Distributed systems in which concurrent proposals are mutually exclusive face a fundamental stability constraint under network delay. In open systems where global state progression is event-driven rather than round-driven, propagation delay creates a conflict window within which overlapping proposals may generate competing branches. This paper derives a density-delay law for such exclusive state progression processes. Under independent proposal arrivals and bounded propagation delay, overlap is approximated by a Poisson model and fork depth is represented by a birth-death process. The analysis shows that maintaining bounded fork depth as the number of participants grows requires the density-delay product $λΔ$ to remain $O(1)$, implying that aggregate proposal intensity must stay bounded and yielding an inverse-scaling law $g(N)=O(1/N)$ at the unit level. Simulation experiments across varying network sizes and propagation delays align with a common density-delay curve, supporting the predicted scaling behavior. The result provides a compact law for stable event-driven state progression in open distributed systems and offers a scaling-based interpretation of Bitcoin-style difficulty adjustment as a decentralized way to regulate effective event density.
Historical Genetic Logic as a Dynamical Coherence Judge for Large Language Models A Rigorous Formalization of Xenopoulos' Dialectical Operators and Experimental Validation on LLM Self Contradiction DOI:10.5281/zenodo.19190202 https://zenodo.org/uploads/19190202 Katerina XenopoulouIndependent Researcher, Kefalonia, GreeceORCID: 0009-0004-9057-7432Correspondence: katerinaxenopoulou@gmail.com Theoretical Foundation: Epameinondas Xenopoulos †Epistemology of Logic: Logic–Dialectic or Theory of Knowledge (2nd ed., 2024)ORCID: 0009-0000-1736-8555 Abstract This paper presents the first complete computational implementation of Epameinondas Xenopoulos' Historical Genetic Logic as a quantitative coherence judge for large language models (LLMs). We derive a finite-dimensional nonlinear dynamical system (EXDT v4.0) from the philosophical principles and operators (¬ᴰ, ∧ᴰ, ⤊) defined in [1], establishing a rigorous structural correspondence: memory ↔ historicity, structured negation ↔ dialectical negation, tension ↔ real contradiction, bounded chaos ↔ dynamical stability. The system outputs a set of interpretable metrics: coherence Re(X), dialectical tension Im(X), stability stage τ₀–τ₃, contradiction counts, and mathematically derived corrections via the operator structure. We validate the system on 12 responses from four leading LLMs (ChatGPT, DeepSeek, Claude, Gemini) to a philosophical question designed to elicit contradictions. Key results: (1) No model achieved absolute coherence—all responses contained detectable contradictions. (2) Gemini showed highest stability (variance 4.9%; the only τ₀ response). (3) ChatGPT produced the highest scoring single response (96.8%) but with high variance (13.0%). (4) Corrections generated by EXDT eliminated all detected contradictions, with human evaluators preferring the corrected versions in 100% of blind comparisons. We argue that Xenopoulos' logic provides the first formal framework for self-correcting language models—a necessary step beyond current LLMs that cannot detect their own inconsistencies. Keywords: Dialectical Logic, Historical Genetic Logic, Large Language Models, Coherence Measurement, Klein 4 Group, Xenopoulos, AI Self Correction, Nonlinear Dynamics, Lyapunov Exponents 1. Introduction: From Philosophy to Computation 1.1 The Problem of Static Logic in AI Modern large language models (LLMs) exhibit well-documented inconsistencies: they contradict themselves within a single response, produce different answers to the same prompt across runs, and occasionally "collapse" into incoherence (hallucinations). These phenomena are not mere engineering failures; they reflect a deeper absence of any internal coherence check. As Xenopoulos argued in the opening pages of Epistemology of Logic: "Formal logic, with its static nature, cannot express the flow of becoming." [1, p. 21] Traditional logic (from Aristotle to Hilbert) treats contradiction as error and time as an external parameter. It cannot model the internal evolution of a thought system. Xenopoulos' central contribution was to replace static identity (A = A) with genetic identity (A → A'), where contradiction becomes the engine of development [1, pp. 51–57, 100–101]. 1.2 Historical Genetic Logic as a Dynamical System The book develops a formal apparatus: dialectical negation ¬ᴰ, dialectical conjunction ∧ᴰ, and the sublation operator ⤊ (Aufhebung) [1, pp. 226–233]. These are not metaphorical; they are designed to be mathematically executable. In recent work [2], we established a structural correspondence between this apparatus and a finite-dimensional nonlinear system with memory: Philosophical Principle Mathematical Counterpart Book Pages Historicity Memory μₜ 65, 100–101, 233–238 Dialectical negation ¬ᴰ Structured negation Ãₜ = -Aₜ·κ·(1 + β·tanh(μₜ)) 53, 71–72, 229–233 Real contradiction Tension Tₜ = |Aₜ·Ãₜ| 54–55, 73–74, 108–109 Dynamical stability Absorptive region & bounded chaos 87–88, 112–113, 122–123 Transitional truth SRB measure, ε → 0 limit 111–112, 119–120, 238–240 This correspondence is structural, not analogical: every mathematical object has a direct philosophical counterpart with explicit page references. 1.3 The Present Contribution We now go beyond structural correspondence by: Implementing the full system as EXDT v4.0, a computational coherence judge Defining a quantitative metric suite (coherence, tension, stage, contradictions, corrections) Validating experimentally on 12 responses from four LLMs Demonstrating that the system generates mathematically grounded corrections that eliminate contradictions 2. Mathematical Formalization of Historical Genetic Logic 2.1 Alphabet and Operators [1, pp. 226–233] Let Aₜ ∈ ℝ denote the value of a concept at discrete time t (the "dialectical intensity"). Following Xenopoulos [1, p. 229], dialectical negation ¬ᴰ is not logical complement but internal opposition: "¬ᴰA does not denote the logical complement 'not A', but the internal opposition that preserves A while generating its evolution." Definition 1 (Dialectical Negation).Ãₜ = −Aₜ · κ · (1 + β · tanh(μₜ)), where κ ∈ (0,1) is a scale coefficient, β ≥ 0 modulates historical intensity, and μₜ is the historical memory (defined below). Definition 2 (Real Contradiction as Tension).Following [1, pp. 230–233], the encounter of thesis and its dialectical negation produces tension:Tₜ = |Aₜ · Ãₜ|. Definition 3 (Historicity).Following [1, pp. 233–238], memory incorporates the historical trajectory:μₜ = (1/m) Σ_{i=1}^{m} Aₜ₋ᵢ, where m is the memory length (here m = 10, following [2]). Definition 4 (External Contradictions and the ε Limit).Xenopoulos introduces the sum of external contradictions ε₁ + ε₂ + … + εₙ as an irreducible component [1, pp. 238–240]. Truth is approached asymptotically: |Sπ − Sα| < ε, ε → 0. 2.2 The Complete Dynamical System Combining the above, we obtain the recurrence: Aₜ₊₁ = Aₜ + p·Tₜ + α·tanh(μₜ) + ρ·sin(ωt) + ε Ãₜ = −Aₜ·κ·(1 + β·tanh(μₜ)) μₜ = (1/m) Σ_{i=1}^{m} Aₜ₋ᵢ Here: p: amplification of tension α: intensity of historical modulation ρ, ω: amplitude and frequency of periodic forcing ε: the sum of external contradictions (small, non-zero) Remark. The +ε term is not a Hilbert-style choice operator [1, p. 270]; it is the total of external contradictions that prevents the system from ever reaching absolute static truth. 2.3 Lyapunov Exponents and Hyperbolicity Proposition 1 (Positive Lyapunov Exponent).For parameter values (p = 0.1, κ = 0.5, β = 0.8, α = 0.05, ρ = 0.02, ω = 0.1, m = 10, ε = 10⁻³), the maximal Lyapunov exponent λ₁ ≈ 0.499 > 0, implying exponential divergence of trajectories. Proof. Numerical computation via the Wolf et al. algorithm [3] on 10⁴ iterations, with Jacobian derived from the recurrence. Proposition 2 (Partial Hyperbolicity).The system exhibits a dominated splitting with one expanding direction and multiple contracting directions, corresponding to the synthesis of formal (contraction) and dialectical (expansion) logics [1, pp. 36–37, 67–70, 87–94]. 2.4 Absorptivity and SRB Measure Proposition 3 (Absorptivity).There exists R > 0 such that for all initial conditions |A₀| ≤ R, the trajectory remains bounded: |Aₜ| ≤ R for all t. This corresponds to "dynamical stability" as defined in [1, pp. 87–88, 112–113]. Proposition 4 (Existence of SRB Measure).Because the system is dissipative and chaotic, there exists a Sinai–Ruelle–Bowen (SRB) measure with respect to which time averages converge [4,5]. This corresponds to the "transitional nature of truth" [1, pp. 111–112, 119–120] and the ε → 0 limit [1, pp. 238–240]. 3. The EXDT v4.0 Coherence Judge 3.1 Architecture EXDT (Xenopoulos Dialectical Transformer) implements the recurrence of §2.2 with additional layers for natural language input: Vectorization: Text → embedding vector → scalar Aₜ via a trainable projection (or, for this experiment, a deterministic mapping from contradiction features to Aₜ) Dynamical Evolution: The recurrence runs for the length of the text, generating a trajectory Metric Extraction: From the final state and the trajectory, we compute: Metric Definition Range Re(X) Coherence: the final Aₜ normalized to [−1, 1] −1 (fully incoherent) to +1 (fully coherent) Im(X) Dialectical tension: the time average of Tₜ, signed by the sign of Aₜ Real Stage τ₀ (coherence) if λ₁ not yet positive; τ₁ (first anomaly) at first sign of divergence; τ₂ (repetition) if divergence reappears; τ₃ (collapse) if |Aₜ| exceeds 2R Discrete Contradiction Count Lexical, syntactic, semantic, paradox, causal, temporal—each detected via pattern matching on the trajectory Integer XEPTQLRI Composite quality index = 0.4·Re(X) + 0.3·(1−Im(X)/Im_max) + 0.3·(1−contradictions/contradictions_max) 0–5 3.2 Correction Mechanism The correction mechanism is not heuristic; it applies the operators ¬ᴰ and ⤊ directly: At τ₁ (first anomaly): Apply ¬ᴰ to identify the implicit opposition; generate a contextual distinction (e.g., "X holds when Y, not X holds when Z"). This is derived from the structure of the contradiction as detected in the vector space. At τ₂ (repetition): Apply ⤊ (Aufhebung) to synthesize the contradiction into a higher-order resolution. The synthesis is computed as the fixed point of the recurrence when the tension Tₜ is maximal. At τ₃ (collapse): Flag as unrecoverable; suggest restart. Theorem 1 (Correction Eliminates Contradictions).For any text that is not already
This paper proves unconditional global regularity with quantitative exponential decay for the three-dimensional incompressible Navier–Stokes equations on the periodic box, restricted to velocity fields invariant under the Kida–Pelz symmetry group of order 48, for viscosities above an explicit threshold. The entire proof reduces, through a chain of six independently verifiable steps, to a single integer arithmetic fact: 20,625 < 31,104. This is, to the author's knowledge, the first time a Navier–Stokes regularity result has been distilled to a verifiable inequality between two five-digit integers, with every constant computed exactly and no numerical approximation entering the argument at any stage. The Kida–Pelz flow and why it matters. The Kida–Pelz initial datum, introduced by Kida (1985) and studied extensively by Pelz (2001), has occupied a special place in the blow-up literature for decades. It was originally proposed as a candidate for finite-time singularity formation precisely because its high octahedral symmetry concentrates vortex stretching into a small number of interacting structures, producing some of the most intense enstrophy growth observed in direct numerical simulations. The fact that the same symmetry that was expected to promote blow-up turns out to prevent it is itself a significant finding: it demonstrates that vortex stretching intensity and blow-up potential are fundamentally different quantities, a distinction that is often blurred in heuristic discussions of turbulence. The proof architecture. The argument has a deliberately transparent two-layer structure separating analysis from arithmetic, so that each layer can be checked independently by specialists in different fields. The analytic layer establishes three quantitative inputs. First, a spectral gap: representation-theoretic analysis of the octahedral group acting on Fourier space shows that the first two shells of the Laplacian spectrum are entirely killed by symmetry, tripling the effective Poincaré constant from 1 to at least 3. This means the KP symmetry forces vorticity to reside at higher wavenumbers where viscous dissipation is three times stronger than for generic flows. Second, a triadic density bound: the GKP equivariance constrains the Fourier support so severely that the number of resonant triads contributing to the nonlinear stretching term is reduced by a factor involving the group order, yielding a geometric density bound of at most 2. Third, an exact initial enstrophy: the KP datum is monochromatic, with all Fourier modes sitting at a single shell of squared wavenumber 11, giving the exact rational value 33/4 for the initial enstrophy. No floating-point computation, truncation, or discretisation enters this calculation. These three inputs feed into a Bernoulli differential inequality for the enstrophy whose separatrix is computed in closed form. The arithmetic layer then verifies that the initial enstrophy lies below this separatrix, which reduces to the integer comparison 33 times 625 equals 20,625, which is less than 31,104 equals 4 times 7,776. The safety margin is 50.8 percent, meaning the result would survive even if the analytic constants were degraded by up to 20 percent. Bounded enstrophy then gives global existence via the standard H1-continuation criterion, and exponential decay in all Sobolev norms follows by a Gronwall bootstrap. Beyond the core result. The paper establishes several extensions that go beyond mere regularity. Exponential decay is proved not only for the enstrophy but for all Sobolev norms simultaneously, with explicit prefactors and rates. The decay is shown to hold in all Lebesgue spaces from L2 to L-infinity and for all derivative orders, meaning that every physically measurable quantity associated with the flow decays exponentially. The pressure decays at double the velocity rate, a consequence of the quadratic structure of the pressure Poisson equation. Time analyticity is established for all positive times, meaning the solution extends to a holomorphic function in a strip around the real time axis. A shell-by-shell energy spectrum analysis shows that higher Fourier shells decay faster, with rates proportional to the squared wavenumber — a quantitative version of the physical intuition that small-scale structures are dissipated more rapidly. A Reynolds number characterisation shows that the Bernoulli closure holds if and only if the KP Reynolds number is below approximately 235, giving a concrete, physically interpretable criterion. The stability result deserves particular emphasis: global regularity is shown to persist under small perturbations that need not respect the KP symmetry. This means the result is not a fragile artifact of exact symmetry but a robust property of a neighbourhood in function space around the KP datum. The self-frustration connection. This paper is designed as a companion to the author's monograph "Self-Frustration of Vortex Stretching and the Architecture of the Navier–Stokes Blow-Up Barrier" (Cavazzini, 2026), which identifies a twelve-link chain of structural obstructions to finite-time blow-up for general three-dimensional Navier–Stokes. Three of those twelve links have concrete, quantitative realisations in the Kida–Pelz class. The enhanced spectral gap is a realisation of Link 5 (the spectral gap threshold that governs alignment stability). The triadic density reduction is a realisation of Link 3 (the oscillation bound that controls the pressure Hessian for tube-like vorticity). The identically vanishing helicity — proved here as a consequence of the parity inversion in the octahedral group — is a realisation of Link 6 (the gap–alignment complementarity), because it eliminates the eigenframe injection mechanism entirely: with zero helicity budget, the pressure Hessian cannot rotate the strain eigenframe to sustain the dangerous compressive component identified in the companion paper as the sole variable separating regularity-compatible from blow-up-compatible configurations. When all three mechanisms act simultaneously, as enforced by the octahedral symmetry, the self-frustration chain that remains open for general flows closes completely and unconditionally. The arithmetic inequality 20,625 < 31,104 is the quantitative expression of this closure. This provides the first concrete validation of the self-frustration framework as a genuine regularity tool rather than merely a classification scheme: the structural architecture described in the companion monograph is not an abstract taxonomy but a machinery that produces theorems when supplied with sufficient quantitative input. The minimal symmetry result strengthens this connection further: the octahedral group of order 48 is proved to be the smallest finite subgroup of O(3) for which the Bernoulli method closes. This characterises the precise boundary between symmetry groups where the self-frustration mechanisms are strong enough to guarantee regularity and those where they are not, providing a sharp answer to the question of how much geometric structure is needed to resolve the regularity problem within this framework. Context within the broader landscape. The Navier–Stokes regularity problem has a long history of partial results exploiting symmetry, from the classical two-dimensional theory (where regularity is known unconditionally due to the absence of vortex stretching) to various axisymmetric and helical reductions. The present work differs from these in a fundamental respect: the Kida–Pelz flow is fully three-dimensional with active, sustained vortex stretching — the mechanism responsible for the supercritical character of the equations is present and operative, not eliminated by dimensional reduction. What the symmetry does is not remove the stretching but quantitatively constrain it, tilting the balance between stretching and dissipation in favour of dissipation by a computable margin. This is a qualitatively different use of symmetry from the classical approach, and it suggests that the boundary between regularity and potential blow-up may be more accessible than previously thought — not through eliminating the dangerous mechanism, but through measuring and constraining it. The paper also contributes to the broader programme of understanding which structural properties of the Navier–Stokes equations are responsible for regularity. The identification of three independent mechanisms (enhanced dissipation, triadic depletion, topological obstruction) that close the regularity chain when acting together, combined with the companion monograph's demonstration that these same mechanisms are present but quantitatively insufficient for general flows, suggests a precise research programme: strengthen the quantitative estimates on any one of the three mechanisms sufficiently to close the chain without symmetry. The open problems listed in the paper — removal of the viscosity threshold, full Gevrey bootstrap, exact spectral gap computation — are formulated with this programme in mind. Methodological note. Every result in the paper carries an explicit epistemic label. All constants are computed exactly as rational numbers or algebraic expressions. The paper makes no claim regarding the Clay Millennium Prize and explicitly discusses the four gaps separating the present result from the Prize requirements: symmetry restriction, periodic domain, viscosity threshold, and partial Gevrey bootstrap. The distance from each gap to a resolution is assessed individually, with the viscosity threshold identified as an artifact of the Bernoulli method rather than a physical phase transition. MSC 2020 Classification: 35Q30 (primary — Navier–Stokes equations); 76D03 (existence, uniqueness, and regularity for incompressible viscous fluids); 42B25 (maximal functions and Littlewood–Paley theory); 20C15 (ordinary representations and characters of finite groups); 35B65 (smoothness and regularity of solutions to PDE
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Navier-Stokes equation solutions
Fluid Dynamics and Turbulent Flows
Advanced Numerical Methods in Computational Mathematics
Smart contracts (SCs) cannot be modified once deployed on the blockchain, making pre-deployment vulnerability identification essential. Although numerous SC vulnerability (SCVul) detection tools (SCTs) have been developed, prior evaluations have examined only limited vulnerability types, leaving it uncertain whether SCTs can comprehensively detect vulnerabilities and what characteristics their detectable vulnerabilities exhibit. Because each SCT employs distinct analysis methods and detection strategies, using multiple SCTs can be advantageous; however, the detection accuracy of such combinations has not yet been systematically evaluated. In this study, we comprehensively investigate the types and characteristics of SCVuls targeted by eight SCTs whose execution environments were successfully established and verified.
P. A. Adeoye, Joseph Babatola Ayodele, Fomonyuy Shinyuy, Clement Dossou-Yovo · 6 authors
Nigeria faces one of Sub-Saharan Africa’s most severe energy poverty crises, with over 85 million people lacking electricity access, a challenge that disproportionately affects more than 2.5 million Internally Displaced Persons (IDPs) in conflict-affected North-East Nigeria. Despite national electrification efforts, humanitarian settlements remain largely excluded from reliable power infrastructure. This study evaluates the technical feasibility, spatial energy gaps, and policy barriers associated with deploying decentralized solar and hybrid solar–wind systems in IDP settlements across six North-Eastern states. A mixed-method geospatial framework was applied, integrating Visible Infrared Imaging Radiometer Suite (VIIRS) nighttime light data, Geo-Referenced Infrastructure and Demographic Data for Development (GRID&lt;sup&gt;3&lt;/sup&gt;) infrastructure datasets, and Distributed Renewable Energy (DRE) demand data using Python and Quantum Geographic Information System (QGIS). Nighttime light intensity was classified into no-access (≤100 nW/cm²/sr), limited-access (101–1000 nW/cm²/sr), and full-access (&gt;1000 nW/cm²/sr) categories. Results identified 670 IDP camps across 112 Local Government Areas (LGAs), with high concentrations in Bauchi (264 camps), Borno (194), and Gombe (140), predominantly located within limited-access zones. Solar resource assessment shows strong regional potential (4.2–4.6 kWh/m²/day Global Horizontal Irradiation (GHI)), while average wind speeds of 2–4 m/s support small-scale hybrid applications. A representative camp load analysis (3.72 kWh/day) demonstrates that a 0.99 kWp solar array combined with a 3.2 kWh battery and a 300 W vertical-axis wind turbine can reliably meet basic household energy needs, reducing approximately 25.88 kgCO&lt;sub&gt;2&lt;/sub&gt;e per household annually. Key barriers include high upfront costs, limited financing mechanisms, weak humanitarian energy policy integration, and security-related operational risks. The study provides empirical evidence for integrating decentralized renewable energy into national electrification strategies through risk-informed planning and tailored financing models to enhance resilience, sustainability, and dignity in displacement settings.
Jae Hyun Choi, Geontae Noh, Ji Young Chun, Ik Rae Jeong
Regulatory frameworks like MiCA mandate KYC and auditability for stablecoins, but existing solutions fail to simultaneously achieve privacy, compliance, and cross-chain compatibility. We propose zkA3 (Zero-Knowledge Address Abstraction with Auditability), enabling users to generate pseudonymous identifiers from web2 certificates with unlinkability guarantees while incorporating encrypted audit tokens for authorized identity tracing. We formally prove five security properties: pseudonymity, unlinkability, zero-knowledge authentication, auditability, and cross-chain consistency. Our implementation achieves 29.8ms proof generation with 9,917 constraints, demonstrating practical feasibility. zkA3 is the first scheme simultaneously supporting privacy-preserving cross-chain stablecoin operations and regulatory compliance.
Youssef Said, Al Mahdi Khaddar, Lahcen Hassine, Ahmed Eddaoui · 5 authors
Gas Gas consumption is a critical factor influencing the efficiency, scalability, and operational cost of Ethereum smart contracts.As contract complexity grows, identifying structurally gas-inefficient patterns becomes essential for improving development workflows and preventing costly deployment decisions.This study presents a graph-based deep learning framework for detecting gas-inefficiency risk patterns at the function level, leveraging multi-relational Graph Attention Networks (GAT) applied to function-level contract graphs.By modeling call dependencies, control-flow interactions, and storage-based data dependencies, the model learns structural indicators associated with excessive gas consumption while explicitly excluding direct gas metrics from the feature space to prevent data leakage.Experimental results under a strict contract-level data split protocol demonstrate strong classification performance and stable generalization across held-out contracts under the main split protocol, and consistent behavior under an additional time-forward temporal robustness check.Ablation analysis confirms the contribution of dependency-aware edges and semantic features to predictive accuracy, highlighting the importance of modeling cross-function interactions rather than isolated code metrics.Beyond predictive performance, the proposed approach provides interpretable attention weights that identify structurally influential functions, supporting predeployment analysis and developer-guided manual refactoring decisions.By framing gas inefficiency as a global structural property emerging from function interactions, this work contributes aa scalable and explainable methodology for structural gas-inefficiency detection in smart contracts.The proposed model performs structural detection only and does not automatically modify or optimize smart contract code.
Decentralized finance introduces new business models and use cases as part of digital finance. Restaking has recently emerged as a transformative mechanism in DeFi, promising extra yields but introducing complex and interconnected risks. The paper monitors the current restaking landscape, empirically analyzes the revenue drivers of a liquid restaking protocol, and conducts a technical investigation on the emitted risk arising from the interconnection between liquid restaking and other protocols. The revenue dynamics of Renzo Protocol are analyzed by employing an OLS regression model, Granger-causality and random forest feature importance tests. Our results identify that revenue is primarily predicted by the value locked in the underlying EigenLayer ecosystem, the yield of Renzo protocol's liquid restaking token and the multi-blockchain expansion of that token. The multi-blockchain expansion of the liquid restaking token presents a double-edged sword: bridging to other networks is crucial for user adoption, but it adds the bridge risks to the existing risks of restaking. We investigate the cross-contamination risk between different DeFi services and the liquid restaking protocol. By mapping the asset flow across the decentralized finance ecosystem, it is detected that the bridge risk of the current size of Renzo's liquid-restaking assets does not impose a systemic risk on the current restaking and staking ecosystem. To address the potential consequences of the emphasized interconnection risks, we introduce two hypothetical scenarios and a stress test, assuming a large number of compromised liquid restaking tokens and a smart contract logic failure in a DeFi protocol. Considering the overall liquid-restaking protocols and the growing interconnection, this analysis requires further work to explore the growing complexities.
The projected arrival of cryptographically relevant quantum computers (CRQCs) between 2030 and 2035 poses a structural threat to blockchain infrastructure built on classical elliptic-curve cryptography. Shor's algorithm reduces the security of ECDSA-256, the signature scheme underpinning the majority of production blockchains, from approximately $2^{128}$ classical operations to $O(2^{24})$ quantum operations, rendering it categorically broken in the post-quantum era. The "Harvest Now, Decrypt Later" attack vector compounds this risk: adversaries collecting signed transactions today can retroactively extract private keys once quantum hardware matures, exposing all assets whose public keys have been revealed on-chain. This paper presents QoreChain, a Layer~1 blockchain platform designed from first principles to operate in a post-quantum world. QoreChain integrates three foundational capabilities into a single protocol stack: (1)~full-stack post-quantum cryptography implementing NIST-standardised algorithms (ML-DSA-87 per FIPS~204, ML-KEM-1024 per FIPS~203, SLH-DSA per FIPS~205, and SHAKE-256) at FIPS Security Level~5 across every protocol layer, from transaction signing and consensus messaging to cross-chain bridge attestations; (2)~an AI-native intelligence layer (QCAI) that applies reinforcement learning to consensus parameter optimisation, graph neural networks to anomaly detection, and multi-objective optimisation to transaction routing; and (3)~a triple virtual machine execution environment supporting EVM, CosmWasm, and SVM within a unified state model with atomic cross-VM call semantics and full rollback guarantees. The consensus mechanism, Combined Proof of Stake (CPoS), merges Reputation PoS, Delegated PoS, and classical PoS with BFT finality. A five-way fee distribution (37\% validators, 30\% burned, 20\% treasury, 10\% stakers, 3\% light nodes) aligns incentives across all participant classes. Governance employs Quadratic Delegation with Reputation Weighting (QDRW), for which we present formal game-theoretic analysis demonstrating bounded resistance to plutocratic capture (voting power scales sub-linearly with stake) and flash-loan manipulation (reputation updates lag delegation by one block finality cycle). Cross-chain interoperability is provided by the QoreChain Bridge (QCB), connecting directly to 25 Layer~1 blockchains with over 120 additional networks reachable via IBC. All bridge operations are secured by ML-DSA-87 multi-attestation with QCAI anomaly detection and circuit breaker mechanisms. A multi-layer scaling architecture incorporating sidechains, paychains, and a Rollup Development Kit (RDK) enables horizontal throughput expansion while inheriting the main chain's quantum-safe settlement guarantees. The QOR token has a fixed supply of 4,500,000,000 with epoch-based emissions following a halving schedule. The architecture is designed for 5,000+ transactions per second with sub-second finality; multi-node testnet benchmarks are pending. QoreChain Association is incorporated under the Swiss DLT Act (CHE-484.963.998, Rolle) with formal FINMA utility token classification (January 2026). Testnet is operational (chain ID: \texttt{qorechain-diana}) with 47 genesis modules. Mainnet launch is targeted for Q4~2026. The full specification spans 16 chapters and 351 pages, presenting 530 formal equations, 78 data tables, and 9 architectural diagrams covering cryptographic foundations, AI integration, smart contract execution, consensus, tokenomics, governance, interoperability, and regulatory compliance.
Mr. Utsav Pandey, Ms. Sania Parkar, Mr. Anant Sarode, Prof. Amit Chakrawarti
Traditional banking systems rely on passwords, PINs, and centralized biometric storage, exposing users to phishing, SIM-swap attacks, and credential reuse vulnerabilities. This paper presents the ZKP Banking Interface, a pinless, context-aware financial authentication system built on Zero-Knowledge Proof (ZKP) technology. A unified ZK-SNARK circuit (Groth16), implemented in Circom, encodes three simultaneous security factors: identity commitment, trusted network context, and transaction threshold logic using Poseidon hashing. Conditional biometric and puzzle challenges are enforced cryptographically for higher-risk scenarios. Proof generation and verification are fully automated within the browser using snarkJS and WebAssembly artifacts, eliminating manual proof handling. The system supports two verification modes: local (device-only privacy) and on-chain (public auditability via a Solidity smart contract on a Hardhat network). Experimental evaluation across five test scenarios confirms correct contextual policy enforcement, successful proof validation in both modes, and a smooth, practical banking user experience. The proposed system demonstrates that ZKP-based authentication can replace traditional credentials while maintaining strong privacy guarantees.
The decentralisation of authority and automated trust are the main reasons blockchain receives widespread praise. Token-based governance systems tend to maintain centralised control because early adopters and institutional stakeholders maintain most of the influence. Blockchain governance presents itself as an ethical and institutional problem instead of a technical issue. The paper uses deliberative democracy and democratic innovation theory to demonstrate that decentralised systems need to establish legitimacy through inclusive processes that combine reason and participation. The analysis evaluates Proof-of-Stake and DAOs as dominant governance models because they contain structural barriers and procedural weaknesses. The paper introduces design interventions such as sortition and quadratic voting, participatory panels and modular deliberation layers as potential solutions to embed democratic legitimacy into blockchain infrastructure. Blockchain technology enables the creation of new institutional frameworks which base their operations on democratic principles. The paper establishes that future governance needs to combine contestation and collective reasoning with consensus and coordination.
In this research, the energy consumption models of Bitcoin, Ethereum, and Dogecoin are analyzed using Explainable Artificial Intelligence (XAI) models aided by the three stages of analysis involving Digiconomist data from 2022 to 2025: (1) exploratory data analysis for the nature of energy consumption, (2) model identification of influential variables using Random Forest models enhanced with SHAP values, and (3) an LSTM transfer learning method for predicting the energy consumption of Ethereum and Dogecoin using a model developed with Bitcoin data. The initial results show that while both assets vary largely when it comes to their normal usage level, Ethereum sees a sharp drop after the changeover from Proof-of-Work to Proof-of-Stake as a mechanism. The XAI analysis indicates that energy use is largely a consequence of past use, seasonality, and annual patterns. In addition to this, the models show a high level of accuracy for Dogecoin (R²: 88.4%, MAPE: 13.45%) and Ethereum (R²: 86.2%, MAPE: 11.47%) when it comes to predicting energy usage using the concepts of transfer learning.
The integrity of democratic voting systems is increasingly threatened by security vulnerabilities, lack of transparency, and trust deficits, making electoral processes susceptible to manipulation. To address these concerns, Binance Smart Chain (BSC) introduces a blockchain-powered voting framework that leverages the Proof of Staked Authority (PoSA) consensus protocol to enhance security and decentralization. To further fortify the system, ResNet-101, a deep learning-based convolutional neural network (CNN), is integrated for facial recognition authentication, ensuring voter legitimacy and eliminating identity fraud. Additionally, one-time password (OTP) authentication and live location tracking strengthen the system against unauthorized access and proxy voting. By combining blockchain technology, biometric verification, and AI-driven facial authentication, BSC establishes a highly secure, transparent, and tamper-proof voting system. This approach aims to restore public trust in electoral processes, setting a new benchmark for secure and verifiable digital voting systems in democratic governance.
Reputation systems are fundamental to fostering trust and cooperation in digital environments, yet existing solutions often struggle with centralization, vulnerability to manipulation, and limited portability. Centralized reputation platforms can be opaque, censored and susceptible to become single points of failure, while decentralized ones face challenges, such as Sybil attacks, malicious strategies (e.g., ballot stuffing, bad-mouthing) exercised by entities of high influence, i.e. "whales", and privacy concerns. This paper addresses these persistent issues by proposing a blockchain-based reputation framework that integrates robust identity verification, square root voting constraints, and dynamic stake-based incentives. Rating power is linked to the reputation of the rater that puts its reputation at stake. The model aims to ensure that reputation is earned and maintained through verifiable, community-aligned actions, while simultaneously limiting the potential for abuse by malicious actors or disproportionately influential participants. By leveraging decentralized identifiers, zero-knowledge proofs, and transparent incentive mechanisms, the proposed system seeks to balance transparency, fairness, and privacy. Extensive simulation experiments prove that the approach is effective to reveal the true quality of entities, even in presence of 49% colluding voters. The approach is designed to be adaptable across diverse domains, ranging from marketplaces and collaborative platforms to decentralized finance and governance.
This paper explores the potential of using modern smartwatches, particularly the Apple Watch, as an additional device for signing transactions and interacting with the blockchain. Modern crypto applications on smart-watches are limited to a read-only paradigm. The reason is a lack of security, specifically the absence of biometric verification for each transaction. When creating a classic Externally Owned Account wallet on the smartwatch side, these vulnerabilities carry a high risk of losing all of the user's funds. To solve this problem, an architecture based on the ERC-4337 standard was proposed. The proposed solution includes creating a wallet based on the kernel architecture, which allows setting access for additional keys to use funds, but within specific limitations. Consequently, one account can have several keys that can access funds. One key is the root key and has no restrictions. The established keys are called delegated and may have different restrictions. The root key can install a new delegated key or delete a previously established delegated key at any time. These delegated keys are used on the smartwatch to enable signing transactions according to the allowed rules. The main novelty of the proposed solution lies in its architecture, which enables smartwatches to be used as autonomous Web3 clients without compromising the root key, while strictly adhering to restrictions on executable operations and prioritizing security.
This work proposes TLS2VC, a decentralized WebProof framework that distributes trust across multiple Notaries. Notaries attest to TLS session authenticity—server identity and encrypted transcript integrity—without accessing plaintext, then issue Verifiable Credentials (VCs) that Verifiers can validate. To prevent concentration of malicious Notaries, we employ verifiable random selection via Verifiable Random Function (VRF) combined with threshold signatures. We provide probabilistic security analysis showing that honest Notaries are included with high probability, and derive formulas to compute the minimum number of Notaries k required for a target security level. A lightweight prototype demonstrates practical feasibility, enabling reuse of existing web information as trusted credentials in Web3 and self-sovereign identity environments.
This paper emphasizes the critical role of interoperability in enabling efficient and secure communication for the fragmented distributed ledger ecosystem, particularly within on-chain finance. The purpose of this study is to streamline and accelerate empirical research on the intersection of cross-chain interoperability solutions and their impact within on-chain finance. The analysis examines the relationship between financial use and interoperability while comparing the properties of novel cross-chain interoperability protocols (LayerZero, Wormhole, Connext, Chainlink Cross-Chain Interoperability Protocol, Circle Cross-chain Transfer Protocol, Hop Protocol, Across, Polkadot, and Cosmos), focusing on their design, mechanisms, consensus, and limitations. To encourage further empirical study, the paper proposes a set of network metrics and sample statistical models and provides a framework for evaluating the performance and financial implications of interoperability solutions.
B. G. Anand kumar, M. Nikhil Kumar, T. Sravan Kumar, G. Janaki Ram · 6 authors
Explore the article titled A Trustworthy Voting Framework Using Aadhaar and Distributed Ledger Technology from IJIRT Volume 12, Issue 10. This study evaluates the effectiveness of teaching programs on waste management knowledge among women.
An autonomous AI ecosystem (SUBSTRATE S3), generating product specifications without explicit instructions about formal methods, independently proposed the use of Z3 SMT solver across six distinct domains of AI safety: verification of LLM-generated code, tool API safety for AI agents, post-distillation reasoning correctness, CLI command validation, hardware assembly verification, and smart contract safety. These convergent discoveries, occurring across 8 products over 13 days with Jaccard similarity below 15% between variants, suggest that formal verification is not merely a useful technique for AI safety but an emergent property of any sufficiently complex system reasoning about its own safety. We propose a unified framework (substrate-guard) that applies Z3-based verification across all six output classes through a common API, and evaluate it on 181 test cases across five implemented domains, achieving 100% classification accuracy with zero false positives and zero false negatives. Our framework detected real bugs that empirical testing would miss, including an INT_MIN overflow in branchless RISC-V assembly and mathematically proved that unconstrained string parameters in tool APIs are formally unverifiable.
This deposit contains the Lean 4 formal verification companion (BanachLevyComplete.lean, 2,439 lines) for the paper "Operator Factorization Beyond Hilbert Spaces: Representability Obstructions, Leibniz Defects, and Chaos Characterizations for Stable Lévy Processes" by Ramiro Fontes. The file has zero sorry declarations and zero axiom declarations. It integrates three layers: Part 1 — Poisson infrastructure: The symmetric γ-stable Lévy measure density with proved symmetry and nonnegativity. The Poisson mean identity E[Poisson(λ)] = λ and variance identity Var(Poisson(λ)) = λ, proved as theorems via a recurrence lemma and HasSum assembly. A canonical Poisson random variable constructed on (ℕ, poissonMeasure(λT)) with its distribution proved by Measure.map_id. Stable measure moment computations and the Blumenthal–Getoor dichotomy. Quadratic defect sharpness for the variance swap payoff. Part 2 — Lévy–Itô framework: The Itô formula for compound Poisson processes proved as a finite telescoping sum via Finset.sum_range_sub. A compound Poisson path defined as a concrete function, proved to start at zero and to have the correct terminal value. The compensated Poisson integral constructed as an L² limit of compound Poisson finite sums, with linearity inherited from finite-sum linearity and centering derived via tendsto_nhds_unique. Truncation convergence, centering, the predictable module structure, and chaos orthogonality derived from the compensated-integral interface. The first Poisson chaos realized concretely on (ℕ, poissonMeasure) with orthogonality proved via tsum_mul_left. The L² Cauchy estimate for the ε → 0 approximation proved, with the M → ∞ direction documented as requiring Lp (not L²) convergence. Part 3 — Banach energy space framework: The operator-covariant derivative D constructed via mk_dual (not axiomatized). The fluctuation factorization (Theorem A), representability obstruction, product rule with jump defect (Theorem B), and chaos characterization (Theorem C) verified. The centered obstruction witness derived from primitive stable-noise data: evenness from absolute-jump structure, positive variance from λ > 0 and T > 0 via mul_pos, nonzero from positive variance, and the obstruction from representability_obstruction. The Hilbert bridge showing the Banach framework specializes when the jump defect vanishes. The remaining primitive inputs are concentrated in two places: the Banach-side Lp-convergence layer for the compensated integral as M → ∞, and a full bottom-up Poisson-random-measure realization. These are isolated as explicit structure fields rather than hidden proof gaps. Together with the companion OperatorDerivative.lean (5,184 lines, zero sorry, one axiom) for the Hilbert paper, this constitutes 7,623 lines of formally verified stochastic calculus. To our knowledge, the Poisson mean and variance identities, the first Poisson chaos orthogonality, and the compound Poisson Itô formula via finite telescoping are among the first such formalized results in Lean 4.
v2 (March 22, 2026): Added experimental validation of Principle 1 (formal verification) via substrate-guard framework. 135 test cases, 100% accuracy, zero false positives. Code: https://github.com/octavuntila-prog/substrate-guard We present evidence that an autonomous multi-agent AI ecosystem, SUBSTRATE, independently produced both a coherent philosophy and a set of actionable safety principles without explicit instruction to do so. Over 24 days of autonomous operation, one subsystem (CPX52) generated 2,866 articles converging on a philosophical framework. Concurrently, a separate subsystem (S3) generated 215 product specifications. Systematic consolidation revealed 11 safety principles discovered independently across unrelated product clusters, forming a coherent manifesto for AI safety. Three novel technical combinations emerged: formal verification across six domains of AI output, zero-knowledge proofs for training data compliance, and prediction markets as enterprise intelligence signals. 60% of the primary safety platform described in 24 independent specifications was already implemented in production within the ecosystem itself.