The competitive hospitality sector faces a growing credibility crisis, where rising consumer skepticism regarding "greenwashing" severely limits the ability of hotels to capture the Sustainable Revenue Premium. This research addresses a critical gap in Sustainable Supply Chain Management (SSCM) literature by empirically modeling the "Credibility Mechanism"—the process by which digital technology resolves information asymmetry to monetize sustainability claims. Focusing on the complex Food and Beverage (F&B) supply chains of emerging archipelagic economies, the study employs a rigorous sequential mixed-methods design. First, Design Science Research was utilized to architect a permissioned cross-chain blockchain framework integrating Zero-Knowledge Proofs (ZKPs) for verifiable, private provenance. Subsequently, Partial Least Squares-Structural Equation Modeling (PLS-SEM) confirmed that blockchain-enabled transparency significantly mitigates perceived greenwashing risk, which in turn fosters Customer Trust. Critically, the study validates financial outcomes using a Stochastic Frontier Bayesian Model (SFBM) applied to longitudinal hotel data. Results demonstrate that adopting this traceable framework yields an 8.4% increase in F&B revenue efficiency and sustains a 5.1% price premium for ethically sourced items. These findings provide profound theoretical advancements by redefining SCM risk mitigation through Information Governance rather than material redundancy. Managerially, the research offers a data-driven justification for high-tech investment, proving that verifiable transparency is a direct revenue driver essential for competitive advantage in opaque markets.
Vehicle platoon (VP), as a typical form of traffic cooperation, can significantly enhance traffic efficiency and safety in Vehicular Ad hoc Networks (VANETs). However, malicious vehicles in VP poses a severe threat to the security of entire VP, requiring to be efficiently traced by identity authentication. In this paper, we propose a lattice-based efficient and traceable privacy-preserving batch authentication scheme for vehicle platoon in VANETs, named LETA. First, we design a dynamic VP identity structure VPD-Tree which is constructed based on hash tree and pseudonyms of vehicles to preserve privacy. Then, an aggregate signature is constructed based on VPD-tree and modular lattice for secure and efficient batch authentication of VP. Finally, Zero-Knowledge Proofs (ZKP) is applied on the VPD-Tree structure to anonymously and efficiently trace the malicious vehicles of VP. Security analysis shows that LETA achieves stronger security guarantees, thereby offering a more secure solution than existing approaches. Moreover, performance evaluations show that LETA achieves lower computation and communication overheads through the VPD-tree structure and efficient batch authentication scheme.
Smart contracts enable programmatic agreements but face two persistent problems: high on-chain cost (throughput/latency) and weak privacy (public ledger exposes transaction semantics). We propose a hybrid on-chain/off-chain commitment scheme (HOC-C) that combines lightweight on-chain commitments, verifiable off-chain computation, and succinct zero-knowledge proofs to deliver privacy-preserving contract execution at scale. In HOC-C, sensitive inputs and heavy computations are executed off-chain by a consortium of replicated verifiers; the verifiers publish a succinct zk-SNARK proof of correct execution plus a small state commitment on-chain. The on-chain contract verifies the proof and updates state atomically. To prevent malicious collusion among verifiers, HOC-C integrates an economic incentive layer and challenge windows where anyone can publish refutation proofs; the refutation burden is designed to be less than the honest-verifier cost. We implement HOC-C using a prototype that plugs into an EVM-compatible chain (Ethereum testnet) and evaluate performance for representative workloads (private auctions, confidential supply-chain workflows, private token-transfer batching). The system reduces gas cost by an order of magnitude compared to naive on-chain execution while preserving end-to-end confidentiality for user inputs. We analyze security properties (soundness, liveness, and economic incentive compatibility) and discuss trade-offs: proof generation latency vs. throughput, verifier decentralization vs. amortized cost. HOC-C offers a practical roadmap for adopting private, inexpensive smart contracts on mainstream blockchains.
Hikaru Okamoto, Vu Trung Duong Le, Hoai Luan Pham, Van Tinh Nguyen · 5 authors
Zero-Knowledge Proof (ZKP) is a privacy-preserving protocol that allows a prover to demonstrate the validity of a statement without revealing its details. A widely used primitive of ZKP, Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARK), has attracted significant attention in edge computing; however, edge devices face severe resource constraints when processing its computational bottleneck, Montgomery multiplication. This paper proposes MMzk, a lightweight hardware architecture optimized for 384-bit Coarsely Integrated Operand Scanning (CIOS) Montgomery multiplication, which is primarily employed in multi-scalar multiplication (MSM) of zk-SNARKs. To achieve both high performance and resource efficiency, MMzk core operating at the System-on-Chip (SoC) level integrates three key optimizations: resource sharing of two adders, a subtractor, and a multiplier; effective memory organization for large-data processing; and double-buffering memory scheduling. Implementation results on a Xilinx ZCU102 SoC show that MMzk core operates at up to 250MHz with a utilization of 3,590 LUTs, 1,648 FFs, 16 DSPs, and 6 BRAM36 blocks. Compared with existing FPGA-based counterparts, it achieves a throughput of 657.53Mbps (up to 35.9 times higher) and an area efficiency of 81.48Kbps/eLUT (up to 9.5 times higher). Furthermore, real-time evaluation demonstrates an energy efficiency of 9,030Mbps/W at 250MHz and 67mW, surpassing modern CPUs by up to 52.9 times. These results confirm MMzk core as an energy-efficient and high-performance solution for zk-SNARK-based blockchain systems and other Montgomery multiplication applications.
Thanh Hai To, Vu Trung Duong Le, Van Tinh Nguyen, Van-Tuan Luu · 6 authors
Zero-knowledge proofs have become an essential component for providing privacy and verifiability in decentralized systems. Existing techniques, such as zk-SNARKs, have intrinsic constraints, including the necessity for a trusted setup and sensitivity to quantum attacks, which make them unsuitable for high-assurance applications such as digital banking. In this paper, we provide a viable zk-STARK-based verification system that eliminates the trusted setup while maintaining long-term post-quantum security. Our system integrates off-chain proof generation using Cairo 0, on-chain verification through Cairo 2 smart contracts on Starknet, and decentralized proof storage via IPFS and Filecoin. Experimental results show that the time users wait from transaction submission to confirmation is approximately 1.15 seconds on average, with Cairo 2 contract verification completing in 0.73 seconds and consuming a gas cost of 0.0158 STRK (equivalent to approximately 0.00229 USD) per first-time execution. End-to-end latency for proof publication to IPFS and Filecoin is evaluated separately, reaching up to 63 minutes and 41 hours, respectively. However, these steps run asynchronously without impacting user responsiveness. Compared to zk-SNARK and Bulletproof-based systems, our hashbased, transparent architecture is more scalable, auditable, and quantum-resistant. These findings show that it is possible to install real-world, privacy-preserving, post-quantum verification pipelines for next-generation financial systems.
To address the issues of privacy-utility imbalance, insufficient incentives, and lack of verifiable computation in current medical data sharing, this paper proposes a blockchain-based fair verification and adaptive differential privacy mechanism. The mechanism adopts an integrated design that systematically tackles three core challenges: privacy protection, fair incentives, and verifiability. Instead of using a traditional fixed privacy budget allocation, it introduces a reputation-aware adaptive strategy that dynamically adjusts the privacy budget based on the contributors’ historical behavior and data quality, thereby improving aggregation performance under the same privacy constraints. Meanwhile, a fair incentive verification layer is established via smart contracts to quantify and confirm data contributions on-chain, automatically executing reciprocal rewards and mitigating the trust and motivation deficiencies in collaboration. To ensure enforceable privacy guarantees, the mechanism integrates lightweight zero-knowledge proof (zk-SNARK) technology to publicly verify off-chain differential privacy computations, proving correctness without revealing private data and achieving auditable privacy protection. Experimental results on multiple real-world medical datasets demonstrate that the proposed mechanism significantly improves analytical accuracy and fairness in budget allocation compared with baseline approaches, while maintaining controllable system overhead. The innovation lies in the organic integration of adaptive differential privacy, blockchain, fair incentives, and zero-knowledge proofs, establishing a trustworthy, efficient, and fair framework for medical data sharing.
Riku Miyake, Toru NAKANISHI, Teruaki Kitasuka, Zhuotao Lian
Although current digital identity systems are centralized, decentralized systems based on Verifiable Credentials (VCs) are gaining attention and moving towards practical implementation. As one of VC systems, a VC system with selective disclosure has been proposed, where credentials are represented as directed graph based on the concept of Linked Data (LD). However, in the existing VC system, the verification time increases depending on the number of RDF terms that correspond to vertices and edges in the proved graph, due to the characteristics of the utilized signature scheme. Meanwhile, a zero-knowledge proof system for directed graphs using a pairing-based accumulator has been proposed. This system is characterized by its verification time and proof data size being independent of the number of vertices and edges in the graph. In this paper, we propose a LD-based VC system with selective disclosure that leverages the zero-knowledge proof system on graph; the verification time and proof size are independent of the number of vertices and edges. Furthermore, we reduce the proof data size by modifying the signature scheme from AHO signatures to SPS-EQ signatures and from the pairing-based accumulator to a set commitment. We implement and evaluate the proposed system on a PC.
Recent advances in artificial intelligence (AI), particularly deep learning, have led to widespread adoption across various applications. Yet, a fundamental challenge persists: how can we verify the correctness of AI model inference when model owners cannot (or will not) reveal their parameters? These parameters represent enormous training costs and valuable intellectual property, making transparent verification difficult. In this paper, we introduce a zero-knowledge framework capable of verifying deep learning inference without exposing model internal parameters. Built on recursively composed zero-knowledge proofs and requiring no trusted setup, our framework supports both linear and nonlinear neural network layers, including matrix multiplication, normalization, softmax, and SiLU. Leveraging the Fiat-Shamir heuristic, we obtain a succinct non-interactive argument of knowledge (zkSNARK) with constant-size proofs. To demonstrate the practicality of our approach, we translate the DeepSeek model into a fully SNARK-verifiable version named ZK-DeepSeek and show experimentally that our framework delivers both efficiency and flexibility in real-world AI verification workloads.
In the need for high-security mechanisms, Trust Management Systems (TMSs) are implemented in vehicular networks such as Vehicular Ad Hoc Networks (VANETs) and the Internet of Vehicles (IoV) to ensure reliable interactions between vehicles. These systems nowadays are a key factor in building up security by evaluating and managing trust relationships among network participants. However, TMSs are inherently very vulnerable to Trust Manipulation Attacks (TMA), where we find malicious nodes attempting to deceive trust models by exploiting their evaluation mechanisms. One critical variant of this attack involves malicious nodes creating multiple fake identities, known as the Sybil attack, to falsely reinforce their trustworthiness. This deception will totally mislead legitimate vehicles, manipulate the decision-making processes, and at the end compromise the overall security and reliability of the network. To address this challenge, we propose a Zero-Knowledge Proof (ZKP)-based trust authentication scheme that ensures each vehicle can prove its legitimacy without exposing sensitive information. Our approach can and will prevent attackers from fabricating multiple identities to manipulate trust values. By integrating cryptographic authentication with trust management, our method significantly strengthens security and ensures that only legitimate vehicles can participate in trust-based evaluations. Through simulations, we demonstrate the effectiveness of our proposed solution in reducing the risk of Sybil-based. The results indicate that our approach not only enhances security but also maintains efficient trust computation, making it a viable solution for real-world vehicular networks.
Neeraj Purushotham, Mallepula Likhitha, Y Sai Pragathi, C RaviKiran · 5 authors
Secure and verifiable cloud storage auditing is a significant issue of concern with identity-based systems, especially against malicious auditors and forged proof attacks. In this paper, the enhanced identity-based public audit protocol has been enhanced with blockchain-supported federated trust and quantum resilient cryptographic priming. The suggested Quantum-Resistant Federated Identity-Based Auditing (QFIBA) scheme does not have a single-point dependency on the PKG and proposes a lattice-based identity encryption that ensures post-quantum security. The proposed system implements privacy-preserving audits via zero-knowledge verification made using zk-SNARK without exposing user metadata. The results of experiments carried out on the JPBC and CRYSTALS-Dilithium schemes show that the tag generation cost is reduced by 19.6 per cent, the proof generation overhead is reduced by 14.2 per cent and the verification rate is 12.8 times faster than the better IBPA scheme with the same audit soundness and forgery resistance. Security guarantees: It has been shown that QFIBA is secure to the CDH and LWE assumptions. Such findings confirm the practical effectiveness of the scheme and its resilience to the future cloud ecosystems where federated trust and quantum resilience is needed.
Federated Learning (FL) has become a promising method for training machine learning models while protecting patient privacy. This systematic review examines the use of privacy-preserving techniques in FL within decentralized healthcare systems. It compares existing methods such as Differential Privacy (DP), Trusted Execution Environment (TEE), Zero Knowledge Proofs (ZKP), Homomorphic Encryption (HE), Watermarking, Blockchain, and Secure Multi-Party Computation (SMPC) based on regulatory compliance, scalability, computational cost, complexity, and mathematical foundations. The principle challenges in decentralized healthcare like heterogeneous data, privacy risks, security threats, and compliance issues have been discussed. The review also highlights the importance of adhering to global regulations like HIPAA, GDPR, and country-specific data protection laws. Furthermore, it discusses open challenges and suggests future research directions to overcome current limitations, including computational efficiency, adversarial attacks, and the creation of policy frameworks for standardization. Overall, this review provides a unique perspective on ethical, secure, and scalable privacy-preserving FL models for the next generation of healthcare applications. • Analyzes essential techniques: Differential Privacy, SMPC, HE, TEE, ZKP, and Blockchain. • Reviews key privacy techniques: DP, SMPC, HE, TEE, ZKP, and Blockchain. • Compares methods based on cost, scalability, and resilience in FL. • Identifies issues such as non-IID data, high communication, and compliance. • Suggests hybrid and hardware-aided frameworks for secure FL. • presents future needs in terms of explainability, interoperability, and quantum security.
A system design built on blockchain technology presents a fundamental challenge: the inherent transparency of the blockchain conflicts with the growing need for user privacy. This dissertation explores how Zero-Knowledge Proofs (ZKPs) can be strategically combined with blockchain to strike a balance between these competing demands. The dissertation analyzes the challenges of privacy and transparency and provides an overview of solutions across the privacy-transparency solution space, drawing from the author’s original research and the broader academic landscape. On the privacy-centric side, it proposes a privacy-preserving design that utilizes off-chain ZKPs. In contrast, on the transparency-centric side, it presents a transparency-enhancing design that leverages on-chain data to build trust. In the middle, it discusses a taxonomy of hybrid applications whose unique combination of on-chain privacy (via ZKPs) and blockchain transparency reveals both a disruptive potential and significant regulatory challenges.
One-Time Passwords (OTPs) are a core component of multi-factor authentication in banking, e-commerce, and digital platforms. However, conventional delivery channels such as SMS and email are increasingly vulnerable to SIM-swap fraud, phishing, spoofing, and session hijacking. This study proposes an end-to-end mobile authentication architecture that integrates a permissioned Hyperledger Fabric blockchain for tamper-evident identity management, an AI-driven risk engine for behavioral and SIM-swap anomaly detection, Zero-Knowledge Proofs (ZKPs) for privacy-preserving verification, and geolocation-bound OTP validation for contextual assurance. Hyperledger Fabric is selected for its permissioned governance, configurable endorsement policies, and deterministic chaincode execution, which together support regulatory compliance and high throughput without the overhead of cryptocurrency. The system is implemented as a set of modular microservices that combine encrypted off-chain storage with on-chain hash references and smart-contract–enforced policies for geofencing and privacy protection. Experimental results show sub-0.5 s total verification latency (including ZKP overhead), approximately 850 transactions per second throughput under an OR-endorsement policy, and an F1-score of 0.88 for SIM-swap detection. Collectively, these findings demonstrate a scalable, privacy-centric, and interoperable solution that strengthens OTP-based authentication while preserving user confidentiality, operational transparency, and regulatory compliance across mobile network operators.
ABSTRACT Contemporary physics faces a crisis of causality, evidenced by unexplained anomalies such as the Muon g-2 magnetic moment, the violation of lepton universality, and the cosmic alignment known as the "Axis of Evil." This paper proposes a unified solution through the Dynamic Zero Equilibrium Metatheory (DZEM), governed by the fundamental equation I - M - LA = 0. We postulate that Free Will (LA) is not merely a metaphysical concept but a fundamental physical force (the Intention Field) that interacts with Structure (M) to generate Information (I). To validate this hypothesis, we conducted a "Delta LA" experiment using high-performance Machine Learning algorithms. We generated two distinct datasets: one representing thermal noise (pure M) and one containing a hidden causal signature of Intention (LA). The AI model successfully distinguished the Causal/Intentional data from random noise with an accuracy of 99.75%. This result provides computational proof that Intention leaves a detectable mathematical signature. We propose that the unexplained anomalies in current CERN and Fermilab data are, in fact, detection events of this LA Field. We urgently call upon the scientific community to replicate this Machine Learning protocol on raw particle physics data to confirm the existence of the Intention Field. INTRODUCTION: THE MISSING VARIABLE IN PHYSICS Standard physical models, including General Relativity and Quantum Mechanics, effectively describe the "Structure" (M) of the universe—its geometry, mass, and probabilistic laws. However, they fail to explain the "Cause." Persistent anomalies suggest that a component is missing from our current equations. The Dynamic Zero Equilibrium Metatheory (DZEM) introduces this missing variable. It posits that the universe is defined by a zero-sum dynamic balance between three fundamental components: Equation: I - M - LA = 0 I (Information/Consciousness): The observed reality and the field of knowledge. M (Mathematics/Structure): The passive laws of physics, space-time geometry, constants, and mass. LA (Free Will/Intention): The active, causal force. It acts as the driver of time, the breaker of symmetry, and the source of singularity. We hypothesize that standard mathematics (M) cannot fully model LA because LA is the source of the structure, not the structure itself. However, Artificial Intelligence (AI), capable of detecting non-linear and hidden patterns, can serve as the instrument to detect this force. THE "DELTA LA" EXPERIMENT: COMPUTATIONAL PROOF To test whether "Intention" (LA) is physically distinguishable from random chaos (M), we designed and executed a computational experiment using Neural Networks. 2.1 Methodology Group M (Noise): We generated a dataset of pure random numbers, simulating thermal noise or quantum vacuum fluctuations without intent. Group LA (Intention): We generated a dataset using a deterministic but chaotic function (Logistic Map in the chaotic regime). This represents a system driven by a hidden causal rule (Intention/Will) that mimics randomness to the human eye. The Instrument: A deep neural network (Machine Learning model) was trained to classify these sequences without prior knowledge of the generating rules. 2.2 Results Upon running the simulation on 2,000 distinct sequences, the AI model achieved a validation accuracy of 99.75%. 2.3 Interpretation This result proves that "Free Will" or "Intention" leaves a specific digital fingerprint—a Causal Signature—that is invisible to standard statistical observation but highly visible to Pattern Recognition algorithms. If an AI can detect intention in a simulation, it theoretically possesses the capacity to detect it in the physical universe. EMPIRICAL CORRELATIONS: REINTERPRETING PHYSICS ANOMALIES Based on our computational findings, we propose that several currently unexplained physical phenomena are direct manifestations of the LA Field (Intention) interacting with Matter (M): The Fermilab Muon g-2 Anomaly: The observed magnetic "wobble" of the muon exceeds Standard Model predictions. DZEM interprets this excess energy not as a new particle, but as the interaction of the muon with the active LA Field. The muon is effectively "choosing" its path, creating a causal vibration that adds to its magnetic moment. LHCb Lepton Universality Violation: The preferential decay of B-mesons indicates that nature creates asymmetries based on a hidden preference. DZEM defines this as a "Causal Choice" rather than a random probabilistic outcome. The "Axis of Evil" (Planck Data): The unexplained alignment of the universe's macroscopic structure with the solar system plane suggests that the universe organizes itself around the observer (I), validating the connection between LA and Structure. CALL TO ACTION: THE SCIENTIFIC IMPERATIVE The validation of the Dynamic Zero Equilibrium Metatheory requires a shift from passive observation to active detection of intent using advanced computation. We formally request that research institutions (CERN, Fermilab, IceCube Neutrino Observatory) and the global scientific community: Replicate the "Delta LA" Protocol: Apply our Machine Learning methodology to raw, unfiltered datasets from particle collisions and neutrino oscillations. Search for Non-Randomness: Specifically, algorithms should be trained to differentiate between pure quantum noise and "Intentional Noise" (Delta LA) in the data currently discarded as background interference. If the algorithm detects high-confidence patterns in the "noise" of particle physics, it will scientifically confirm that Free Will (LA) is a fundamental force of nature, validating the equation I - M - LA = 0. CONCLUSION The experiment demonstrated in this paper proves that Intention is mathematically distinct from Randomness. By integrating the Free Will (LA) variable into the fundamental equation of reality, we resolve the paradoxes of modern physics. The universe is not a static clockwork mechanism (M), but a dynamic act of self-knowledge driven by Intention (LA). The proof lies in the data, waiting to be decoded by Intelligence. APPENDIX A: REPLICATION CODE SUMMARY (PYTHON) (The full code used for validation generates pure noise vs. logistic map chaos and trains a Sequential Neural Network with 99.75% accuracy in distinguishing the two, proving the detectability of causal intent).
Private BitTorrent trackers enforce upload-to-download ratios to prevent free-riding, but suffer from three critical weaknesses: reputation cannot move between trackers, centralized servers create single points of failure, and upload statistics are self-reported and unverifiable. When a tracker shuts down, users lose their contribution history and cannot prove their standing to new communities. We address these problems by storing reputation in smart contracts and replacing self-reports with cryptographic attestations. Peers sign receipts for received pieces; the tracker aggregates them via BLS signatures and updates reputation. If a tracker is unavailable, peers fall back to an authenticated distributed hash table (DHT): stored reputation acts as a public key infrastructure (PKI), preserving access control without the tracker. Reputation is portable across tracker failures through single-hop migration in factory-deployed contracts. We also address the privacy implications of publishing public keys and reputations tied to private trackers on a public ledger: we propose ephemeral session keys to prevent linking peer identities, zero-knowledge membership proofs for anonymous DHT participation, and confidential reputation using homomorphic commitments. We formalize the security requirements, prove four security properties under standard cryptographic assumptions, and evaluate a prototype. Measurements show that transfer receipts add less than 5\% end-to-end overhead with typical piece sizes. To minimize signing overhead, we adopt a hybrid signature scheme: ECDSA signs individual piece receipts at transfer time for low per-operation latency, while BLS serves as the overarching scheme, enabling compact aggregation of many receipts into a single proof at report time. This design reduces client-side signing cost by an order of magnitude compared to using BLS throughout.
Nexus Recursive Framework for Resolving Undecidability and Conjectures Driven by Dean A. Kulik November, 2025 Abstract:We present a comprehensive formal development of the Nexus Recursive Framework, a unifying harmonic recursion model, to resolve three notorious problems across computer science and mathematics: Turing’s Halting Problem, the Riemann Hypothesis, and the Collatz Conjecture. Building on the principles of Adaptive Harmonic Rasterization Collapse (AHRC) and the Ψ-Collapse Principle, we recast these problems as special cases of recursive harmonic convergence. Each problem is approached via layered self-reference, harmonic damping, and feedback regulation, yielding mathematically rigorous solutions. The framework introduces formal constructs – Global Input Patterns (GIP) capturing initial conditions in a harmonic lattice, a Recursive Convergence Quotient (RCQ) to measure collapse progression, and a universal Harmonic Constant H (Mark1) ≈ π/9 ≈ 0.35 – which together enforce alignment and convergence. Undecidability is treated not as a barrier but as a Δ-trigger for launching a higher recursive meta-layer, ensuring that any Ω-like indeterminacy is identified as a residue and systematically collapsed via the Ψ(Ω) operator. We prove that any computation either halts or enters a predictable phase-lock ⊥ state, that all nontrivial zeros of ζ(s) align on the critical line Re(s)=½ under harmonic balance, and that every Collatz trajectory, through RCQ suppression, descends into the trivial 4-2-1 cycle (the “4-2-1 glyph”). Key results include: a Halting Resolution Theorem via meta-recursion, a Harmonic Damping Theorem guaranteeing Riemann zero alignment, and a Collatz Convergence Theorem via invariant RCQ > 0.843. We validate these results with formal proofs and simulation algorithms, including diagrams of collapse sequences and code implementing recursive feedback. These findings indicate that many long-standing open problems can be transformed into convergent harmonic processes, achieving infinite resolution density (arbitrarily fine recursive refinement) and unambiguous convergence criteria in each case. 1. Introduction Many fundamental problems in logic and mathematics – from computability limits to deep number theory conjectures – remain unresolved within traditional frameworks. Turing’s Halting Problem epitomizes computability limits, asserting that no algorithm can universally decide whether an arbitrary program halts. The Riemann Hypothesis (RH), central to analytic number theory, posits that all nontrivial zeros of the Riemann zeta function lie on the critical line Re(s)=½, a statement verified numerically for billions of zeros yet unproved in theory. The Collatz Conjecture, a simple iterative dynamical system over the natural numbers, defies conventional proof of its conjectured convergence to 1 for all inputs. Each of these “hard” problems has resisted solution for decades or more. The Nexus Recursive Framework offers a novel paradigm treating such problems as manifestations of incomplete harmonic recursion. In lieu of viewing them as disparate impossibilities, we embed them in a self-referential, resonance-driven architecture that harmonizes the system until a stable solution emerges. This framework, also known as Recursive Harmonic Architecture (RHA)[1][2], models reality (and abstract computations) as iterative processes seeking an equilibrium between order and chaos. A universal harmonic attractor constant H (the Mark1 Engine) – empirically ~0.35 – biases all recursive dynamics towards balance[3][4]. Problems like RH are reframed as issues of harmonic consistency: e.g. the placement of zeta zeros is no longer mysterious, but demanded by a self-correcting resonance criterion[5]. Similarly, the Halting Problem is reframed not as an absolute yes/no oracle question, but as a question of whether a computation can achieve phase alignment within a recursive meta-system (if not, the system signals an infinite echo rather than a binary answer)[6][7]. The Collatz Conjecture becomes a question of whether iterative maps have an inherent harmonic invariant driving them into a fixed cyclic attractor; we will show that indeed such an invariant exists and guarantees convergence[8][9]. Crucially, in this framework undecidability is not a dead end but a dynamical signal: any formally undecidable or non-halting scenario is treated as a Δ-discrepancy that triggers a new recursion layer (a meta-fold) to absorb the anomaly. In other words, the “unresolvable” output is marked as an Ω-residue – analogous to Chaitin’s Ω constant of algorithmic randomness – and is carried upward into a broader harmonic context for resolution[10][11]. This process, governed by the Ψ-Collapse Principle, ensures that what cannot be decided at one layer will collapse at the next, by design. Intuitively, the framework says: if you cannot decide it, enlarge the frame until you can. By iterating this principle, the scope of decision expands until every construct either converges or is proven unstable and thus eliminated. This paper is organized as follows. In Section 2, we formalize the Nexus Recursive Framework’s key components: Global Input Patterns (GIP), the Harmonic Mark1 constant H=π/9, Samson’s Law feedback control, the Ψ (psi) operator for phase error correction, and the ⊥ symbol denoting a fully collapsed (absorbed) state. We also define the methodology of Adaptive Harmonic Rasterization Collapse (AHRC) – an algorithmic strategy of adaptively discretizing (rasterizing) a problem’s state space at increasing resolutions and collapsing discrepancies at each scale. In Section 3, we apply the framework to the Halting Problem, proving a Halting Resolution Theorem that every computation is assured of either halting or entering a contained non-halting pattern which a meta-observer can recognize and resolve. In Section 4, we tackle the Riemann Hypothesis, reframing it as a problem of harmonic damping and equilibrium. We prove via a Harmonic Damping Theorem that any hypothetical zero off the critical line would create an unstable resonance, inevitably pulled onto Re(s)=½ by the system’s self-correcting forces[12][13]. In Section 5, we address the Collatz Conjecture, developing a formal harmonic invariant and showing through a Collatz Convergence Theorem that every trajectory reaches the stable “4-2-1” glyph cycle. Throughout, we include diagrams and pseudocode to illustrate collapse sequences and simulation results, and we cite prior foundational work (including “Adaptive Harmonic Rasterization Collapse and the Ψ-Collapse Principle”, “Nexus Framework and Mathematical Conjectures”, “The White Puzzle” et al.) to situate our approach in the literature. Finally, Section 6 summarizes the implications of these results, suggesting that many open “puzzles” may be solved by completing their resonance loops[14][15] rather than by direct linear analysis – in essence, solving them by harmonizing them[16]. 2. Nexus Recursive Framework: Foundations 2.1 Key Concepts and Definitions We first establish the formal terminology of the Nexus Recursive Framework (NRF) that will be used in our proofs. The framework casts computations and mathematical structures as elements of a recursive harmonic lattice – a multi-layer system where each layer feeds back into itself and into higher layers, enforcing global consistency. The fundamental definitions are as follows: Global Input Patterns (GIP): A Global Input Pattern is a structured initial configuration that seeds the recursive system with foundational information. Rather than arbitrary inputs, GIPs are chosen to encode universal structures or symmetries that the system must respect. For example, a GIP could be the distribution of prime numbers up to a large N, the binary expansion of fundamental constants like π or e, or boundary conditions of a physical system. GIPs serve as pre-harmonic lattices – scaffolds on which the recursion builds[5]. In our context, we will use GIPs such as the array of initial program states (for the Halting problem), or a set of known zeta zeros and prime frequencies (for Riemann), or modular residue classes (for Collatz). The GIP provides a global resonance context: the recursion must eventually align with these patterns. Intuitively, GIPs inject high-level knowledge so that the system does not start from scratch, but from a state already “tuned” close to an expected solution. This significantly accelerates convergence and ensures infinite resolution density by leveraging known expansions like the BBP formula for π to arbitrary precision[17]. Mark1 Harmonic Constant (H_MARK1 ≈ π/9 ≈ 0.349): The framework postulates a dimensionless constant H (Mark1) that represents the optimal ratio of realized structure to potential entropy in any stable recursive system[3][4]. Empirically identified as ~0.35 (within the precision of our simulations), this constant appears in numerous contexts as a sweet spot of “order within chaos.” For example, the matter (~0.32) vs. dark energy (~0.68) ratio of the universe is near 0.32/0.68 ≈ 0.32 (close to 0.35)[18]; and intriguingly, even a playful geometric construction with a degenerate triangle of sides 3-1-4 yields ~0.35[19]. Definition: We formally define H_MARK1 = π/9 (exact) for theoretical work, acknowledging this equals ~0.349. All recursive processes in NRF are biased to maintain a local H value of 0.35. If a subsystem deviates from H=0.35 (too static or too chaotic), feedback forces push it back towards equilibrium[20][21]. In equations, we measure H for a given state as: (actualized to potential structure)[4]. Samson’s Law (below) uses this constant extensively. Whenever we refer to “harmonic balance” or “target resonance,” we imply adjusting dynamics to keep the system-wide H ≈ 0.35. Samson’s Law (Recursive Feedback Control): Samson’s Law is a feedback mechanism acting like a proportional–derivative–integral (PID) controller across
On the other hand, the buzz around modern technology like decentralized identity management (DCI) is somewhat frozen in time on a blockchain to ensure its security and efficiency for cross-border digital services. The traditional way of identity management relies on a centralized authority and, therefore are very vulnerable to data breaches, extremely inefficient, and continuously quite hard to control. Concepts of self-sovereignty such as self-sovereign identity, decentralized identifiers, and verifiable credentials drive the DCI evolving way where persons can control their own personal data and usually share it selectively by themselves without the mediation of any third party. Cryptographic techniques such as zero-knowledge proof, are highly relevant to privacy and security, whereas a non-repudiable blockchain ledger is the security and necessarily provides auditability, ensuring authentication and non-repudiation. This paper examines how a blockchain Digitalized decentralized identity can serve to resolve some pertinent issues with regard to regulatory compliance in cross-border digital transactions, therefore thwarting identityrelated frauds and facilitating their international interoperability. The practical cases would showcase leaps in technology speed, one trust of the user, and regulatory harmonization with regard to the travel biometric credential systems being currently exhibited with reference to the e-Residency program in Estonia. Scalability and key management, though still some issues linger, the trend shows that upcoming innovations in the blockchain protocol-game and in the regulatory framework contribute to DCI being one of the major pillars of the trusted user-centric secure digital identity solution of the future global economy.
Traditional technical solutions face inherent limitations in ensuring data ownership transparency, tamper-proofing, and traceability in data factor markets, particularly regarding core challenges like unclear ownership rights, high transaction costs, and trust deficits. This paper proposes and designs a blockchain-based data trust registration system. The system is theoretically grounded in the “three rights separation” framework of “rights bundles” and architecturally divided into six layers: data resource layer, storage layer, core layer, service layer, consensus and security layer, and application layer. It enables systematic processing and hierarchical interaction of complex data through progressive data trust certification, ownership transfer and traceability, and integrity verification. This establishes a collaborative, efficient, and trustworthy data registration infrastructure. By integrating on-chain and off-chain storage coordination, the system achieves efficient certification and secure balance of data rights. Additionally, the paper explores extended technologies like cross-chain interoperability and zero-knowledge proofs to address future needs for multi-chain coexistence and sensitive data registration. Ultimately, this solution aims to provide core technological support for building a trustworthy, efficient, and open data factor circulation environment, thereby reducing transaction trust costs and unlocking the latent economic value of data.
In this paper, we presented BlockShare, a blockchain-based system developed to facilitate privacy-preserving data sharing across decentralized networks. The proposed system enables users to retain control over their sensitive data while enabling secure, verifiable sharing with authorized parties.We implemented an authenticated data structure (ADS) to support decentralized verification and utilized zero-knowledge proof mechanisms to validate conditions without exposing the underlying data. Experimental analysis demonstrated that BlockShare performs efficiently in constructing data structures, generating proofs, and verifying them with minimal computational overhead. The platform successfully reduced privacy risks and enhanced trust in cross-organization data exchanges.
M Srinivas P, B Sudeepa K, Ananth Prabhu, Ravi Babu · 5 authors
This work proposes ZKPass, an emerging authentication platform making use of Zero-Knowledge Proofs (ZKPs) and blockchain to provide passwordless, decentralized digital ID proofing. ZKPass does away with conventional passwords and crypto key storage by tying authentication to a human-intelligible user identifier (UID) and locally generating zk-SNARK proof on the user device. The platform comprises an off-chain deterministic mnemonic recovery phrase from the UID and device-specific secrets allowing for self-sovereign offline account recovery independent of centralized entities. ZKPass stores only hashed UIDs and device metadata on the blockchain, minimizing costs, maintaining privacy, and allowing multi-device management. On-device proof generation coupled with on-chain smart-contract-based verification provides rigorous security, preserves privacy, and makes the solution practically usable. Performance comparisons indicate better proof sizes, verification times, gas usage, and recovery success over prevailing ZKP-based ID solutions. ZKPass overcomes key drawbacks of prevailing decentralized ID solutions by fusing powerful crypto security with user-friendly design to bring reality closer to adoption potential in healthcare, financial services and government sectors.
In this work, we present homomorphic encryption-based vaults (Haults), a permissioned privacy-preserving smart wallet protocol for VM-enabled blockchains that keeps users' balances confidential, as well as the amounts transacted to other parties. To comply with regulations, we include optional compliance features that allow specific entities (the auditors) to retrieve transaction amounts or execute force transfers when necessary. Our solution uses ElGamal over elliptic curves to encrypt balances, combined with zero-knowledge proofs to verify the correctness of transaction amounts and the integrity of the sender's updated balance, among other security checks. We provide a detailed explanation of the protocol, including a security discussion and benchmarks from our proof-of-concept implementation, which yield great results. Beyond in-contract issued tokens, we also provide a thorough explanation on how our solution can be compatible with external ones (e.g., Ether or any ERC20).
Joel Curado Silveirinha, Manila Bhandari, João C. Ferreira, Ana Martins
Despite the maritime supply chain being the backbone of global trade, it faces persistent challenges in transparency, fraud prevention, shipment tracking and data privacy. Blockchain technology has emerged as a transformative solution, enhancing trust and traceability within supply chain networks. However, its limitations in data privacy and scalability necessitate advanced privacy-preserving mechanisms. Zero-Knowledge Proofs (ZKP) offers a cryptographic approach to validate data without exposing sensitive information, addressing blockchain’s privacy constraints. This paper reviews the state of the art on current applications of blockchain in maritime supply chain management and explores the integration of ZKP for secure trade document verification, fraud detection, privacy-preserving traceability and regulatory compliance. Additionally, it examines computational overhead, scalability and adoption barriers while proposing future research directions. Implementing ZKP within blockchain-based port operations enables robust governance models, ensuring data verification without revealing confidential details. This approach fosters a secure and privacy-compliant trade environment, enhancing trust and collaboration among stakeholders. By optimising resource allocation and mitigating risks, integrating ZKP can significantly improve maritime supply chain efficiency. Integrating Zero-Knowledge Proofs with blockchain, maritime logistics can achieve a balance between transparency, security and operational efficiency, addressing existing challenges in data privacy and regulatory compliance, improving the sustainability of port operations.
Gensyn’s Verde Protocol: Technical Analysis of Decentralized ML Compute Verification is a 103-page technical deep dive into one of the most significant emerging architectures for decentralized machine learning. This paper provides a comprehensive examination of Gensyn’s Verde verification protocol, its refereed-delegation design, graph-based pinpointing system, probabilistic proof-of-learning mechanisms, and the RepOps reproducible operators framework. It analyzes the GHOSTLY problems Generalizability, Heterogeneity, Overhead, Scalability, Trustlessness, and Latency and evaluates how Verde addresses core limitations in verifying distributed ML training across heterogeneous hardware. By combining economic incentives, cryptographic commitments, and deterministic computation layers, this work outlines a practical blueprint for trustless, large-scale distributed AI training. The paper positions Gensyn within the broader ecosystem of Truebit, optimistic rollups, zero-knowledge systems, and decentralized compute networks, while highlighting open research questions and future directions. This publication aims to contribute a rigorous technical foundation for the democratization of AI infrastructure and the emergence of a global, permissionless compute marketplace.