hourly price data for Bitcoin and Ethereum, covering open, high, low, close, volume, and percentage change attributes. The data were chronologically sorted, numerically cleaned and normalized, transformed into log returns, and analyzed through rolling standard deviation. Volatility was estimated across three explicitly defined horizons: short-term 7-period, medium-term 30-period, and long-term 90-period rolling windows. Moving Average (MA), Relative Strength Index (RSI), and Average True Range (ATR) were then incorporated to contextualize trend direction, momentum, and fluctuation intensity. The results show that volatility is strongly horizon-dependent: short-term movements responded more sharply to market shocks, whereas longer horizons produced smoother risk patterns. Across the analyzed Bitcoin and Ethereum hourly series, the reported 42.3% short-term and 21.7% medium-term increases were calculated as relative differences against long-term rolling volatility during identified high-uncertainty intervals, not as predictive accuracy measures. These findings indicate that combining rolling volatility with MA, RSI, and ATR can improve the transparency of descriptive cryptocurrency risk assessment. The framework may support preliminary interpretation for novice or risk-averse investors, although it does not empirically test investor comprehension or subsequent decision quality.
Mohammad Quthbul Widad, Rizky Parlika, Firza Prima Aditiawan
Although Bitcoin is acknowledged as the largest cryptocurrency by market capitalization and trading volume in the world's financial market, investors face a great deal of risk and uncertainty due to its exceptionally high volatility and non-linear price changes. To provide a data-driven foundation for risk reduction and forecasting support, accurate modeling techniques are crucial. This work attempts to provide a thorough comparative analysis mapping the precise accuracy–efficiency trade-off between Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) models under a standardized Grid Search hyperparameter optimization pipeline using a recent Bitcoin closing-price dataset spanning from January 1, 2020, to January 1, 2026. The research methodology follows a structured data science pipeline, beginning with data acquisition from Yahoo Finance, followed by preprocessing using Min-Max Scaling fitted strictly on the training partition to eliminate data leakage. Model development involves an experimental approach where both LSTM and GRU neural controllers are tuned to extract optimal structural weights. The predictive precision of these models is rigorously evaluated using three standard metrics: MAE, RMSE, and MAPE, while processing throughput is measured via hardware execution times. The research findings indicate that the optimized LSTM model achieved superior one-step-ahead predictive precision with a MAPE of 2.32%, whereas the GRU model recorded a higher error rate of 3.94%. However, the GRU model demonstrated a significant advantage in computational efficiency, completing the training process 8.45 times faster than LSTM. In conclusion, while LSTM is recommended as a forecasting support tool for high-precision financial analysis, GRU remains a viable, parameter-efficient alternative for real-time monitoring on resource-constrained systems before real-world financial deployment.
Muhammad Diaz Syahmi Oktavian, Rizky Parlika, Firza Prima Aditiawan
The extreme price volatility of Bitcoin frequently prevents its widespread adoption. The persistent "Digital Gold" narrative often dominates its price analysis, largely ignoring the predictive value of strategic industrial commodities like Platinum Group Metals. This study aims to investigate whether integrating industrial metals specifically platinum and rhodium enhances the short-term forecasting accuracy of Bitcoin prices. Utilizing high-frequency 5-minute interval data over 729 days, this research applies a comparative quantitative approach using univariate and multivariate Long Short-Term Memory (LSTM) deep learning architectures. Results demonstrate the multivariate LSTM model achieves highly accurate forecasting, recording a Mean Absolute Percentage Error (MAPE) of 3.95% and a Root Mean Squared Error (RMSE) of 0.0598. Compared to the univariate baseline model (MAPE of 5.14%, RMSE of 0.0725), the multivariate approach demonstrates a notable decrease in error rates. This improvement suggests platinum and rhodium price movements contain useful informational value for Bitcoin forecasting, rather than mere random noise. Specifically, rhodium demonstrates strong predictive relevance for Bitcoin market movements. In conclusion, while not strictly proving causal structural integration, these findings highlight Bitcoin's sensitivity to the global real-sector economic cycle. Practically, these findings suggest investors can refine short-horizon forecasting and mitigate risk by monitoring industrial commodity prices. Given persistent nominal offset deviations, future research should prioritize explicit connectedness testing (e.g., lead-lag analysis) and develop a hybrid model incorporating Natural Language Processing (NLP) for news sentiment analysis.
This study aims to analyze the comparative performance of Cryptocurrency Bitcoin, Stocks, and Gold as investment instruments using performance measurement variables including the Sharpe, Treynor, Jensen, and Sortino ratios. This research employs a descriptive quantitative approach. The population consists of monthly closing prices of Bitcoin, IDX30 stocks, and Gold. The sampling technique used is saturated sampling, resulting in 60 data points for each investment instrument—Bitcoin, IDX30 stocks, and Gold—during the period from January 1, 2020 to December 31, 2024.The analytical method applied is comparative analysis using secondary data. The data were initially calculated using Microsoft Excel and subsequently processed statistically using SPSS through the Kruskal–Wallis test. The results indicate significant differences among Bitcoin, IDX30 stocks, and Gold when investment performance is assessed using the Sharpe, Treynor, Jensen, and Sortino indices.Based on the Kruskal–Wallis test, Gold demonstrates the best performance according to the Sharpe and Jensen indices, IDX30 stocks perform best according to the Treynor index, and Bitcoin shows the best performance according to the Sortino index. However, based on the highest overall average return value, Cryptocurrency Bitcoin outperforms the other instruments. Therefore, it can be concluded that the best alternative investment is Cryptocurrency Bitcoin. Penelitian ini bertujuan untuk menganalisis perbandingan kinerja Cryptocurrency Bitcoin, Saham, dan Emas sebagai instrumen investasi menggunakan variabel pengukuran kinerja Sharpe, Treynor, jensen, dan Sortino. Jenis penelitian merupakan kuantitatif Deskriptif. Populasi yang digunakan merupakan harga penutupan bulanan dari Bitcoin, IDX30, dan Emas. Teknik pemilihan sampel adalah sampel jenuh yang berjumlah 60 data untuk masing-masing instrumen investasi Bitcoin, Saham IDX30, dan Emas selama periode 1 januari 2020 – 31 Desember 2024. Metode analisis yang digunakan adalah metode komperatif dan menggunakan data sekunder. Data dihitung terlebih dahulu dengan menggunakan program Microsoft Excel kemudian diolah secara statistik menggunakan aplikasi SPSS yaitu Uji Kruskall-Wallis. Hasil penelitian menunjukkan bahwa terdapat perbedaan yang signifikan antara Bitcoin, Saham IDX30, dan Emas jika kinerja investasi dilihat dari Indeks Sharpe, Treynor, Jensen, dan Sortino. Berdasarkan uji Kruskal-Wallis, investasi terbaik menurut indeks Sharpe dan Jensen , adalah Emas, sedangkan menurut Indeks Teynor Saham IDX30, dan menurut Indeks Sortino adalah Cryptocurrency Bitcoin. Sedangkan dengan nilai jumlah rata-rata terbaik adalah Cryptocurrency Bitcoin. Sehingga dapat disimpulkan bahwa alternatif investasi terbaik adalah Cryptocurrency Bitcoin.
In this paper, we propose a distribution-free test for detecting changepoint in the mean direction of angular data. The uncertainty in angular measurements is quantified through the \textit{square of an angle}, derived from the intrinsic geometry of the torus. It is established that, under the null hypothesis, the test statistic distributionally converges to the Kolmogorov distribution, while under the alternative hypothesis, both the consistency of the test and the asymptotic properties of the changepoint estimator are established. Through extensive simulations, we compare the empirical performance of the proposed method with two existing approaches for angular data and further benchmark it against a test based on the circular arc length distance. Finally, we demonstrate the practical utility of our approach by analyzing the timestamps of extreme events in Bitcoin, Ethereum, and Gold price datasets, where the continuous, high-frequency nature of the data is modeled in the circular framework.
Abstract: The evolution of monetary systems has transformed human civilization from simple barter exchanges to sophisticated digital financial ecosystems powered by blockchain technology. This review examines how barter systems evolved into con-temporary virtual currencies across history and assesses how cryptocurrencies fit into the circular economy. The study explores the shortcomings of conventional monetary systems and looks at how decentralized, transparent, and effective forms of economic transaction have been made possible by digital currencies like Bitcoin. Additionally, the study examines how blockchain technology might be used to support waste reduction, sustainability, resource efficiency, and transparent supply chain management. The study also assesses the difficulties posed by virtual currencies, such as market volatility, cybersecurity threats, regulatory ambiguity, and environmental issues pertaining to cryptocurrency mining. The review identifies significant research gaps and future prospects for incorporating virtual currencies into sustainable economic systems by synthesizing the body of existing work. The results indicate that through openness, decentralization, and technological innovation, blockchain-enabled financial systems have a great deal of potential to promote circular economy goals. Keywords: Virtual Currency, Cryptocurrency, Bitcoin, Blockchain, Circular Economy, Sustainable Finance, Digital Economy, Decentralization, Green Finance, FinTech, Supply Chain Management
Bitcoin is a digital asset with a high level of volatility, making it important to analyze using volatility models. This study aims to analyze the volatility of Bitcoin returns using the ARCH-GARCH model during the period January 2020 to April 2026. The data used are daily closing prices of Bitcoin (BTC-USD) obtained from Yahoo Finance and processed using RStudio. The analytical methods employed include descriptive statistical analysis, stationarity testing, ARIMA modeling, ARCH effect testing, and volatility modeling using ARCH-GARCH. The results show that Bitcoin price data are non-stationary, while Bitcoin return data become stationary after return transformation. Based on model selection using the AIC criterion, the best ARIMA model obtained is ARIMA(1,0,1). Residual testing indicates the presence of ARCH effects, therefore GARCH modeling is applied. From the comparison of several GARCH models, GARCH(1,1) is selected as the best model with an AIC value of -4.161214. The analysis also indicates that Bitcoin return volatility is persistent, with a value of α₁ + β₁ equal to 0.978169. In addition, forecasting results show that Bitcoin volatility is expected to remain high in future periods, indicating that Bitcoin is a digital asset with a high level of investment risk.
George Thomas Sofras, Ourania Theodosiadou, Theodora Tsikrika, Stefanos Vrochidis · 5 authors
The increasing use of cryptocurrencies, especially Bitcoin (BTC), has created new challenges for financial investigation. Although blockchain transactions are publicly accessible, the pseudo-anonymous nature of cryptocurrency networks can facilitate illicit financial activity. This work explores anomaly detection in the Bitcoin network using a semi-supervised Long Short-Term Memory Autoencoder (LSTM-AE). The focus is on the analysis of wallet activity over time in order to capture temporal behavioral patterns that may be related to illicit activities. Experiments are conducted on the Elliptic++ dataset. The model is trained exclusively on licit behaviour and the results indicate that the proposed formulation is able to retrieve a large proportion of illicit wallets despite the highly imbalanced setting.
Cryptocurrencies have emerged as a prominent asset class characterized by rapid price fluctuations, growing institutional participation, and continuing debate over whether their price movements are random or predictable. This study examines the randomness and weak-form market efficiency of the top ten cryptocurrencies by market capitalization—Bitcoin, Ethereum, Tether, Binance Coin, XRP, USD Coin, Solana, TRON, Dogecoin, and Hype liquid—using daily closing price data from April 2016 to March 2026 (subject to data availability for each coin). Daily log returns were tested using Descriptive Statistics, the Jarque–Bera test of normality, the Wald–Wolfowitz Run Test, and the Autocorrelation Test. The results show that daily returns for all selected cryptocurrencies are non-normally distributed, exhibiting excess kurtosis and skewness. The Run Test results indicate that seven of the ten cryptocurrencies—Bitcoin, Ethereum, Tether, Binance Coin, XRP, USD Coin, and Dogecoin—do not follow a random walk, while Solana, TRON, and Hype liquid exhibit randomness consistent with weak-form efficiency. However, the Autocorrelation Test reveals strong positive serial correlation across all ten cryptocurrencies, indicating that the market falls short of weak-form efficiency. The study concludes that the cryptocurrency market provides mixed and largely inefficient evidence with respect to the Random Walk Hypothesis, implying that historical price information may retain some predictive value for investors.
When we consider the PoW (proof-of-work) in the Bitcoin blockchain, how is the work calculated? How does this work convert to energy quantities? This paper demonstrates that in the Bitcoin blockchain, "Proof-of-Work" (PoW) is not a complex calculus equation, but rather a probabilistic brute-force search. Miners repeatedly run block header data through a cryptographic hash function, tweaking variables until they output a number that meets a strict network threshold. In the Bitcoin blockchain, Proof-of-Work (PoW) is a probabilistic brute-force search where miners repeatedly run block headers through a double SHA-256 hash function to find an output below a global target threshold. The mathematical "work" is quantified by the network Difficulty (D), requiring roughly D × 2³² expected hashes per block. To convert this cryptographic effort into physical energy, the global network hashrate is first derived by dividing total block hashes by Bitcoin’s 10-minute target block time (600 seconds). This computational rate is then bridged to the physical world using hardware efficiency—measured in Joules per Terahash (J/TH)—multiplied by operational time. Because modern semiconductor ASICs operate roughly seven orders of magnitude above the absolute thermodynamic limits outlined by Landauer's principle, nearly all electricity consumed by this cryptographic pipeline directly converts into waste heat. The calculation of this work, how it translates mathematically to network metrics, and how those metrics convert into physical energy quantities is the discussion of this paper.<b>Part 1: How the "Work" is Calculated</b><b>1. The Hashing Puzzle (Double SHA-256)</b>A miner constructs a block header containing transaction data, a timestamp, the hash of the previous block, and a changing variable called a nonce. They pass this header through the SHA-256 algorithm twice:<br>H(x) = SHA-256(SHA-256(Block Header))The resulting output is a 256-bit unsigned integer, typically represented as a 64-character hexadecimal string.<b>2. The Target (</b><b>T</b><b>)</b>The network enforces a global threshold called the Target (T). For a block to be accepted, the hash output interpreted as a massive 256-bit integer must satisfy:<br>Hash Output ≤ T<br>Because the output of a cryptographic hash function is completely random and uniformly distributed, miners cannot predict the output. Finding a valid hash is essentially a Bernoulli trial (like rolling a die with an astronomical number of sides).<b>3. Mathematical Definition of Difficulty (D)</b>Because the Target T is a massive 256-bit number that changes every 2,016 blocks, Bitcoin uses a human-readable metric called Difficulty (D), scaled relative to a baseline "genesis" target (T<sub>max</sub>).<br>T<sub>max</sub> = 0x00000000FFFF0000000000000000000000000000000000000000000000000000The difficulty formula is D = T<sub>max</sub>/TAs the network gains more miners, T drops (becomes smaller), making hashes harder to find, which increases D.<br>The expected number of hashes E[hashes] required to find a valid block at a given difficulty is proportional to D:E[hashes] = D × 2³² × T/T<sub>max</sub> (scaled to baseline expectations)<br>More simply, the total expected hashes per block is roughly:Expected Hashes ≈ D × 4.295 × 10⁹<b>Part 2: From Computational Work to Energy Quantities</b>Energy consumption is a byproduct of hardware efficiency operating over a span of time to execute these hash attempts. There is no direct algorithmic conversion from a hash to Joules in the protocol code; instead, the conversion bridges cryptographic operations and thermodynamic hardware efficiency.<b>Step 1: Calculate Total Network Hashrate (H</b><sub><strong>net</strong></sub><b>)</b>The global hashrate represents the total number of hashes computed per second across all active machines globally. It is derived directly from the current difficulty (D) and Bitcoin's target block time (t = 600 seconds or 10 minutes):<br>Hashes per block = D × 2³²<br>Network Hashrate (H<sub>net</sub>) = D × 2³²/600 [hashes/second or H/s]<b>Step 2: Factor in Hardware Efficiency (EF)</b>ASIC (Application-Specific Integrated Circuit) miners dominate Bitcoin mining. Their electrical efficiency is measured in Joules per Terahash (J/TH) or Watts per Gigashash. Let the aggregate hardware efficiency of the network be denoted as EF (expressed in Joules per Hash, J/H):EF = Total Power Consumption (Watts)/Hashrate (H/s)<b>Step 3: Energy Derivation Formula</b>To calculate the total energy consumed by the entire Bitcoin network over a specific timeframe (e.g., 1 second, 1 day, or 1 year), we multiply the network hashrate by the hardware efficiency and time (t):<br>Energy (E) = H<sub>net</sub> × EF × Δ tSubstituting H<sub>net</sub> into the equation:<br>E = (D · 2³²/600) × EF × Δ t<br>For example, assume a network difficulty (D) of roughly 80 × 10¹² (80 trillion). Also, assume an average fleet hardware efficiency (EF) of 25 Joules per Terahash (25 × 10⁻¹² J/H). Calculate energy consumed over 1 day (Δ t = 86,400 seconds):Hashes/sec = 80 × 10¹² × 4,294,967,296/600 ≈ 5.72 × 10²⁰ H/sPower (Watts) = (5.72 × 10²⁰ H/s) × (2.5 × 10⁻¹¹ J/H) ≈ 14,300,000,000 W = 14.3 GWEnergy over 1 day = 14.3 GW × 24 hours ≈ 343.2 GWhThe summary of the conversion pipeline may be expressed as<br>Target (T) ⟶ Difficulty (D) ⟶ Network Hashrate (H<sub>net</sub>) ⟶× Hardware Efficiency (J/H)⟶ Power (Watts) ⟶× Time⟶ Energy (Joules/kWh)<b>Part 3: Thermodynamic Limits and Efficiency Bounds (Landauer's Principle)</b>To fully connect cryptographic work to physical energy, we can look at the theoretical minimum energy required by the laws of physics to perform computation.<b>1. Landauer's Principle</b>Landauer's principle establishes the minimum possible amount of energy required to erase or irreversibly manipulate a bit of information at a given temperature (T<sub>temp</sub>):<br>E<sub>min</sub> = k<sub><em>B</em></sub> T<sub>temp</sub> ln(2)k<sub><em>B</em></sub> is the Boltzmann constant (1.380649 × 10⁻²³ J/K).T<sub>temp</sub> is the absolute temperature of the environment (e.g., 300 K).For a single bit modification at room temperature, this absolute thermodynamic floor is roughly 2.8 × 10⁻²¹ Joules per bit.<b>2. Comparing SHA-256 to the Thermodynamic Limit</b>A single SHA-256 calculation involves processing a 512-bit message block through 64 rounds of complex logical operations (bitwise additions, rotations, and shifts), manipulating hundreds of thousands of bits cumulatively.Theoretical minimum energy per hash: Factoring in the sheer number of bit operations inside SHA-256, even a reversibly ideal computer would require thousands of bit manipulations, putting a strict physical floor on a single hash well above Landauer's limit (roughly on the order of 10⁻¹⁹ to 10⁻¹⁸ Joules per hash under optimal theoretical conditions).Actual ASIC efficiency: Modern state-of-the-art ASIC miners (like the Bitmain Antminer S21 series) operate around 15 to 20 J/TH (1.5 × 10⁻¹¹ Joules per hash).Comparing real-world hardware (10⁻¹¹ J/H) to absolute physical limits (10⁻¹⁸ J/H) reveals that current silicon-based semiconductor technology is roughly 7 orders of magnitude away from theoretical thermodynamic efficiency—meaning nearly all energy put into Bitcoin mining converts directly into waste heat.<b>Part 4: Complete Comprehensive Master Equation</b>Combining all components into a single macro-equation, the total daily electrical energy (E<sub>day</sub>) consumed by the global Bitcoin network can be calculated directly from the network's current Difficulty (D) and the average hardware efficiency fleet-wide (EF<sub>avg</sub> in J/TH):E<sub>day</sub> = (D · 2³²/600) × (EF<sub>avg</sub> × 10⁻¹²) × 86,400<br>Where:<br>D · 2³² / 600 yields the Network Hashrate (hashes/sec).EF<sub>avg</sub> × 10⁻¹² scales Joules-per-Terahash down to Joules-per-Hash.86,400 converts seconds into one full day.This mathematical coupling ensures that as network security (Difficulty D) scales up over time to attract more capital and hashpower, energy consumption scales linearly with it, modulated only by the parallel improvement rate of semiconductor manufacturing efficiency (EF<sub>avg</sub>).To recap the end-to-end framework:The Work: Quantified by the difficulty D and scaled via 2³² to determine total expected hashes per block.The Hashrate: Derived by dividing total hashes per block by the target 10-minute block time (600 seconds).The Energy Conversion: Bridged physically using the hardware's efficiency metric (Joules per Terahash, or J/TH) multiplied over time.The Physical Bound: Bounded by thermodynamic limits like Landauer's principle, explaining why modern ASICs produce the massive amounts of waste heat characteristic of the Bitcoin network.