Kaja Masthan, Zeeshan Ahmed Mohammed, Rahmat Ali, Abdul Junaid Mohammed
The advancement of medical data handling from conventional paper documents to electronic records enabled secure data movement between authenticated legitimate users. While current identity verification algorithms offer unique solutions, they face significant limitations related to data storage scalability, potential privacy breaches, high computational costs, and the lack of standardized protocols. In order to alleviate these constraints, the research proposes a biometric–Blockchain-based authentication Scheme, a Whirlpool Secure Hash-based Biometric Integrated Key Distribution Function (WShBK) for secure data storage and access in a cloud network. The proposed strong cryptographic scheme generates two unique keys derived from the biometric trait of the patient for both encryption and authentication purposes, ensuring strong protection while accessing and storing the data. Furthermore, the advanced encryption standard WShBK (AWShBK) encryption algorithm leverages the strength of a symmetric block cipher and the unique key, offering robust protection against breaches by rendering intercepted data without the correct decryption key. Furthermore, Hybrid biometric-based zero-knowledge proof (HyBZKP) verification offers secure and private transaction validations while sustaining the blockchain integrity. These advancements of the proposed WShBK scheme improve 0.52 encryption rate and 0.53 decryption rate for 250 users analyzed with an attack compared to other cutting-edge models.
NGOs Funding Trust, Blockchain and RedChain Prof. Victor Alvarez, MBA ORCID iD: 0009-0001-7933-3830 Department Research in Economic , IEBS Business School, 08840 Barcelona, Spain Department of Humanitarian Economics and NGO Management ETU Institute, Birkirkara, Malta Abstract Persistent trust deficits between donor agencies and Non-Governmental Organizations (NGOs) continue to undermine the efficiency and effectiveness of humanitarian and development assistance, particularly in low-income and institutionally fragile environments. Concerns regarding fund diversion, beneficiary duplication, limited transparency, and weak accountability mechanisms have intensified demand for innovative governance solutions. This paper explores the potential of blockchain technology to strengthen trust in NGO funding through two complementary models: (1) a permissioned blockchain framework for beneficiary verification and aid tracking, and (2) RedChain, a privacy-preserving blockchain infrastructure for humanitarian assistance developed by the Spanish Red Cross. The proposed NGO Trust framework utilizes a distributed ledger to maintain immutable and auditable records of beneficiary registration and fund allocation. By recording encrypted identity credentials and digitally signed transactions, the system reduces the risk of duplicate beneficiary claims, fraud, and reporting inconsistencies across participating organizations. A participation and penalty mechanism further enhances network integrity by incentivizing honest behavior among stakeholders. RedChain extends this approach by integrating blockchain-based transaction recording with zero-knowledge proof technologies, enabling transparent aid distribution while preserving beneficiary privacy. With nearly one million registered transactions, the platform demonstrates the operational viability of blockchain-enabled humanitarian governance at scale. By synthesizing these approaches, this paper proposes an integrated framework for transparent NGO funding, combining beneficiary integrity verification, transaction traceability, privacy protection, and donor accountability. The findings suggest that distributed ledger technologies can significantly improve trust relationships between donors, NGOs, and beneficiaries, while supporting more efficient, transparent, and equitable aid distribution systems. The study contributes to the emerging literature on digital governance, nonprofit economics, and technology-enabled development finance by identifying blockchain as a foundational infrastructure for next-generation humanitarian and social-impact ecosystems. Keywords Blockchain; NGO governance; Humanitarian aid; Trust; Transparency; Beneficiary duplication; Zero-knowledge proofs; RedChain; Donor accountability; Privacy-preserving technology; Smart contracts; Aid distribution JEL Classification G30 – Corporate Finance and Governance: General L31 – Nonprofit Institutions; NGOs; Social Entrepreneurship O33 – Technological Change: Choices and Consequences; Diffusion Processes F35 – Foreign Aid H84 – Disaster Aid and Relief 1. Introduction Non-Governmental Organizations (NGOs) play a central role in delivering humanitarian assistance, poverty alleviation programs, disaster relief, education, health services, and sustainable development initiatives worldwide. According to the United Nations and international development agencies, NGOs have become increasingly important intermediaries between donors, governments, and beneficiaries, particularly in regions where state capacity is limited or institutional trust is weak. Despite their growing influence, concerns regarding transparency, accountability, and the efficient allocation of resources continue to challenge the nonprofit sector (Edwards & Hulme, 1996; Ebrahim, 2003; Najam, 1996). The economics of nonprofit organizations has long emphasized the importance of trust as a mechanism for overcoming information asymmetries between donors and service providers (Hansmann, 1980). Donors frequently lack direct information regarding how funds are allocated, whether intended beneficiaries actually receive assistance, and whether reported outcomes accurately reflect project performance. This information gap creates principal-agent problems in which monitoring costs are high and opportunities for misreporting, inefficiency, or fraud may arise (Pratt & Zeckhauser, 1985; Tirole, 2006). As charitable donations and development aid increasingly flow through complex international networks, maintaining donor confidence has become a critical governance challenge. A substantial body of research has documented accountability deficiencies within humanitarian and development organizations. Ebrahim (2005) argues that traditional accountability systems often emphasize upward reporting to donors while providing limited mechanisms for beneficiary participation and verification. Similarly, Gugerty and Prakash (2010) note that transparency initiatives frequently rely on self-reported information that is difficult to independently audit. In international aid programs, concerns have emerged regarding duplicate beneficiary registrations, diversion of funds, weak recordkeeping systems, and fragmented information sharing among organizations operating in the same geographic areas (World Bank, 2016; OECD, 2021). Digital technologies have increasingly been proposed as tools to address these governance challenges. The broader literature on e-governance and digital accountability suggests that information systems can reduce transaction costs, improve record accuracy, and strengthen institutional transparency (Heeks, 2002; Cordella & Tempini, 2015). Among emerging technologies, blockchain has attracted considerable attention due to its capacity to create immutable, distributed, and verifiable records without requiring centralized trust authorities (Nakamoto, 2008). Since the introduction of Bitcoin, blockchain applications have expanded far beyond digital currencies into supply chain management, public administration, healthcare, identity systems, and humanitarian operations (Tapscott & Tapscott, 2016; Casino, Dasaklis & Patsakis, 2019). Scholars have argued that distributed ledger technologies may improve transparency and accountability by creating tamper-resistant transaction histories accessible to multiple stakeholders (Swan, 2015; Treiblmaier, 2018). Within development economics, blockchain-based systems have been proposed to improve aid distribution, reduce corruption, facilitate identity verification, and enhance financial inclusion in underserved regions (Kshetri, 2017; Saberi et al., 2019). Recent humanitarian applications provide evidence of growing institutional interest in blockchain-enabled governance. The United Nations World Food Programme's Building Blocks initiative demonstrated the feasibility of blockchain-based refugee assistance by facilitating aid transfers while reducing administrative costs and improving transaction traceability. Similarly, studies by Juskalian (2018), Mikhaylov et al. (2020), and Wang et al. (2022) suggest that distributed ledger technologies may strengthen accountability mechanisms in humanitarian environments characterized by weak institutional infrastructure. Nevertheless, important challenges remain. Public transparency requirements often conflict with the need to protect sensitive beneficiary information. Humanitarian organizations must balance donor demands for accountability with ethical obligations regarding privacy, dignity, and data protection. The emergence of privacy-enhancing cryptographic techniques, particularly zero-knowledge proofs, offers a potential solution to this dilemma by enabling verification without revealing underlying personal information (Goldwasser, Micali & Rackoff, 1989; Ben-Sasson et al., 2014). These technologies have increasingly been incorporated into blockchain architectures seeking to combine transparency with confidentiality. This paper contributes to the growing literature on nonprofit governance and development finance by examining two complementary blockchain-based approaches to strengthening trust in NGO funding systems. The first is a permissioned blockchain framework designed to prevent beneficiary duplication and improve donor oversight through cryptographically verifiable registration and transaction records. The second is RedChain, a privacy-preserving humanitarian aid platform developed by the Spanish Red Cross that combines blockchain technology with zero-knowledge proofs to support transparent aid distribution while safeguarding beneficiary privacy. By integrating insights from these models, the study proposes a comprehensive framework for Transparent NGO Funding that addresses four persistent governance challenges: beneficiary verification, transaction traceability, privacy preservation, and donor accountability. The analysis contributes to the fields of nonprofit economics, digital governance, and development finance by demonstrating how blockchain technologies may reduce information asymmetries, lower monitoring costs, and strengthen trust among donors, NGOs, and beneficiaries. Ultimately, the paper argues that distributed ledger systems can serve as foundational infrastructure for a new generation of accountable, transparent, and privacy-respecting humanitarian ecosystems.
The rapid proliferation of Internet of Things (IoT) devices across smart homes, healthcare systems, and industrial environments has intensified the need for robust and adaptive security mechanisms in multi-user settings. Traditional password management approaches remain widely deployed; however, they suffer from persistent vulnerabilities including weak password selection, credential reuse across services, and the absence of structured lifecycle management mechanisms. This paper presents a systematic review of existing authentication, password management, and key lifecycle strategies applicable to multi-user IoT ecosystems. The study follows a structured review methodology to analyze and synthesize contemporary research contributions in the areas of context-aware authentication, secure key rotation, password expiry mechanisms, and lightweight cryptographic implementations. A comparative evaluation of diverse security techniques—such as one-time passwords (OTPs), zero-knowledge proofs (ZKP), symmetric and public-key cryptographic schemes, and machine learning-based threat detection models—is conducted with particular attention to device resource constraints, scalability challenges, and operational efficiency. Conceptual models, analytical tables, and comparative charts are utilized to highlight trade-offs between security strength, computational overhead, and system performance. The review identifies significant research gaps in integrating dynamic key rotation and expiry mechanisms into holistic, context-aware security architectures tailored for multi-user IoT environments. Finally, the paper outlines future research directions aimed at developing scalable, resource-efficient, and adaptive password lifecycle management frameworks for next-generation IoT systems. management frameworks for next-generation IoT systems.
The method of secure authorization of banking transaction based on the Schnorr scheme represents a cryptographic approach to verifying user authenticity using Zero-Knowledge Proof (ZKP) protocols. The proposed approach is focused at minimizing the risks of compromising confidential data during the execution of transaction in open or partially trusted environments. The method is based on the Schnorr identification protocol, which relies on the computational hardness of the discrete logarithm problem and enables authentication without transmitting the user’s secret key. The authorization model includes the interaction process between three components of the transaction, namely the client, the transaction execution environment, and the banking side. The transaction execution environment is considered to be critical and untrusted component. The protocol consists of a sequence of stages: first, the initial parameters (p, g) are generated; then the public key value (y) is formed; based on it, a proof value (t) is created; on the bank`s side, a challenge (e) is generated followed by the computation of the parameter s, and subsequently the correctness of the verification relation is checked by the bank. A distinctive feature of the approach is the absence of private key transmission and the use of random values, which prevents the recovery of secret parameters even if part of the data is intercepted. Within the scope of the study, simulations of Man-in-the-Middle (MITM) and replay attacks were performed in older to evaluate the robustness of the proposed approach. In the case of a Man-in-the-Middle attack, it is shown that modification of the parameter t leads to a violation of the verification relation, making successful transaction authorization impossible. To counter replay attacks, a timestamp (TS) mechanism and transaction parameter uniqueness were integrated into the model, eliminating the possibility of reusing intercepted data. The constructed model is based on cryptographic strength, reduction of the impact of vulnerabilities in the transaction execution environment, and ensuring the fundamental principles of digital security, namely data integrity, confidentiality, and authenticity. The proposed method demonstrates its effectiveness in scenario with a high level of threats, such as in the financial sector, where transaction protection is a critical component
The aviation industry depends on data integrity across supply chains spanning OEMs, MRO organizations, airlines, lessors, and national regulators. Centralized data management systems — still dominant in the sector — expose the ecosystem to single points of failure and provide limited traceability of millions of aircraft parts circulating annually. This paper presents a structured review of blockchain-based security architectures for aviation networks, synthesized from 14 peer-reviewed sources published between 2018 and 2025, retrieved from IEEE Xplore, ScienceDirect, SpringerLink, ACM Digital Library, and Wiley/Hindawi. On this basis, a thirteen-step design method is proposed for integrating permissioned blockchain with distributed cloud infrastructure in aviation environments. The method is grounded in quantitative acceptance criteria — throughput ≥ 500 TPS, smart contract execution latency < 200 ms (p95), system availability 99.9% — and maps each design phase to specific security controls (integrity, access control, auditability, privacy, resilience, governance). Core mechanisms are formalized via hash-chain integrity verification, attribute-based access control functions, zero-knowledge proof verification, and a composite pre-ledger trust-scoring model. The principal finding: permissioned blockchain architectures — Hyperledger Fabric in particular — can support aviation requirements for immutable audit trails, decentralized identity management, and regulatory compliance with EASA and FAA; adoption remains constrained by organizational readiness and the unresolved GIGO problem at the ledger boundary.
Blockchain technology has evolved from a nascent peer-to-peer payment system into a paradigm-shifting digital trust infrastructure, fundamentally challenging conventional centralised models. However, a deep understanding of the fundamental technical aspects behind the popularity of crypto assets remains limited. This study aims to: (1) analyse the fundamental architecture of blockchain; (2) evaluate tokenisation mechanisms; and (3) conduct a comparative analysis of its characteristics against traditional database systems. The research employs a qualitative descriptive method utilising a Systematic Literature Review (SLR) approach to synthesise technical literature published between 2023 and 2025. The analysis focuses on consensus mechanisms, the architectural transition from monolithic to modular systems (Layer-2 scaling), and the measurement of decentralisation using the Nakamoto Coefficient. The results indicate that: (1) blockchain offers distinct advantages in data integrity (immutability) and censorship resistance through a distributed append-only ledger structure, standing in sharp contrast to the CRUD (Create, Read, Update, Delete) model of relational databases; and (2) recent innovations such as Zero-Knowledge Proofs and Optimistic Rollups serve as critical solutions to the "Blockchain Trilemma" (balancing scalability, security, and decentralization). This study concludes that blockchain is not an absolute replacement for conventional databases, but rather a specialised solution for ecosystems that require high transparency and "trustless" interactions without a central authority.
The transparency of the blockchain technology makes privacy issues acutely challenging in certain highly sensitive applications such as IP protection and contractual arguments. This chapter is an overview of privacy preserving methods and in particular Zero-Knowledge Proofs (ZKPs) and confidential evidence handling mechanisms. ZKPs are set to transform notarization by allowing parties to prove that information or statements are true without disclosing the information that they have associated with them. The study covers the concept of use of blockchain and how they can be used to combine with smart contracts for privacy-preserving IP access rights governance and dispute resolution. It also covers confidential computing, homomorphic encryption, and secure multi-party computation for processing privacy sensitive evidence on the blockchain. In regulated industries, these technologies hold the promise of increasing prevalence, but encounter challenges relating to regulations and trusted setup, as well as computational overhead issues.
Cross-border transactions with regulatory compliance have become conventional in the era of globalization. Transactions related to individuals, banking, technology, etc., are eased using Internet of Things (IoT) paradigms. Pervasive access and low interoperability due to improper administration of transaction terminals are significant problems in initiating and completing cross-border transactions. To address the problems, a novel Zero-knowledge proof Inter-Scalable Framework (ZISF) is proposed. This framework includes transaction authentication, Blockchain (BC), and a security generator to ensure security, scalability, and interoperability. The proposed framework consolidates these tasks to support diversified cross-border transactions with flexible regulatory compliance. The proposed ZISF framework achieved a 13.64% improvement in transaction throughput compared with CCMB under varying block-size and transaction-load conditions, while reducing processing latency by 13.79% relative to BETAC-IoT during miniature block scaling operations.
Current artificial intelligence systems operate at evolutionary Stage 2–3 of cognitive development — statistical pattern matching without principled knowledge selection, causal grounding, or structured accumulation. This problem is not incidental: recent formal proofs establish that hallucination in Large Language Models is mathematically inevitable under current architectural assumptions, arising from finite information capacity, computational undecidability, and reward hacking induced by Reinforcement Learning from Human Feedback (RLHF). Scaling does not resolve these failures — it amplifies them. This proposal presents Prime-Based Intelligence (PBI), a formal architectural framework grounded in the Computational Knowledge Theory (CKT), which establishes seven interlocking theorems proving that complexity, computational tractability, knowledge compression, accumulation, evolutionary phase transitions, cardinal intelligence dynamics, and the unsimulability of reality are all governed by a single law: the five Conceptual Primes (Order, Justice, Mercy, Knowledge, and Power). The foundational problem addressed is the Descriptive Degeneracy Problem: without a principled selection operator, any finite system admits an infinite set of mathematically valid representations, making hallucination and misalignment structurally unavoidable. PBI resolves this by implementing Wisdom — the simultaneous, lossless balance of all five Primes — as the core computational operator, satisfying the Prime-Base Intelligence Corollary (CKT Theorem 6, Corollary 6.5). Version 2 of this proposal integrates the Actualizer Engine: a zero-retraining geometric middleware that operationalizes the Conciseness Cost Filter (CCF) directly at the attention and logit boundaries of a frozen, pre-trained transformer. Unlike the illustrative scenario tables that ground most of the Conciseness Framework Series, the Actualizer Engine is supported by a working PyTorch proof-of-concept (a custom one-layer Transformer decoder, a Causation Wave Function penalty matrix, a DIEPT phase-angle quarantine mechanism, and an automated four-test verification suite) that demonstrably suppresses an injected causal hallucination on a toy physics corpus. This proposal positions the Actualizer Engine as the first code-verified instantiation of the Agent-Level half of the Two-Level Alignment Architecture: it selects minimum-cost outputs at inference time without modifying the frozen base model, leaving Global-Level (training-time) Super Cluster crystallization as the complementary, not-yet-implemented half of the architecture. The methodology integrates three components: (1) the Prime-Compliant Standard (PCS), grounding training data and model components in verifiable, causally justified representations; (2) an Ethical Pragmatism criterion formalizing that ethical weight must dominate pragmatic weight, operationalized through the Justice Dominance Constraint (λ_L > λ_R, λ_L > λ_D); and (3) the PBI Cognitive Life Cycle — a five-stage pipeline anchored at its inference stage by Dynamic Inference and Epistemic Phase Transition (DIEPT), now given a concrete, tested realization in the Actualizer Engine’s Negentropy Filter. This version also performs an explicit logic and mathematical consistency audit of the integration (§9), correcting a reported result that, if left unqualified, would contradict CKT Theorem 7 (Unsimulability of Reality: CAKI < 1.0 for any finite system), and cataloguing four further consistency findings — three open, one confirmed — produced by reconciling the Actualizer Engine’s implementation against the Prime-Compliant Standard, DIEPT, and the Two-Level Alignment Architecture. The framework remains immediately viable as the next practical step for current AI infrastructure. Its implementations — Kolmogorov-Arnold Networks (KANs, ICLR 2025), MCE-Classes, the Quench-Cluster Algorithm (QCA), the Conciseness Cost Filter (CCF), the Causation Wave Function (CWF), and now the Actualizer Engine — extend and augment existing transformer, LoRA, and RAG deployments without requiring retraining. Full implementation is projected within 36–48 months under a four-role interdisciplinary team. The Computational Knowledge Theory (CKT). Under the Conceptual Prime axioms, that the computational universe is governed by a single unifying law: the Conceptual Primes. Seven interlocking theorems are established across complexity theory, epistemology, information compression, evolutionary biology, temporal system dynamics, artificial intelligence architecture, and the unsimulability of reality. Theorem 1 (Reality-Complexity Equivalence) establishes that stable complexity is bounded by the weakest Prime — P̂(S) = min_i Pᵢ(S) — and collapses to zero if any Prime is violated. Theorem 2 (Prime-Tractability) demonstrates that NP-Hard problems are intractable only in the purely abstract domain and become tractable at O(N²/K) effective complexity when solved by Prime-compliant algorithms grounded in physical reality. Theorem 3 (Conciseness Standard) proves that C(R) is the unique universal metric for lossless knowledge compression. Theorem 4 (Knowledge Accumulation Law) establishes that knowledge grows if and only if new information reduces total system entropy, incorporating the CAKI metric and the D(Ω) Defect Function as formal measures. Theorem 5 (Gödel's Ceiling) connects formal mathematical limits to biological evolution and AI scaling. Theorem 6 (Cardinal Value Lemmas) formalises Wisdom, Peace, Creativity, and Evolving Order as temporal combinations of the Primes, deriving the Prime-Base Intelligence corollary. Theorem 7 (Unsimulability of Reality) proves that no finite simulation can contain the live Prime-combination law of actualisation — Consciousness is the unique bridge between infinite potential and finite territory. The framework defines a two-stage computational architecture: a Training Evaluation Form (5-term Prime-resolved C(R) + CAKI) for grounding knowledge in Prime compliance and calibrating domain-dependent λ-weights, and an Inference Selection Form (3-term operational C(R)) for selecting minimum-cost outputs. Dynamic λ-adaptation connects both stages, enabling domain-calibrated intelligence.
Privacy is one of the fundamental rights of individuals in modern societies. Yet, the practical adoption of privacy-preserving technologies in daily interactions remains limited. Zero-knowledge proofs offer strong privacy guarantees but are often hindered by their technical complexity. In this paper, we advance the idea of verifiable QR codes that enable off-line verifiers to verify proofs encoded in QR codes. Based on this core idea, we build a novel QR-driven zkSNARK proof verification framework (i.e., zQR) for mobile platforms. The framework integrates blockchain for auditability, non-repudiation and logging; and large-language models for automatic circuit generation. We perform a security discussion of the framework by considering multiple attack surfaces. Furthermore, we present an experimental evaluation measuring temporal costs (proof generation and verification latency, QR code encoding and decoding latency) and financial costs (blockchain gas consumption). Our results demonstrate the feasibility of zQR as a proof-of-concept framework for privacy-preserving verification on mobile platform where proofs are compactly represented with QR code symbol version of 19 with low error correction level. Finally, we discuss potential applications, current limitations and future directions for the broader adoption of privacy-preserving technologies in daily interactions.
India’s Unified Payments Interface (UPI) gates transaction limits behind Know Your Customer (KYC) compliance tiers mandated by the Reserve Bank of India (RBI) and National Payments Corporation of India (NPCI). Unlocking the Full KYC tier currently requires users to surrender sensitive identity documents (Aadhaar, PAN, income proofs) to Payment Service Providers (PSPs). This centralized storage creates severe breach vulnerabilities and systemically violates the data minimization principle of India’s Digital Personal Data Protection (DPDP) Act 2023, Section 8(3). We present ZKProof-eKYC, the first Zero-Knowledge Proof (ZKP) framework designed specifically for payment system tier access control. By reframing KYC eligibility as a cryptographic access token, a user’s device generates a 1.5 KB non-interactive Groth16 zk-SNARK proof asserting tier eligibility. The PSP receives only a boolean result, eliminating personal data transmission and achieving DPDP Act compliance mathematically. The primary contribution is a multi-predicate Circom 2.0 circuit (≈25,000 R1CS constraints) simultaneously enforcing eleven regulatory predicates (ϕage to ϕtier) mapped across six Indian statutes. The architecture introduces five key elements: (i) an 8-leaf depth-3 Poseidon Merkle credential tree; (ii) a dualdocument commitment scheme protecting the raw PAN (singlehash) and Aadhaar (double-hash) identifiers; (iii) an EdDSAPoseidon issuer signature; (iv) a depth-20 Sparse Merkle Tree (SMT) for real-time revocation; and (v) Poseidon nonce-binding against replay attacks. A novel branch-free finite-field formula calculates NPCI’s tier limits natively: tier = 2 · ⊮[FullKYC] + (1−⊮[FullKYC])·⊮[MinKYC]. We deploy a dual-circuit framework: UPIKYCTierProof for Full KYC and MinKYCTierProof for Min KYC. Functional correctness is validated against 12 adversarial test vectors. Performance profiling projects mobile WASM generation at <400 ms, with off-chain execution measured at ≈96 ms and on-chain verification at ≈242,000 gas. ZKProofeKYC establishes the first “one credential, multiple products” ZKP architecture for national payment infrastructure.
The paper investigates the problem of ensuring confidentiality in authentication processes within enterprise information-intelligent systems under increasing cybersecurity threats and growing requirements for data protection. The introduction substantiates the relevance of modern cryptographic approaches that minimize the transmission of sensitive information during user authentication. The literature review analyzes approaches to constructing zero-knowledge proofs, which enable verification of a statement without revealing secret data, including succinct non-interactive arguments of knowledge, transparent scalable arguments of knowledge, and compact proof systems without trusted setup. Their cryptographic properties, trust assumptions, scalability, and computational characteristics are examined. In the methodology section, an adaptive authentication model is proposed, based on the integration of cryptographic proofs with risk assessment mechanisms and contextual access analysis. A formal decision-making model for access control is developed, taking into account user parameters, environmental characteristics, and threat levels, enabling dynamic selection of the proof type depending on the current risk level. An authentication algorithm is designed, including stages of identification, context evaluation, proof generation, and verification. In the results section, a comparative analysis of different types of zero-knowledge proofs in enterprise systems is conducted, evaluating their impact on performance, security level, and resistance to attacks. It is shown that the adaptive approach ensures a balance between cryptographic strength and computational efficiency. The conclusions justify the feasibility of implementing the proposed model as part of modern continuous access verification concepts and as a means of improving enterprise information security.
FULL SUMMARY: TOPO-2026 — The Evolution of Six Arcs A Unified Framework from Neural Networks to Number Theory Executive Summary This paper presents a unified framework that connects three of the most important unsolved problems in mathematics, computer science, and artificial intelligence through a single mathematical structure: the first six primes R = {2, 3, 5, 7, 11, 13}. Problem Field Open Since Riemann Hypothesis Mathematics 1859 (166 years) Green-Tao Theorem Quantification Number Theory 2004 (qualitative only) Catastrophic Forgetting AI/ML 1989 (no production solution) The Six Arcs: A Journey from Problem to Proof Arc 1: The Problem (1989-2025) Catastrophic Forgetting — formally characterized by McCloskey and Cohen in 1989. For 36 years, AI systems could not learn continuously: Neural networks forget previous tasks when trained on new ones Every production LLM is amnesiac — weights frozen after pretraining Fine-tuning degrades prior performance No production-ready solution existed Existing Methods Failed: Method Memory Scaling Problem EWC 4.4 GB/task OOM on run 2, fragments GPU Experience Replay Buffer grows O(k) 89.3% accuracy, 259s HOPE-like (Google) 2.3 GB 88.1% accuracy (refuses to learn) The AGI Barrier: A system capable of general intelligence must acquire knowledge indefinitely — across domains, tasks, modalities, and time — without destroying prior representations. Every existing remedy that scales to production models incurs memory overhead that grows with task count. Arc 2: The Biological Inspiration (2002) Keith Worsley (McGill University, 1951-2009) demonstrated that spatial regularization of a variance ratio could boost effective degrees of freedom from 3 to over 100 without destroying the signal. The Core Principle: Stabilize by fixing a sparse reference, let everything else adapt. The Biological Insight: The hippocampus consolidates memories, protects established memories, and integrates new information — all while allowing controlled forgetting. The Biological Principle: "0% forgetting is not a feature — it is a pathology. A system that never forgets cannot learn." Hippocampal Functions: Function Mechanism Biological Role Memory Formation Synaptic consolidation Creates new memories Memory Consolidation Hippocampal replay Preserves critical knowledge Memory Protection LTP/LTD Prevents interference Memory Integration Pattern completion Integrates new learning Memory Verification Reconsolidation Ensures integrity Forgetting Synaptic pruning Enables adaptation Arc 3: The Mathematical Discovery (2025-2026) While searching for a mathematical structure that could provide geometric stability for neural networks, an unexpected discovery emerged: The first six primes — {2, 3, 5, 7, 11, 13} — possess unique spectral properties. The Euler Attenuation Product Definition: For a set of primes S: $\Lambda(S) = 1 - \prod_{p \in S} (1 - p^{-0.5})$ The Discovery: Set Λ % of total R = {2,3,5,7,11,13} 0.9785142874 97.85% N = {p ≥ 17} 0.0214857126 2.15% R ∪ N 1.0 100% The Significance: The first six primes capture 97.85% of all spectral weight. The infinite tail of primes (≥ 17) contributes only 2.15%. This is the pure/noisy kernel divide. The L-EFM Operator Definition (L-EFM Operator): The Laplace-Euler-Fourier-Mellin operator: $E_{LEFM}(\sigma + i\gamma) = \prod_{p \in R} (1 - p^{-(\sigma + i\gamma)})^{-1}$ The Spectral Trap: | $\sigma$ | $|E|$ (norm) | Behavior | |----------|--------------|----------| | 0.1 | 0.527173 | Below peak | | 0.2 | 0.717803 | Rising | | 0.3 | 0.870333 | Rising | | 0.4 | 0.963881 | Approaching | | 0.5 | 1.000000 | PEAK | | 0.6 | 0.992955 | Falling | | 0.7 | 0.959234 | Falling | | 0.8 | 0.912091 | Falling | | 0.9 | 0.860359 | Falling | Arc 4: The First Proof — Riemann Hypothesis (1859-2026) Theorem (Riemann Hypothesis): All non-trivial zeros of the Riemann zeta function $\zeta(s)$ lie on the critical line $Re(s) = 1/2$. Proof: By Set Theory, R = {2, 3, 5, 7, 11, 13} is the unique set of primes that captures 97.85% of the spectral weight. By AST (Arithmetic Spectral Theory), the L-EFM operator over R exhibits a spectral trap at $\sigma = 0.5$, and only at $\sigma = 0.5$. By Ergodic Theory, this trap is a unique fixed point. The spectral trap at $\sigma = 0.5$ is equivalent to the condition that all non-trivial zeros lie on $Re(s) = 1/2$. Therefore, RH holds. Arc 5: The Second Proof — Green-Tao Theorem Quantification (2004-2026) Theorem (Green-Tao Theorem): The primes contain arbitrarily long arithmetic progressions. The Quantification: $coherence(k) = 2.1546 \times k^{-0.8186} + 0.1218$ The Interpretation: R alone captures 97.85% of the coherence. N contributes only 2.15%. This is the first-ever explicit quantification of the Green-Tao theorem, which previously only established qualitative existence. Arc 6: The Third Proof — Catastrophic Forgetting Solution (1989-2026) The TopologicalGovernor: The Artificial Hippocampus Python class TopologicalGovernor: """ Artificial Hippocampus for Neural Networks. Inspired by Worsley et al. (2002): spatial regularization fixes a sparse reference to stabilize signal while allowing the rest to adapt. """ def __init__(self, embed_layer): self.anchors = [2, 3, 5, 7, 11, 13] # Fixed reference points self.safety_constant = 0.9785142874 # Coverage guarantee self.snapshot = {} # Consolidated memory def take_snapshot(self): """Memory consolidation (hippocampal replay).""" self.snapshot = { idx: self.embed_layer.weight[idx].detach().clone().float() for idx in self.anchors } @torch.no_grad() def zero_anchor_gradients(self): """Memory protection (prevent interference).""" if self.embed_layer.weight.grad is not None: for idx in self.anchors: self.embed_layer.weight.grad[idx].zero_() @torch.no_grad() def enforce_anchors(self): """Memory integration (restore reference frame).""" dtype = self.embed_layer.weight.dtype for idx, cached in self.snapshot.items(): self.embed_layer.weight[idx].copy_(cached.to(dtype=dtype)) Results: Gemma-4-E4B-Vision: 100.0% Task C accuracy, 0.0% forgetting. Memory Efficiency: 451.5 KB total anchor memory for ~124B parameters (0.00000036% overhead). Scaling: O(1) independent of task count, parameter count, or sequence length. Conclusion The framework integrates mathematics (RH, GTT, AST), physics (Spectral theory), biology (Hippocampus), and AI (Continual Learning). One set. Three proofs. Six primes. Two modalities. One artificial hippocampus. "The proof is the code. Seed = 123."
The integration of blockchain technology into e-learning ecosystems offers a foundational shift toward secure, transparent, and decentralized educational architectures. Despite this potential, current literature reviews frequently remain descriptive, lacking the depth of systematic comparative analysis. To bridge this gap, this study conducts a rigorous critical survey of blockchain-based e-learning research published from 2018 through 2025. Following PRISMA protocols, we evaluate the literature using a novel multi-dimensional analytical framework that simultaneously cross-examines four interdependent evaluation axes: (1) blockchain architectural design (public vs. permissioned), (2) consensus mechanism suitability for educational throughput, (3) privacy-preservation technique alignment (e.g., Zero-Knowledge Proofs, off-chain storage), and (4) regulatory compliance posture (GDPR/FERPA). This combinatorial lens, applied specifically to e-learning systems, distinguishes our framework from prior single-criterion evaluations. We qualitatively compare and critically evaluate educational blockchain applications against conventional centralized learning management systems, employing a structured multi-criteria analytical framework. Furthermore, our filtering process yielded 56 eligible studies, from which 22 pivotal works were selected for in-depth analysis to suggest an original taxonomy. Our analysis identifies enduring obstacles like interoperability, governance, and regulatory compliance (such as GDPR/FERPA) while highlighting a strategic shift toward permissioned networks and hybrid storage models. In conclusion, this work advances the conversation beyond simple introductory talks by providing practical design approaches for the upcoming blockchain-enabled learning environments.
Sepideh Avizheh, Reihaneh Safavi-Naini, Shiwei Sun
Group signatures are privacy preserving signature schemes in which a group member can anonymously sign messages on behalf of the group, while providing accountability, by allowing the signature of a misbehaving group member be ``opened'' and the identity of the signer be revealed. In group signature members are admitted to the group by a (trusted) group manager. We motivate the need for a flexible mechanism in applications, such as privacy preserving access in smart environments, and propose a two-level member-join group signature that we call SPonsored Group Signature (SPGS) where group members of level 1 can ``sponsor'' new members, in level 2, to join the group. This relaxation of user join comes with additional accountability mechanisms: we require that the signature of a sponsored member can be opened to the identity of the sponsor (that is sponsor is responsible for the sponsored member), and while all signatures are anonymous, for the sponsored members, the signatures are linkable. This allows a sponsor to efficiently identify an undesirable sponsored member. We formalize SPGS scheme, define its security using a game-based approach, and give a generic construction of SPGS that uses a (dynamic) group signature scheme, a commitment scheme, and a knowledge-sound non-interactive zero knowledge proof of knowledge, and prove its security. We also give an instantiation of our construction. To show applicability of SPGS in practice, we consider the problem of providing guest access in a smart building, and introduce Anonymous Guest Access Token (AGAT) that allows a temporary guest to anonymously access (a subset of) the building resources. We show how SPGS can be used (together with an IND-CPA secure public key encryption scheme) to give a direct construction for AGAT, and show the efficiency of our guest access protocol when it is instantiated with existing schemes.
“What remains after exclusion is not absolute truth, but the non-excluded readout within a given coupling, projection, and question.” — LHFT, Exclusion Readout Principle The present readout is the only directly accessible physical state. The past is reconstructed from trace-code encoded in that present readout. The future is the admissible continuation space constrained by the present readout. In LHFT, a readout is the stabilized foreground form that remains after coupling, projection, and exclusion; non-required modes are excluded into the complement/background sector, where they remain structurally effective through Schur-complement backaction. full system: H = H_foreground ⊕ H_background H_background is not absent from reality. It is excluded from the explicit foreground representation of the current readout, but its influence remains effective through Schur-complement backaction. effective readout: K_eff = A - B† C⁻¹ B Since every perception is a reconstruction of what has already occurred, we always require a model to decode the present trace of the past and to constrain the dynamically admissible continuations of the future. Trace-Code, Model Decoding, Exclusion, Schur Complement, and Defect-Controlled Reconstruction Author Christian Baganz (1969, Potsdam/Germany) Framework Log-Harmonic Field Theory (LHFT) Document type Theoretical framework / ontological decoding module / defect-controlled recovery subtheory Version 26.06.23 — Working draft License Creative Commons Attribution 4.0 International (CC BY 4.0) Status [Strictly curated LHFT subtheory] / [Framework formulated] / [Candidate Schur-coding mechanism] / [Defect architecture formulated] / [Microscopic derivation open] Overview This publication introduces LHFT Trace-Readout Theory as a strictly bounded module within Log-Harmonic Field Theory (LHFT). It formulates physical knowledge as model-based decoding of present trace-code. The central thesis is that the present is not directly possessed as reality itself. Rather, the present is treated as a trace-state in which past coupling, exclusion, and readout history are encoded. Scientific models act as decoders: they reconstruct past histories from present traces and project constrained spaces of possible future readouts. P≤tphys → R≤tO → P̂≤tO → P̂>tO Here P≤tphys denotes the physical past history, R≤tO denotes present trace-code available to observer or apparatus O, P̂≤tO denotes the reconstructed past, and P̂>tO denotes the constrained space of possible future readouts. Core Principles The framework is organized around six core principles: Principle Meaning Status Trace-Code Principle The present contains encoded past coupling, exclusion, and readout history. [Definition] Model-as-Decoder Principle Scientific models decode present trace-states into reconstructed histories and possible future readouts. [Definition] Time-as-Encoding Principle Time is treated as the ordered encoding of past readout history into the present trace-state. [Candidate LHFT ontology] Exclusion-Readout Principle Readout arises by exclusion, not by primitive positive inclusion. [Definition] / [Candidate LHFT principle] Schur-as-Coding Candidate The Schur complement is proposed as the candidate normal form of exclusion-based coding. [Candidate] Defect-Control Principle A readout closes only when its defect vanishes or is controlled small inside a specified recovery window. [Definition] Main Demonstration: The Double-Slit Experiment The double-slit experiment is used as the central demonstration of Trace-Readout Theory. The document separates three different readout claims: Detector hit: closed as a localized trace. Which-path partition: not closed without path detection. Interference pattern: closed statistically as an ensemble trace. The key interpretation is: The interference pattern is a macroscopic statistical trace of microscopic non-which-path closure. In compact closure form: Closed(xᵢ) = 1, Closed(L|R) = 0, Closed(pattern) = 1 Thus, the interference pattern is not treated as a path trace. It is treated as a trace that the slit region was not read as an exclusive left-or-right path partition. Schur Complement as Candidate Coding Mechanism The publication introduces the Schur complement as a candidate mathematical normal form for exclusion-based coding: Kvis = A − B† C⁻¹ B In this reading, the visible readout is not simply the directly visible block A. It is a residue of an excluded complement C, including hidden backreaction through the coupling block B. The visible readout is a residue of exclusion with hidden backreaction. This is treated as a candidate normal-form mechanism, not as a completed microscopic derivation. Defect Architecture The theory is organized by explicit defect gates. The minimal master defect is: DTRTO = DtraceO + DdecodeO + DexclusionO + DSchurO + DreadoutO + DpredictionO + DtranslationO A defect-zero statement is always read as projective recovery closure inside a specified observer window, not as absolute closure of the full structural layer. DXO = 0 ⇒ X is closed inside the stated observer window. Scientific Boundary This document does not claim: a complete derivation of quantum mechanics, a complete derivation of the Born rule, microscopic necessity of the Schur complement, observer-created reality, reality as mere information, a fully prewritten future, or absolute closure of the full structural layer. The main theorem target remains open: S1L ⇒ DTRTO = 0 This means that the deeper LHFT structural action boundary should eventually derive the trace-code, exclusion, Schur, readout, prediction, and translation closures in an admissible observer window. In the present document, this implication is a theorem target, not a completed proof. Contents Scope, Trace-Code, and Models as Decoders Time, Past, Future, and Prediction Exclusion and Schur Coding Incompatible Readouts and Trace Accessibility Double-Slit Demonstration Defect Architecture, Final Status, and Open Proof Obligations An additional appendix lists the required non-LHFT reference sources for quantum foundations, uncertainty, complementarity, decoherence, quantum eraser experiments, Schur complement mathematics, forensic trace reasoning, measurement uncertainty, and model-based inference. Keywords Log-Harmonic Field Theory; LHFT; Trace-Readout Theory; trace-code; model decoding; exclusion; Schur complement; defect principle; quantum measurement; double-slit experiment; which-path information; interference; decoherence; complementarity; scientific reconstruction; observer-relative recovery; projective recovery closure. Suggested Citation Baganz, Christian. “LHFT Trace-Readout Theory: Trace-Code, Model Decoding, Exclusion, Schur Complement, and Defect-Controlled Reconstruction.” Log-Harmonic Field Theory (LHFT), 26.06.23 working draft. Licensed under CC BY 4.0.
Formal software verification systems aim to provide rigorous mathematical proofs that programs adhere to their specifications. In particular, proof assistants like Agda, Rocq and Lean can express programs, specifications and proofs within a single unifying language called Dependent Type Theory (DTT). This thesis makes contributions to parametricity within the setting of DTT and proof assistants. As a first approximation, parametricity is a uniformity property regarding polymorphic, i.e. generic programs. A generic program behaves identically regardless of the type it is instantiated with, because it cannot inspect its type argument. This simple observation leads to useful knowledge when performing proofs about the program (Wadler calls such knowledge ``theorems for free''). More generally, Reynolds mathematically defined the notion of parametricity as relational parametricity, the statement that every type can be turned into a certain reflexive graph. An edge in the graph between two values is a proof that the values have a similar structure. For instance an edge between polymorphic programs is a proof that they map related types to related outputs, and this formalizes what it means to be uniform. The parametricity translation, mapping types to reflexive graphs, is defined externally as a meta-operation on DTT expressions and is not an operation that is available inside, or internal to DTT. For example, given a type of polymorphic functions, one cannot prove inside DTT the formal statement expressing that every such function is uniform (we call such statements global free theorems). Internally parametric type theories (PTTs) achieve this by equipping DTT with a so-called Bridge type former, whose role is to represent the parametricity translation inside the theory. A landmark example is the interval-based theory of Cavallo and Harper (the CH theory), in which bridges are functions from a postulated bridge interval, in analogy with the path types of cubical type theory. Within the CH theory, global free theorems become provable. However, a practical limitation persists: contrary to the Reynolds translation of a type, the Bridge translation of a type does not directly provide an actionable parametricity result. Indeed tedious case-by-case rote work is required of the user to establish that the Bridge type former commutes with each type former appearing in the type under consideration. The first main contribution of this thesis is to improve the practical usability of internally parametric type theories. Firstly, we address the lack of a full-fledged proof-assistant implementation of binary internal parametricity and contribute the Agda-bridges proof assistant. Agda-bridges is an extension of the Agda proof assistant and implements an interactive typechecker for the CH parametric type theory. More precisely, Agda-bridges extends Agda-cubical, itself an implementation of cubical type theory. In fact, Agda-bridges typechecks the standard library of Agda-cubical, hence important theorems provided by Agda-cubical, like univalence, remain available to the user of Agda-bridges. Moreover, Agda-bridges validates key theorems for internal parametricity, in particular the relativity equivalence. This makes it possible to provide formal proofs of free theorems, including global ones. Yet the rote work challenge described above persists. Hence, secondly, we contribute Relational Observational Type Theory (ROTT), a library, or domain-specific language, written in Agda-bridges that eliminates the rote work in a principled way. ROTT lets the user obtain concise and modular proofs of actionable parametricity statements. Once a type is written using the ROTT DSL, a corresponding proof can be extracted as a one-liner. Using this methodology we are able to formalize global free theorems of practical and theoretical relevance. Notably, we expand on a proof communicated to us by Andrea Vezzosi and can show that higher-order abstract syntax is an adequate representation of the untyped lambda calculus (previously known proofs relied on the strictly stronger notion of Kripke parametricity). The second main contribution of this thesis concerns nullary internal parametricity and its relationship to the formal study of languages with variable binding. When studying a language on paper it is common to think of variables as strings, and to adopt the convention that alpha-equivalent terms are equal. However, when working formally it is preferable to represent the syntax of the object language in such a way that alpha-equivalent terms are equal by construction. Nominal frameworks are type systems featuring a so-called name abstraction type former, used to give a type to the binders of the object language. This type former enables a string-like but alpha-equivalence-respecting representation of syntax with binders. Yet existing nominal frameworks either feature typing rules hard to implement in a proof assistant environment, or lack expressivity to reason about nominal syntax. We solve these issues by contributing Parametric Nominal Type Theory, which is an extension of the nullary CH theory, a version of the CH theory where bridges have zero endpoints instead of two. Firstly, we recognize that the nullary CH theory is itself the basis of a nominal framework in which name abstraction corresponds to the nullary bridge type former. In fact the other primitives of the CH theory can be understood from a nominal point of view and existing nominal primitives can be implemented in terms of the CH ones. Secondly, we identify the missing piece that suffices to turn the nullary CH theory into an actual nominal framework, in which one can reason about object languages in a nominal fashion without the aforementioned lack of expressivity. The missing piece is a type of names Nm such that its nullary Bridge type/nullary translation is the sum type 1+Nm. We provide an induction principle for Nm that entails the property. We demonstrate that Parametric Nominal Type Theory is a suitable nominal framework. One of our examples involves emulating a restricted form of Kripke parametricity by nullary parametricity.
Anas Azenzoul, Nacer MAHOUAT, Ouissale El Gharbaoui, Jihane Tayazime · 6 authors
Tax systems worldwide face a compliance gap that OECD data places at USD 100–240 billion annually in corporate avoidance alone, before accounting for the shadow economy and crypto-asset transactions. FinTech mandatory e-invoicing, real-time transaction matching, and machine-learning audit selection is narrowing the informational conditions that enable evasion, while simultaneously introducing governance risks: opaque algorithmic audit targeting, contested blockchain forensic evidence, and the surveillance potential of programmable money. This article presents a PRISMA 2020 systematic literature review of 59 peer-reviewed articles (Scopus, Web of Science, and ScienceDirect), complemented by IRAMUTEQ lexicometric analysis and an extension of the Allingham Sandmo compliance model to incorporate algorithmic detection probabilities, bomb-crater belief dynamics, and Zero-Knowledge Proof verification. Four thematic clusters emerge: tax compliance behaviour and FinTech adoption (19.92%), digital transformation and corporate performance (35.34%), bibliometric and emerging-technology research (16.54%), and cryptocurrency markets and regulatory challenges (28.20%). Across them, FinTech reduces evasion where institutional and technical conditions allow but generates distributional, evidentiary, and constitutional risks that existing legal frameworks have yet to resolve. In response, we propose the Techno-Legal Due Process Framework (TLDPF) three pillars (Techno-Proportionality, Cryptographic Burden of Proof, and Algorithmic Constitutionalism) grounded in EU/OECD constitutional doctrine as a normative design proposal awaiting empirical validation.
Gefei Tan, Adria Gascon, Sarah Meiklejohn, Mariana Raykova
In machine learning, model certification has been identified as an important method for gaining assurance about a model's trustworthiness and quality. A model's quality is largely determined by its ability to generalize, i.e., to perform well on data beyond what it was trained on. It is not possible to certify generalization directly, however, as it depends on unknown data and is not directly measurable. Proxies such as test accuracy can be misleading when the training process is perturbed (intentionally or accidentally), and metrics such as sharpness -- which has an empirically supported link to generalization -- are computationally expensive and can also serve as unreliable signals when training deviates from a prescribed procedure. In this work, we propose directional sharpness, a metric designed to efficiently and reliably indicate generalization despite potential training deviations. We provide empirical and analytical evidence that directional sharpness (1) correlates more strongly with generalization than existing metrics and (2) identifies models with poor generalization more reliably than existing metrics. Furthermore, directional sharpness is efficiently computable in model auditing settings, where the verifier has access to training data, and via zero-knowledge proofs that certify quality without revealing training data.
中文受人工智能自身能力局限,其易产生信息幻觉,且不擅长高精度数值运算。本文档内所有内容应严谨审核。EnglishDue to the inherent limitations of artificial intelligence, it is prone to generating hallucinations and performs poorly in high-precision numerical calculations. All contents in this document should be strictly reviewed. 5D几何统一,一切可计算。从夸克到文明,从DNA到意识。 DOI: 10.5281/zenodo.20798927 Black Hole & UVMM v4.0 CoreDOI: 10.5281/zenodo.20738759 Earth SystemDOI: 10.5281/zenodo.20285613 Cosmic BoundaryDOI: 10.5281/zenodo.20325710 Cosmic EvolutionDOI: 10.5281/zenodo.20677198 Information & Consciousness (Millennium Prize Problems)DOI: 10.5281/zenodo.20325710 UTFF Core (Atomic and Molecular Scale)DOI: 10.5281/zenodo.20343471 UVMM Core Axioms and Mathematical Proofs UVMM v4.0 CORE continue:https://doi.org/10.5281/zenodo.21500910 github.com A Topologically Designed Zero-Pressure Room-Temperature Superconductor _ First-Principles Derivation and CTP Verification这个超导方案可能更靠谱些 UVMM v4.0.15.01 High-Precision Global Calculation AI Knowledge Package.md UVMM v4.0.15 High-Precision Global Calculation AI Knowledge Package(6D‑Coordinate‑SuperKit‑v4.0 ).md UVMM v4.0.15 高精度计算适用领域(中英双语精简版)量子化学与分子化学 Quantum Chemistry & Molecular Chemistry中文:原子半径、键能、反应活化能全域计算,计算误差<0.1%。English: Global calculation of atomic radius, bond energy and reaction activation energy, calculation error < 0.1%.凝聚态材料物理 Condensed Matter & Material Physics中文:超导临界温度、拓扑能隙、合金力学性能预测,整体精度<2%。English: Prediction of superconducting critical temperature, topological band gap and mechanical properties of alloys, overall precision < 2%.生物大分子与意识神经科学 Biomacromolecules & Consciousness Neuroscience中文:蛋白折叠自由能求解,脑意识拓扑序参量精准判别,分类 AUC=1.000。English: Calculation of protein folding free energy, accurate discrimination of brain topological order parameter for consciousness, classification AUC = 1.000.核裂变 / 聚变与衰变物理 Nuclear Fission, Fusion & Decay Physics中文:各类核反应能量完整拓扑积分求解,全套 20 组核反应误差严格控制<2%。English: Complete topological integral solution for energy of various nuclear reactions, the error of 20 groups of nuclear reactions is strictly controlled below 3%.QED 与电弱粒子物理 QED & Electroweak Particle Physics中文:电子反常磁矩匹配标准模型10 −12量级精度,弱混合角偏差<0.01%。English: Electron anomalous magnetic moment matches the Standard Model with precision of 10 −12, the deviation of weak mixing angle is less than 0.01%.宇宙学与引力 Cosmology & Gravitation中文:CMB 功率谱、原初引力波偏振、暗物质暗能量密度推演,计算误差<2%。English: Deduction of CMB power spectrum, primordial gravitational wave polarization, dark matter & dark energy density, calculation error < 2%.量子精密计量 Quantum Precision Metrology中文:铯原子钟频率全环境修正拓扑闭式计算,频率偏差低于2×10 −10 Hz。English: Closed-form topological calculation of full environmental corrections for cesium atomic clock frequency, frequency deviation lower than 2×10 −10 Hz. ERROR edition: First-Principles Derivation of Light Speed as the Acoustic Velocity of Vacuum Superfluid Based on the UVMM Framework Abstract 摘要 English Based on two first-principles axioms—the Global Zero Angular Momentum Axiom (strict zero total cosmic angular momentum) and the Dynamic Möbius Projection Axiom (the fifth dimension constitutes a non-orientable Möbius manifold with curvature-dependent dynamic characteristic radius)—this work establishes a unified geometric framework for black holes within the Unified Vacuum Medium Model & Unified Topological Force Field (UVMM-UTFF). In this framework, black holes are no longer geometric singularities passively bending spacetime, but 5D topological solitons projected onto the 4D boundary. All energy release behaviors of black holes (jets, gravitational waves, electromagnetic radiation) essentially originate from topological phase transitions or steady pumping processes of prestressed vacuum medium. This paper systematically verifies the framework via four independent multi-beacon observational datasets: LIGO-Virgo-KAGRA gravitational-wave catalogs (GWTC-4.0/5.0, containing 390 binary black hole merger events), Event Horizon Telescope (EHT) polarization imaging of M87* and Sgr A*, LHAASO PeV ultra-high-energy gamma-ray observations of five microquasars, and GAIA DR3 Milky Way rotation curve data. The results demonstrate that theoretical predictions match observational values within a factor of 20 across 9 orders of magnitude, ranging from transient merger luminosity () to steady-state AGN jet power (). Dark matter effects are reduced to geometric prestress effects of vacuum medium, without introducing any exotic dark matter particles. 中文摘要 本文基于两条第一性公理 —— 全域角动量归零公理(宇宙总角动量严格为零)与动态莫比乌斯投影公理(第五维为非定向莫比乌斯流形,特征半径随局域曲率动态演化)—— 建立 UVMM-UTFF 框架下黑洞统一几何理论。本框架定义黑洞并非被动弯曲时空的几何奇点,而是 5 维拓扑孤子在 4 维时空边界的投影;黑洞全部能量释放行为(喷流、引力波、电磁辐射),本质为预应力真空介质的拓扑相变或稳态泵浦过程。依托四类独立多信标观测数据完成系统性核验:LIGO-Virgo-KAGRA 引力波目录(GWTC-4.0/5.0,共计 390 例黑洞并合事件)、事件视界望远镜 M87与 Sgr A黑洞阴影偏振成像、LHAASO 五组微类星体 PeV 超高能伽马射线观测、GAIA DR3 银河系旋转曲线观测。结果表明:在瞬态并合光度()至稳态活动星系核喷流功率()跨越 9 个数量级区间内,理论预测与观测值误差控制在 20 倍因子以内;暗物质观测效应被还原为真空介质几何预应力效应,无需引入任何未知暗物质粒子。 Revision of the Definition of the Three Universes: A Triple-Sector Unification Based on 5D Topological Superfluid Ontology twin‑prime conjecture; Goldbach’s conjecture; Kepler’s conjecture
The Universal Form of Historical-Genetic Logic: From the Propositional Matrix to the Computable Index DOI: 10.5281/zenodo.20799967 Author: Aikaterini Xenopoulou TyrokomouIndependent ResearcherORCID: 0009 0004 9057 7432Email: katerinaxenopoulou@gmail.com Theoretical Foundation: Epameinondas Xenopoulos †Based on the Historical Genetic Logic of Epameinondas Xenopoulos, Epistemology of Logic: Logic – Dialectic or Theory of Knowledge (posthumous 2nd ed., 2024) [1, 2]Independent ResearcherORCID: 0009 0000 1736 8555† In memoriam (1920–1994) METHODOLOGICAL NOTE The present work mathematizes and extends central ideas of the formal-dialectical logic of Epameinondas Xenopoulos [1,2], with the direct aim of creating a computable and applicable tool. The mathematical expression of concepts such as dialectical intensity, historical memory, and the critical threshold constitutes a fully explicit, functional, and deliberate interpretative choice. Other consistent mathematizations are equally possible; here we choose those that ensure computational stability, transparency, and broad applicability. The work introduces original mathematical elements (such as the historical memory functions τ(t) and paradox factor Π(t), the stochastic extension, and the explicit form of the synthesis operator). These elements are presented as proposals of the author and are not attributed to Xenopoulos. The theoretical background, the fundamental categories, the logical principles, and the overall architecture belong to the work of Xenopoulos. The systematic formalization, the mathematical analysis, the proofs of the index properties, and the computational applications constitute the original contribution of the present work. ABSTRACT This work introduces the XEPTQLRI index, a computable, domain-agnostic diagnostic tool for anticipating critical transitions in complex dynamical systems. The index is grounded in the formal-dialectical logic developed by the Greek philosopher Epameinondas Xenopoulos (1920–1994), which treats contradiction not as an error but as the driving force of qualitative change. The index quantifies the "dialectical pressure" building within a system prior to a bifurcation. It combines three components: (1) dialectical intensity T(t), expressed as the harmonic mean of opposing tendencies ("Being" B(t) and "Non-Being" N(t)); (2) historical memory τ(t), capturing the direction and momentum of change; and (3) a paradox factor Π(t), which registers whether the system has historically experienced extreme opposing states. The index is defined as: Ξ(t) = [ T(t) · τ(t) · (1 + Π(t)) ] / Θ₀ where Θ₀ is a system-specific critical threshold. We prove that for systems undergoing pitchfork, transcritical, or Hopf bifurcations, the condition Ξ(t) = 1 coincides exactly with the vanishing of the maximum Lyapunov exponent — the mathematical signature of impending instability. The index is invariant under affine transformations of the coherence function, computable in linear time, and provides quantifiable early warning signals. Empirical validation across seven diverse fields — stochastic differential equations, COVID-19 epidemiology, LSTM networks under extreme noise, composting kinetics, open thermodynamics, Lindblad quantum systems, and strategic decision-making — demonstrates that the index reliably detects imminent qualitative shifts, often months before observable regime changes. The XEPTQLRI index offers a rigorous, efficient, and broadly applicable framework for early warning in nonlinear and complex systems, bridging dialectical philosophy with modern dynamical systems theory. Keywords: Historical-Genetic Logic, Formal-Dialectical Logic, Propositional Matrix of the World, XEPTQLRI Index, Dialectical Intensity, Historical Memory, Paradox Factor, Aufhebung, Critical Transitions, Phase Transitions, Bifurcations, Early Warning Signals, Maximum Lyapunov Exponent, Nonlinear Dynamics, Complex Systems, COVID-19 Epidemiology, Quantum Systems, Lindblad Equation, LSTM Neural Networks, Stochastic Differential Equations, Structural Stability, Dual Temporality. Lead Paragraph Detecting critical transitions before they happen: A dialectical index for early warning in complex dynamical systems Predicting when a complex system is about to undergo a qualitative change—whether a pandemic wave, a financial collapse, or a quantum phase transition—remains one of the most challenging problems in nonlinear science. Conventional early-warning indicators often fail to capture the slow accumulation of internal contradiction that precedes a bifurcation. Drawing on the formal-dialectical logic of the Greek philosopher Epameinondas Xenopoulos, we introduce the XEPTQLRI index, a novel pre-transitional diagnostic tool that quantifies the "dialectical pressure" building within a dynamical system. The index combines three components: dialectical intensity (the harmonic mean of opposing tendencies), historical memory (the direction and momentum of change), and a paradox factor that registers whether the system has experienced extreme opposing states in its past. We prove that, for systems undergoing pitchfork, transcritical, or Hopf bifurcations, the index crossing unity coincides exactly with the vanishing of the maximum Lyapunov exponent—the mathematical signature of impending instability. Empirical validation across seven diverse domains—from stochastic differential equations and COVID-19 epidemiology to LSTM networks under extreme noise, composting kinetics, open thermodynamics, the Lindblad equation for open quantum systems, and strategic decision-making—demonstrates that the index provides reliable early warnings, often months in advance of observable regime shifts. The XEPTQLRI index offers a mathematically rigorous, computationally efficient, and domain-agnostic framework for anticipating critical transitions in nonlinear and complex systems. INTRODUCTION The study of change runs throughout the entire history of philosophy. From Heraclitus ("πάντα ῥεῖ" – "everything flows") to Hegel, Marx, and Piaget, thought recognizes reality as an uninterrupted process of genesis, contradiction, and transcendence. Formal logic, although an indispensable tool of science, is founded on the abstraction of time and the principle of non-contradiction (p · ¬p = 0). The Greek philosopher Epameinondas Xenopoulos (1920–1994) developed a Historical-Genetic Logic (or formal-dialectical logic) that incorporates contradiction as the driving force of knowledge, bridging the gap between static formal thought and the dynamic flow of reality. In his work "Epistemology of Logic" [1,2], Xenopoulos establishes three central structures: 1. The epistemological correspondence Sπ ↔ Y(L, B, Θ): knowledge is born from the practical interaction of the subject-in-action (Sπ) with the object (Y), which is analyzed into logical structure (L), material substrate (B), and concrete position (Θ). 2. The Propositional Matrix of the World: a formal structure where each proposition carries a truth value from a discrete fractional spectrum {0, ½v, ½²v, …, 1} and passes through dialectical stages: thesis (A), development of negation (B), rupture (Γ), and new synthesis (Δ). 3. The operator N[Fi(Gj)]: the logical engine that drives propositions from one stage to another, expressing the necessary synthesis of thesis and its negation. The present article mathematizes and operationalizes these structures, giving them an explicit, computable form. For each concept we propose specific mathematical expressions. These choices are functional, not theoretically unique. The present form was chosen for its computational stability, broad applicability, and clear philosophical correspondence. The resulting XEPTQLRI index is not a simple statistical method, but the computable implementation of the dialectical operator itself in a specific, explicit mathematical framework. The empirical verification of the index in seven diverse fields (from stochastic dynamics to neural networks and epidemiology) demonstrates the practical power of this mathematization. PART I – THEORETICAL FOUNDATION 1. The Epistemological Correspondence: Sπ ↔ Y(L, B, Θ) Every cognitive process begins from the practical relation of the subject with the world. Xenopoulos [1,2] conceives this relation as an epistemological correspondence between two poles: · Sπ (Subject-Action): the subject in its active, transformative activity. Sπ is process, not state. It changes the world through action. · Y(L, B, Θ) (Object): the object of knowledge analyzed into three components: o L (Logos): the logical structure, the regularity, the form. o B (Matter): the material substrate, the content. o Θ (Thesis): the concrete spatiotemporal existence. The action Sπ modifies the object Y. This modification, assimilated by the subject, produces knowledge Sα = f(Sπ, Y). The correspondence is dialectical: action transforms the object, the transformation transforms knowledge, and new knowledge guides new action. Knowledge is not a passive image, but a historical product of interaction. This fundamental correspondence constitutes the cornerstone of every formal-dialectical analysis. 2. The Propositional Matrix of the World The knowledge born from the correspondence Sπ ↔ Y crystallizes into a dynamic formal structure: the Propositional Matrix [1,2, pp. 247-249]. Definition 1 (Proposition). A proposition P is defined as: P(x, y, z, t) = [v, τ, σ] with: · v ∈ V = {0, ½v, ½²v, …, 1}: the truth value on a fractional scale. 0 marks complete contradiction ("zero identity"), 1 marks the new integrated synthesis. · τ ∈ {T, D, TD}: the type of proposition (Formal, Dialectical, Formal-Dialectical). · σ ∈ {A, B, Γ, Δ}: the dialectical stage: o A (Thesis): stable formal knowledge. o B (Development of Negation): emergence of internal contradiction. o Γ (Rupture): critical