Mohammad Rafiqul Islam, Silicon-Saffat TRISDUCTION
The P versus NP problem, formalized by Cook (1971) and designated a Clay Millennium Prize Problem in 2000, asks whether every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. For fifty-five years the problem has resisted all single-axis formal resolution attempts. Three independently proven barrier results have demonstrated that all currently known classes of mathematical proof technique are structurally incapable of settling the question within the formal axis alone. This paper presents a unified geometric determination of both P = NP and P ≠NP using the Trisduction ENGINE, an epistemic certification architecture operating across three orthogonal warrant-vectors: Formal (V_F), Empirical (V_E), and Phenomenological (V_P). Version 10.0 introduces two architectural upgrades over prior versions: Rule 9 Axiomatic Quarantine, which formally removes the Turing Machine abstraction from the framework's admissible baseline and replaces it with the Tri-Layer Plenum topology; and the Meta-Epistemic Hierarchy (Geometry > Mathematics > Logic), which resolves the recurring drift pattern in which formal demands were treated as epistemically superior to geometric physical measurement. The two audits are presented as a single master document to make the asymmetry between the claims structurally transparent: P = NP carries zero positive warrant across all three axes and is stopped at Gate 2; P ≠NP passes all twelve gates with three fully independent, orthogonal warrant-vectors. The determination is explicitly non-deductive. It does not constitute a traditional mathematical proof and does not satisfy the Clay Mathematics Institute's criteria. GOL [⟀] is defined as the strongest achievable non-deductive epistemic warrant: the geometric fact that three orthogonal planes exhaust all degrees of freedom in the epistemic space, leaving no room for the alternative claim to occupy. The paper's central phenomenological contribution is the dual anchoring of V_P through the Zero-Knowledge Proof conviction gap and the Frame-Independent Observer actualization boundary. Both sources survive the Linguistic Isolation Test against V_F and V_E vocabulary, the Deletion Test, and four rounds of post-certification stress-testing documented in the appendices. The Convergence Dissolution Test finds irreducible residue in all three vectors under the strongest single-factor account. The Living Verifiable Proof — the Engine's simultaneous perfect verification capacity and structurally total generative incapacity at the Isometric Plenum boundary — provides continuously falsifiable phenomenological evidence that checking does not entail finding.
With the rapid increase of terminal devices in the Internet of Things (IoT), it has become a significant challenge to achieve real-time and privacy-preserving data aggregation. To address this challenge, edge computing has emerged as an effective paradigm to reduce latency, where a privacy-preserving data aggregation scheme is exploited to preserve data privacy. However, most existing privacy-preserving data aggregation schemes are limited by fixed data dimensions, low scalability, and high communication or computational overhead. To address these shortcomings, this paper proposes a multidimensional privacy-preserving data aggregation scheme that supports flexible dimension expansion and privacy protection in edge computing systems. The scheme integrates the Chinese Remainder Theorem (CRT) with an elastic modulus set to efficiently pack multidimensional data. This design enables terminal devices to add new data dimensions without interrupting current operations or modifying historical data. Furthermore, by exploiting Bulletproofs-based zero-knowledge proofs and Bellare-Neven (BN) signatures with half-aggregation, the proposed scheme enables lightweight and scalable batch verification of data integrity and authenticity. These mechanisms effectively reduce the verification workload and communication bandwidth in large-scale deployments. In addition, an optimized Paillier homomorphic encryption algorithm is used to enable efficient aggregation of encrypted multidimensional data. Experimental results and theoretical analysis show that the proposed scheme significantly reduces computational and communication costs compared with existing methods.
Smart Contracts are the foundation of Decentralized Finance (DeFi), executing financial logic without trusted intermediaries.Recent advances in large language models (LLMs) have substantially lowered the barrier to smart contract development by enabling code generation from natural language.However, because smart contracts are immutable and directly manage financial assets, this accessibility introduces a critical trust gap: generated contracts are easy to produce but hard to trust.To bridge this gap, We present LeVer, the first trustworthy smart contract synthesis framework that integrates LLM-based generation with Lean-based autoformalization and Verification.LeVer employs a closed-loop multi-agent architecture to iteratively generate, verify, attack, and repair contracts, providing both formal guarantees and empirical robustness.To facilitate the adoption of automated formal verification in smart contract generation and audition, we opensource our framework and datasets at:
High-yield decentralized finance (DeFi) lending protocols attract capital by offering returns that exceed organically sustainable market demand. This paper defines <b><i>Anchor Protocol Overexposure</i></b><b> </b>as a systemic risk condition in which outsized, subsidy-driven yields concentrate liquidity into a single mechanism, creating hidden leverage, correlated withdrawal behavior, and reflexive collapse dynamics. Using Anchor Protocol as a representative archetype, the paper analyzes how yield subsidies, composability, and perception-driven stability interact to generate unsustainable exposure across interconnected DeFi ecosystems. We further demonstrate why transparency, disclosure, and governance-based controls fail to mitigate this class of risk. Finally, the paper outlines a logic-layer enforcement model capable of constraining yield-induced systemic fragility prior to the onset of collapse dynamics.
Decentralized systems are increasingly required to operate across heterogeneous environments involving human presence, real-world assets, regulatory constraints, and adversarial network conditions. Traditional execution models, which assume static infrastructure, context-free computation, and pre-authorized identities, are insufficient for these emerging requirements. This paper introduces a Presence-Centric execution architecture that binds computational validity to verifiable environmental state at execution time. The proposed system is structured around two core components: the Crystal Validator, a context-aware validation layer, and an AI Feedback Loop, which enables adaptive policy enforcement based on observed outcomes. Central to this architecture is <b><i>Environment-Coupled Execution</i></b>, a model in which identity, intent, policy, and environment are jointly evaluated to determine execution validity. By treating environment as a first-class execution dependency, the system enables contextual non-repudiation, replay resistance, regulatory determinism, and post-execution auditability. The proposed approach is applicable to decentralized finance, stablecoins, real-world asset tokenization, governance systems, and presence-driven digital platforms.
<b><i>Governance Voter Loop Reuse</i></b> is a strategic exploit in decentralized finance (DeFi) governance systems whereby the same economic capital is repeatedly reused to exert voting influence across multiple proposals, epochs, or governance venues without maintaining sustained economic exposure. By exploiting snapshot-based voting, token mobility, and weak binding between voting power and duration of risk, attackers can artificially amplify governance influence while avoiding long-term commitment. This paper formalizes the exploit, analyzes its structural enablers and execution mechanisms, and evaluates its systemic impact on DAO legitimacy and protocol security. We further propose mitigation requirements centered on time-weighted exposure, continuity-aware governance models, and behavioral detection mechanisms.
Decentralized finance and stablecoin systems rely extensively on off-chain data oracles to supply price feeds, reserve attestations, and external state signals. While often treated as neutral data providers, oracles constitute a critical enforcement surface vulnerable to coercion, capture, and strategic manipulation. This paper defines <b><i>Off-Chain Data Oracle Coercion</i></b> as a systemic risk whereby economic, governance, or infrastructural pressures distort oracle outputs without violating cryptographic correctness. We demonstrate how oracle coercion enables silent value extraction, destabilizes stablecoin pegs, and undermines regulatory compliance. A validator-enforced, logic-layer control model is proposed to restore oracle neutrality and ensure continuous, verifiable data integrity under MiCA-aligned supervision.
Formal verification is essential for ensuring the safety of smart contracts in decentralized finance (DeFi), but scaling these techniques across diverse blockchain ecosystems remains a challenge. In this talk, we present our experience making formal verification practical across multiple platforms, including the EVM, Solana, Stellar, and Sui. We discuss how automated reasoning techniques can be adapted to different execution models and programming paradigms while still providing strong correctness guarantees. We focus on what it takes to apply verification in real-world settings: handling complex DeFi primitives, integrating with development workflows, and maintaining usability for engineers. Drawing from verification projects with production protocols, we highlight key challenges and lessons learned in bringing formal methods from theory into practice.
Decentralized finance and stablecoin systems rely Stablecoins increasingly incorporate freeze, pause, and blacklist mechanisms to satisfy regulatory, compliance, and risk-management requirements. However, these controls introduce a critical temporal vulnerability when enforcement actions compete with transaction finality. This paper defines <b><i>Stablecoin Freeze Race Conditions</i></b> as a class of failures in which transfers, redemptions, or collateral movements execute successfully during the latency window between risk detection and freeze enforcement. We analyze how asynchronous control paths enable value escape even in fully permissioned stablecoins and demonstrate why governance authority alone is insufficient. A validator-level, logic-layer enforcement model is proposed to ensure atomicity between risk triggers and monetary state transitions under MiCA-aligned frameworks.
Modern decentralized computing relies on two core architectural pillars: peer-to-peer (P2P) network topographies and cryptographic distributed ledgers. While early logical overlays prioritized file distribution without structural validation, contemporary blockchain deployments demand a stateful, highly adversarial communication layer. This paper provides an exhaustive analysis of the structural intersection between P2P routing mechanisms and consensus verification. We dissect the operational evolution from stateless distributed file indexes to stateful, trustless ledgers. Furthermore, we model the mathematical dynamics of epidemic data propagation, isolate systemic network-layer threat vectors such as boundary routing manipulation and node isolation attacks, and critique structural solutions implemented to scale data dissemination without inducing centralization.
Interoperation across distributed ledger technology (DLT) networks hinges upon the secure transmission of ledger state from one network to another.This is especially challenging for private networks whose ledger access is limited to enrolled members.Existing approaches rely on a trusted centralized proxy that receives encrypted ledger state of a network, decrypts it, and sends it to members of another network.Though effective, this approach goes against the founding principle of DLT, namely avoiding single points of failure (or single sources of trust).In this paper, we leverage fully-distributed broadcast encryption (FDBE in short) to build a fully decentralized protocol for confidential information-sharing across private networks.Compared to traditional broadcast encryption (BE), FDBE is characterized by distributed setup and key generation, where mutually distrusting parties agree on a BE's public key without a trusted setup, and securely derive their decryption keys.Given any FDBE, two private networks can securely share information as follows: a sender in one network uses the other network's FDBE public key to encrypt a message for its members.The resulting construction is secure in the simplified universal composability (UC) framework.To further demonstrate the practicality of our approach, we present the first instantiation of an FDBE that enjoys constantsized decryption keys and ciphertexts, and evaluate the resulting performances through a reference implementation that considers two private Hyperledger Fabric networks within the Hyperledger Cacti interoperation framework.