Blockchain Papers

Akiva Groskin

The Connes–van Suijlekom truncated Weil quadratic form, indexed by a cutoff parameter c that controls the primes p ≤ c entering the operator, produces a ground state whose Fourier–Mellin zeros provably lie on the critical line; whether they converge to the Riemann zeros as c → ∞ is open (Connes 2026; Connes–Consani–Moscovici 2025). We present, to our knowledge, the first independent public implementation of the Connes–van Suijlekom Galerkin matrix at sixteen cutoffs (c = 13 through 67, plus c = 100). Across the in-sample window c = 13 through c = 67 at N = 100, the first-zero absolute error |γ1 − γ1Riemann| shrinks monotonically from ∼2×10−55 to ∼1.5×10−168, a 113-OOM convergence across fifteen cutoffs. The smallest-positive even-sector eigenvalue λmineven separately reaches ∼10−334 at c = 100, N = 250 (275-OOM span from c = 13). Out-of-sample test at c = 100. On the four-point N-sweep N ∈ {100, 150, 200, 250} at dps = 500, consecutive first-difference ratios 0.837 and 0.836 match to two decimal places. Aitken-Δ2 on the two overlapping triples yields log10|λ∞even| ≈ −536.8 and ≈ −533.7, approaching the Connes 2026 §6.4 heuristic prediction (≈ −530.4) monotonically with N (6.4 and 3.3 OOM gaps out of |x∞| ∼ 530). The same eigenvector recovers γ1, …, γ10 to 307–329 matching digits at N = 250, dps = 500. Under the unitary equivalence with Connes–Consani–Moscovici Lemma 5.1, this is the deepest such Galerkin-truncation recovery in the public Connes–van Suijlekom / Connes–Consani–Moscovici literature, subject to a hypothesis-status caveat. The raw finite-N matrix carries a small block of negative-sign eigenvalues at the finite archimedean cutoff T = 800; these are an artifact of that cutoff and are absent once T is increased, so the smallest-positive even-sector eigenvalue is the genuine smallest one (continuum positivity of QWλ is RH-equivalent and is not assumed at λ = √100). The fit |log10 λmin| ≈ 13.24 c0.634 on c ≤ 67 at N = 100 is shown to be a finite-N rate, falsified at c = 100, N = 200 by 49 OOM in the direction of faster decay. Structural observations include approximate eigenvector c-invariance (overlap ≥ 0.9498 on all 105 cutoff pairs despite eigenvalues differing by 113 OOM), multi-zero convergence universality (all ten detectable zeros within 3.8% of each other), an empirical Galerkin-convergence exponent s(c) ≈ 55 log c − 128, un-rescaled Galerkin bulk-spectrum Poisson statistics (β < 0.05; this is a structural diagnostic of the truncated operator, not a test of Montgomery's conjecture, which applies to locally-rescaled zero spacings), and tight bulk invariants log|det Qc| ≈ −65.6 c + 542 (R2 = 0.997). We make no claim of proof; the contribution is reproducible numerical data and its careful interpretation under the existing CvS / CCM framework. All code, data, and ancillary files are publicly available. Version 3.3 (2026-06-26) correction. The negative-sign eigenvalue blocks reported at c = 100 and for L(s, χ3) at c = 23, 29 are a finite archimedean-cutoff (T) artifact, not a feature of the operator: they are stable in working precision but vanish once T is increased, so cutoff-free the relevant even sectors are non-negative and the smallest-positive branch is the genuine smallest eigenvalue. No quantitative result changes. See ERRATA.md and the paper's note added in revision. The cutoff sensitivity was independently identified by B. W. A. Silva, consistent with the naturally even, positive ground state reported by R. Andrews; the investigation was prompted by A. Connes.

Giovanni Seraghiti, Kévin Dubrulle, Arnaud Vandaele, Nicolas Gillis

Nonnegative matrix factorization (NMF) approximates a nonnegative matrix, $X$, by the product of two nonnegative factors, $WH$, where $W$ has $r$ columns and $H$ has $r$ rows. In this paper, we consider NMF using the component-wise L1 norm as the error measure (L1-NMF), which is suited for data corrupted by heavy-tailed noise, such as Laplace noise or salt and pepper noise, or in the presence of outliers. Our first contribution is an NP-hardness proof for L1-NMF, even when $r=1$, in contrast to the standard NMF that uses least squares. Our second contribution is to show that L1-NMF strongly enforces sparsity in the factors for sparse input matrices, thereby favoring interpretability. However, if the data is affected by false zeros, too sparse solutions might degrade the model. Our third contribution is a new, more general, L1-NMF model for sparse data, dubbed weighted L1-NMF (wL1-NMF), where the sparsity of the factorization is controlled by adding a penalization parameter to the entries of $WH$ associated with zeros in the data. The fourth contribution is a new coordinate descent (CD) approach for wL1-NMF, denoted as sparse CD (sCD), where each subproblem is solved by a weighted median algorithm. To the best of our knowledge, sCD is the first algorithm for L1-NMF whose complexity scales with the number of nonzero entries in the data, making it efficient in handling large-scale, sparse data. We perform extensive numerical experiments on synthetic and real-world data to show the effectiveness of our new proposed model (wL1-NMF) and algorithm (sCD).

haruhito

This paper introduces the Quantum Tensor Sequence (.qtsq) format, a universal file format built to compress any kind of data — whether it's images, audio, video, text, structured data, or raw binary. Instead of treating everything as a generic stream of bytes like most compressors do, .qtsq looks at what the data actually is before deciding how to compress it. An internal component we call the "Spaghettification Engine" analyzes the input, figures out which of 16 data types it belongs to, and picks the best compression strategy for it: Iterated Function Systems (IFS) for images, Discrete Fourier Transform (DFT) for audio and signals, dictionary-schema encoding for text and structured data, and procedural seed generation for binary data. Everything is packed into a single 80-byte header that supports 11 features: type-aware compression, lazy partial decompression, AES-256-GCM encryption, Schnorr zero-knowledge proofs, Reed-Solomon error correction, inter-file deduplication through wormhole links, compressed-domain differential updates, multi-resolution quality scaling, and adaptive size thresholds. The whole thing is organized around a five-layer architecture inspired by black hole physics — each region of the black hole maps to a stage of the compression pipeline. As far as we know, no existing file format brings all of these capabilities together in one place. Based on the theoretical properties of the algorithms involved, we expect compression ratios somewhere between 18:1 and 55:1 on mixed-type data. Real-world benchmarks using the reference implementation will follow in a separate paper.

Xin Liao, Hao Wu, Tiantian He, Xin Luo

Cryptocurrency services, as one of the most successful applications of blockchain technology, have recently garnered significant attention from the graph learning community. Its large-scale dynamic transaction records contain a variety of behavioral patterns and rich knowledge involving accounts, making the dynamic cryptocurrency transaction network embedding (DCTNE) a hot, yet thorny research topic. As the trading accounts increase and time accumulates, considerable transaction services are dispersed into various time slots, leading to very sparse transaction data within a time slot, that is, the transaction service data is high-dimensional and incomplete (HDI). To efficiently mine high-value knowledge from HDI data, this article proposes a proximal-ADMM-incorporated nonnegative latent-factorization-of-tensors (PNL) model for DCTNE that adopts threefold ideas: 1) incorporating the proximal terms into the alternating-direction-method-of-multipliers (ADMMs)-based learning scheme to reduce the oscillations for high estimation accuracy and fast convergence; 2) implementing a parallel training process with hyperparameter self-adaptation for high computational efficiency; and 3) proving that the proximal-incorporated learning scheme guarantees the convergence to a Karush–Kuhn–Tucker (KKT) stationary point. Experimental results on eight real-world DCTNs show that the PNL significantly outperforms several state-of-the-art (SOTA) models, demonstrating not only high efficiency and accuracy in performing DCTNE, but also strong potential to enhance the operational reliability and stability of cryptocurrency transaction systems.

M. K. Ghosh, Raju Halder, Joydeep Chandra

The Ethereum blockchain platform has witnessed a surge in crypto-cybercrimes, particularly phishing attacks, resulting in significant financial losses. Analyzing the Ethereum transaction network to detect phishing users poses a set of critical challenges, including network sparsity, dynamic network fluctuations, large-scale data and significant class imbalance. Existing literature in this area primarily leverages traditional feature engineering or network representation learning to retrieve crucial information from transaction records to identify suspected users. However, these methods mainly rely on manually handcrafted features or conventional node representation learning while ignoring the inherent network sparsity and dynamic fluctuations. Hence, to alleviate these challenges, this paper introduces a novel tensor-based representation learning framework, TREAT (Temporal andRelationalAttention-basedTensor Representation Learning). TREAT models the Ethereum transaction network as a 3-dimensional tensor to preserve structural, transactional, and temporal aspects in a standalone architecture, thereby observing the rich correlation among these. The framework is coupled with a two-way self-attention mechanism alongside a rank-based tensor decomposition to comprehend the underlying evolving transaction interaction patterns while addressing the network sparsity. A Graph Neural Network layer with edge attention elevates the final representation quality, thereby yielding a 3%~4% improvement inF1-Scorewith respect to the existing baselines.

S.Y. Wang, Laurence T. Yang, Debin Liu, Ruonan Zhao · 7 authors

Due to the strong untraceability of mixing services, numerous criminals exploit these services to engage in illicit activities, posing a significant threat to the blockchain ecosystem. This paper addresses the challenge of linking transaction addresses in Tornado Cash, a popular mixing service on Ethereum. While existing state-of-the-art solutions like MixBroker attempt to address this problem, two fundamental limitations persist: insufficient utilization of neighbor information and neglect of address information asymmetry. To address these gaps, a novel framework termed “MixLinker” is proposed, which enhances neighbor information utilization and models information asymmetry. Specifically, a Normalized Adjusted Personal PageRank (NAPPR) module is designed to prioritize significant neighbor nodes while mitigating interference from super and irrelevant addresses. Additionally, tensors are employed to model transactions, capturing rich interaction features related to transaction attributes. Based on historical transaction sequences, Tensor Long Short-Term Memory (TLSTM) is used to obtain high-quality initial input features for the Graph Neural Network (GNN) module, enabling effective learning of nonlinear dynamics. To ensure symmetric output results and model asymmetric information, a temporal-aware symmetry classifier is constructed that leverages asymmetric information through permutation operations and an order-aware classifier. Extensive experiments demonstrate that MixLinker outperforms other methods, validating the effectiveness of the proposed approach and confirming the two underlying motivations.

Yue Zhou, YuTing Ding, Yan Xia

Cryptocurrency transaction networks (CTNs) are frequently encountered in real-world applications. Due to practical constraints, it is generally not feasible to observe complete interactions among all nodes at every time slot, leading to numerous missing links in CTNs. A link prediction model based on Non-negative Latent Factorization of Tensors (NLFT) has demonstrated effectiveness in predicting these missing links within a temporal network. However, existing NLFT models do not adequately capture the evolving relationships within a temporal network, limiting their ability to predict temporal links effectively. To address this limitation, this paper proposes an Autoregressive-incorporated Non-negative Latent-Factorization of Tensors (ArNLFT) model. The core idea is to adopt an autoregressive model to represent the evolving relationships in temporal networks, thereby constructing an autoregressive-incorporated objective function. Additionally, a non-negative parameter learning scheme, based on a single latent factor-dependent, non-negative, and multiplicative update rule, is designed to ensure the non-negativity of the proposed model. The effectiveness of the ArNLFT model is ultimately verified through temporal link prediction tasks on two real CTNs, with results showing that ArNLFT achieves a significant accuracy improvement compared to its peers.

Xiaokang Wang, Laurence T. Yang, Dongdong Huo, Lei Ren · 5 authors

Internet-of-Things (IoT), is the comprehensive interconnection systems of computational, networking and physical devices with the important goal of providing proactive and personalized services efficiently. The foundation of such services is big data integration and processing among various devices, which brings important challenges including data fusion, transferring and sharing of computational results. On the other hand, decentralized blockchain platforms provide novel technologies for reliable IoT data integration and processing. In addition, to facilitate decentralization and distribution of IoT big data, tensor-train (TT), as a tensor decomposition method, can play a vital role. Therefore, in this paper, a tensor-train-based permissioned-private (P2) blockchain is proposed to realize the organization, integration, sharing and applications of IoT data for intelligent IoT services. To demonstrate the performance of the proposed method, case studies with IoT data are carried out on permissioned-private chain platform to measure its performance.

Jérémy Charlier, Radu Statem, Jean Hilger

Smart contracts are autonomous software executing predefined conditions. Two of the biggest advantages of the smart contracts are secured protocols and transaction costs reduction. On the Ethereum platform, an open-source blockchain-based platform, smart contracts implement a distributed virtual machine on the distributed ledger. To avoid denial of service attacks and monetize the services, payment transactions are executed whenever code is being executed between contracts. It is thus natural to investigate if predictive analysis is capable to forecast these interactions. We have addressed this issue and propose an innovative application of the tensor decomposition CANDECOMP/PARAFAC to the temporal link prediction of smart contracts. We introduce a new approach leveraging stochastic processes for series predictions based on the tensor decomposition that can be used for smart contracts predictive analytics.

Jérémy Charlier, Radu State, Jean Hilger

Background: Past few months have seen the rise of blockchain and cryptocurrencies. In this context, the Ethereum platform, an open-source blockchain-based platform using Ether cryptocurrency, has been designed to use smart contracts programs. These are self-executing blockchain contracts. Due to their high volume of transactions, analyzing their behavior is very challenging. We address this challenge in our paper. Methods: We develop for this purpose an innovative approach based on the non-negative tensor decomposition Paratuck2 combined with long short-term memory. The objective is to assess if predictive analysis can forecast smart contracts activities over time. Three statistical tests are performed on the predictive analytics, the mean absolute percentage error, the mean directional accuracy and the Jaccard distance. Results: Among dozens of GB of transactions, the Paratuck2 tensor decomposition allows asymmetric modeling of the smart contracts. Furthermore, it highlights time dependent latent groups. The latent activities are modeled by the long short term memory network for predictive analytics. The highly accurate predictions underline the accuracy of the method and show that blockchain activities are not pure randomness. Conclusion: Herein, we are able to detect the most active contracts, and predict their behavior. In the context of future regulations, our approach opens new perspective for monitoring blockchain activities.