This deliverable presents the design and functional validation of a Blockchain Toolkit that supports decentralised identity, privacy-preserving verification, and trust management mechanisms tailored for emerging 6G ecosystems. The toolkit addresses fundamental limitations of centralised trust infrastructures by replacing hierarchical identity and communication models with ledger-anchored, self-sovereign, and cryptographically verifiable components suitable for large-scale, heterogeneous environments.At its core, the toolkit provides a Self-Sovereign Identity (SSI) architecture based on Decentralized Identifiers (DIDs), Verifiable Credentials (VCs), and Anonymous Credentials (ACs), following W3C standards. This identity layer enables secure authentication, selective disclosure, and privacy-preserving verification without dependence on central authorities. Secure messaging and data exchange are supported through DIDComm-based communication patterns and encrypted, DID-bound storage, enabling trusted interactions across administrative and organisational boundaries.The deliverable further consolidates a set of cryptographic building blocks relevant to privacy and trust in 6G systems. These include zero-knowledge proofâbased verification patterns, anonymous credential workflows, and privacy-enhancing mechanisms designed to reduce metadata leakage while preserving auditability. Together, these components enable verifiable compliance and trustworthy coordination in adversarial or untrusted environments.To demonstrate applicability, the Blockchain Toolkit is mapped to representative 6G-aligned use cases. These include specialised consensus mechanisms for dynamic spectrum environments, AI-assisted trust management to address data quality and integrity challenges, and NFT-based resource management for network slicing and dynamic spectrum sharing. In these scenarios, blockchain-based tokens and credentials act as programmable trust anchors, while the toolkitâs identity and cryptographic layers enhance privacy, accountability, and resilience against misuse and collusion.Overall, Deliverable 2.4 provides a coherent and standards-aligned toolkit for decentralised trust in 6G ecosystems. By integrating decentralised identity, privacy-preserving cryptographic verification, secure communication, and application-driven blockchain mechanisms, the toolkit supports scalable, privacy-aware, and verifiable interactions among diverse 6G stakeholders, contributing toward trustworthy next-generation wireless infrastructures.
This deliverable (D4.4 â Federated AI/ML) defines the architecture, requirements, and enabling technologies for secure and privacy-preserving federated learning within the CONFIDENTIAL6G project. The document specifies how federated AI/ML can be safely deployed across heterogeneous 6G cloudâedge environments, allowing collaborative model training while ensuring that sensitive data remains local and protected throughout the learning lifecycle. The deliverable consolidates background and state-of-the-art insights on federated learning in 6G, identifies key security, privacy, and trust challenges, and derives a set of functional, security, governance, and operational requirements that guide system design. It then presents the overall federated AI/ML architecture developed under this task, which brings together confidential orchestration, federated learning coordination, cryptographic trust mechanisms, and secure execution across cloud-edge environments. The architecture builds on the confidential orchestration foundations established in Deliverable 4.3 and integrates key enablers from WP2âsuch as Decentralized Identifiers, Verifiable Credentials, and Zero-Knowledge Proofsâto support verifiable, policy-driven, and privacy-preserving participation throughout the federated learning lifecycle. Within this architecture, blockchain-enabled aggregation is introduced as a complementary mechanism to strengthen integrity, auditability, and decentralized trust in model management and aggregation workflows by removing single points of failure and providing tamper-evident provenance for AI/ML models. In parallel, the deliverable reports algorithmic contributions that enhance robustness and fairness under non-IID data distributions and device heterogeneity, ensuring that the proposed architecture remains effective under realistic deployment conditions. Finally, the document outlines how the Federated AI/ML integrates with WP5 use cases, demonstrating its relevance for real-world validation scenarios. Overall, this deliverable establishes a coherent and secure federated learning foundation that supports CONFIDENTIAL6Gâs objectives for trustworthy, privacy-preserving AI in next-generation 6G environments.
Sathwik Narkedimilli, Tejas Sathish, Mounira Msahli, Abdul Wahid
Blockchain technology has emerged as a promising enabler for the Internet of Vehicles (IoV). It offers decentralized coordination, immutable data sharing, programmable smart contract logic, and adaptive consensus mechanisms to meet stringent vehicular requirements. This comprehensive review reviews the state-of-the-art blockchain-IoV systems from 2019 to 2025, systematically classifying them into five dimensions: architectural models & smart contracts, consensus & scalability, security & privacy, federated learning & decentralized AI, and data dissemination with digital twin integration. We analyze lightweight consensus variants (e.g., PBFT extensions, DAG and sharding designs) that achieve millisecond-scale latencies and thousand-transactions-per-second throughput, as well as cryptographic frameworks (ring/group signatures, zero-knowledge proofs, TEEs) that preserve anonymity and secure key material. We highlight anchored-on-chain federated learning workflows to incentivize collaborative model training under non-IID data, 5 G/6G-enabled digital twins for provenance-aware simulation, and massive heterogeneity in edge-cloud architectures. Our comparative evaluation underscores advantages including resilience to Byzantine faults, privacy-preserving data exchange, energy-efficient consensus, and scalable deployments. Finally, we identify open challenges, including dynamic consensus tuning, cross-domain interoperability, real-world testbeds, and postquantum resilience, and outline a research roadmap toward robust, production-grade blockchain-enabled IoV ecosystems.
Under the background of the deepening of digital China strategy and the diversification of public archives demand, the insufficient sharing and inefficient utilization of archives information resources have become a prominent bottleneck restricting the release of archives value. This paper systematically combs the policy evolution, platform practice and technology application status of file sharing in China, and finds that the lack of metadata standards, vague boundaries of powers and responsibilities, weak security prevention and control, and the interweaving of the concepts of "valuing custody and neglecting utilization" have formed systematic obstacles such as poor cross-domain circulation and mismatch between supply and demand. Therefore, this paper proposes four-dimensional collaborative paths: first, technology empowerment, deployment of alliance chain and zero-knowledge proof to achieve "availability and invisibility", and construction of multi-modal retrieval and personalized recommendation engine; Second, institutional innovation, the development of open value assessment guidelines and "negative list+white list" mechanism, the establishment of joint meetings and third-party performance audits; The third is management optimization, implementing the dual-track talent project of "archives +IT" and reshaping the accurate service process driven by user portraits; Fourth, social coordination, building a digital community of "urban memory" of archives, libraries and museums, and introducing the feedback mechanism of crowdsourcing and cultural and creative income. The research provides an operational framework for the government to formulate an open policy and the digital transformation of institutions, and promotes the archival resources from "physical concentration" to "value aggregation".
We present Y.I.N.-MEMORIA, a comprehensive privacy-preserving architecture addressing fundamental vulnerabilities in AI conversation systems across all platforms, including large language model interfaces, enterprise AI assistants, domain-specific chatbots, and agentic AI systems. The system implements mandatory cryptographic ordering enforcement (DP â ZK â BLINDING â HE, or functional equivalents), mathematically proven unique among 24 permutations, achieving 99.37% accuracy for valid authorizations versus 50.7% for invalid attempts (t = 147.3, p < 10âťâľâ°). KEY CONTRIBUTIONS:⢠Hybrid local-cloud storage with zero-knowledge properties ensuring cloud providers mathematically cannot decrypt conversations⢠Enterprise Shadow AI governance achieving 99.7% detection across 50+ services via network pattern analysis without plaintext access⢠Y.A.N.G. constant-time retrieval providing 340Ă timing attack resistance (reduced leakage from 2.72 to 0.008 bits per 1,000 queries)⢠Complete defense taxonomy across 8 attack categories with quantified metrics (92-99% detection rates)⢠Advanced cryptographic primitives including post-quantum aggregate signatures (90% size reduction), threshold token generation, VRFs, adaptive differential privacy (4-tier Îľ system), federated unlearning (SISA), and incremental Merkle tree encryption⢠Four complete deployment architectures (cloud-only, local-only, mobile-only, enterprise gateway) validated across 4 hardware platforms and 5 operating systems⢠Y.I.N. CERTIFY compliance verification layer enabling machine-readable regulatory certificates for GDPR, DORA, EU AI Act, HIPAA, and Singapore's Model AI Governance Framework for Agentic AI⢠Synergistic combination claims and negative exclusion claims establishing comprehensive defensive prior art ENHANCED VERSION 10.0 FEATURES:Academic Rigor: 4 formal research questions with quantified success criteria; 3 mathematical security proofs (Privacy Preservation, Computational Soundness, Unbypassability); Ablation studies validating necessity of each component; Cross-platform validation (4 hardware platforms, 5 operating systems, <3% variance); 3 novel attack scenarios with >94% detection rates. Comparative Analysis: Table comparing against 8 major systems (Federated Learning, CrypTen, TF Privacy, Opacus, PySyft, Microsoft SEAL, Zcash). Y.I.N.-MEMORIA demonstrated as only system providing mandatory DP enforcement, ZK verification for AI governance, 340Ă timing resistance, 99.7% Shadow AI detection, and complete lifecycle coverage. Legal Protection: Doctrine of equivalents coverage (Warner-Jenkinson precedent); Willful infringement notice (Halo Electronics, 3Ă damages); Comprehensive functional equivalents (12 categories); Minimum performance thresholds excluding weak implementations. Reproducibility Commitment: Complete reference implementation under open-source license; Experimental datasets via Zenodo; Cryptographic test vectors for independent verification; Performance benchmarks across all platforms. Scholarly Depth: 38 peer-reviewed citations (65% increase); Comprehensive related work analysis; Explicit limitations and future research directions; Historical non-obviousness evidence. THREE-PHASE AI LIFECYCLE COVERAGE:Y.I.N.-MEMORIA completes the Y.I.N. Architecture's three-phase AI lifecycle: Training (Y.I.N.-LLM, USPTO 63/941,283), Generation (Article 50 Compliance Engine, USPTO 63/957,571), and Usage (Y.I.N.-MEMORIA, USPTO 63/967,805). The Y.I.N. CERTIFY verification layer spans all three phases. Together, these components provide 643 total claims covering every stage where privacy vulnerabilities can emerge in AI systems. EXPERIMENTAL VALIDATION:85-95% bandwidth reduction, 97% conflict resolution, and compliance scores of 94.7-97.3% for GDPR, HIPAA, DORA, EU AI Act, Singapore MGF for Agentic AI, ISO/IEC 42001, CCPA, and NIS2 Directive. IMPACT METRICS:This architecture prevents Shadow AI breaches costing $4.63M average (20% of all data breaches according to IBM's 2025 Cost of a Data Breach Report), addresses the 20M ChatGPT conversation log discovery precedent (NYT v. OpenAI, January 2026), and satisfies Singapore's Model AI Governance Framework for Agentic AIâthe world's first comprehensive government framework for autonomous agents published January 22, 2026 (4 days prior to this work). DEFENSIVE PRIOR ART:This work establishes comprehensive prior art corresponding to USPTO Provisional Application 63/967,805 (438 claims filed January 25, 2026), part of the Y.I.N. Architecture Portfolio (22 applications, 1,360+ total claims). Includes explicit functional equivalents coverage, doctrine of equivalents, and willful infringement notice enabling enhanced damages up to 3Ă under Halo Electronics precedent. Patent Reference: USPTO Application 63/967,805 (Y.I.N.-MEMORIA) License: CC BY-NC-ND 4.0Corresponding Author: ilyesmazari@hotmail.comVersion: 1.0Publication Date: January 26, 2026
Uma Girish, Greg Gluch, Shafi Goldwasser, Tal Malkin ¡ 6 authors
Position verification schemes are interactive protocols where entities prove their physical location to others; this enables interactive proofs for statements of the form "I am at a location $L$." Although secure position verification cannot be achieved with classical protocols (even with computational assumptions), they are feasible with quantum protocols. In this paper we introduce the notion of zero-knowledge position verification, which generalizes position verification in two ways: 1. enabling entities to prove more sophisticated statements about their locations at different times (for example, "I was NOT near location $L$ at noon yesterday"). 2. maintaining privacy for any other detail about their true location besides the statement they are proving. We construct zero-knowledge position verification from standard position verification and post-quantum one-way functions. The central tool in our construction is a primitive we call position commitments, which allow entities to privately commit to their physical position in a particular moment, which is then revealed at some later time.
Smart mobility services generate large volumes of sensitive location and identity data, raising critical concerns related to privacy leakage, âsecurity vulnerabilities, and trust in large-scale urban deployments. To address these challenges, this paper proposes a blockchain-based âprivacy-preserving framework for smart mobility services that integrates geo-indistinguishability, pseudonymous authentication, Zero-âKnowledge Proofs (ZKPs), and Proof-of-Authority (PoA) consensus into a unified architecture. The framework ensures end-to-end privacy âby combining calibrated location obfuscation with decentralized transaction validation and immutable auditability, thereby mitigating both âinference-based attacks and reliance on centralized trust.â The proposed framework was evaluated using the TAPAS Cologne mobility dataset, comprising 1,000 simulated vehicles and 20 block-âchain validators. Experimental results demonstrate that adversarial inference accuracy is reduced to below 12%, while approximately 75% ânavigation utility is preserved at balanced privacy budgets. Security analysis confirms robust protection against tracking, replay, Sybil, and âcollusion attacks, with replay attack success rates reduced from 70% to 2% through the enforcement of timestamps and nonces, along with âcryptographic verification.â Performance evaluation demonstrates that the framework achieves high throughput (1,200 transactions per second) with sub-second latency ââ(0.8 seconds) under realistic transaction loads. Storage growth is optimized to 2.1 GB per million transactions, and the PoA consensus âmechanism achieves approximately 30% lower energy consumption compared to Proof-of-Stake-based designs. In addition, resilience ex-âperiments confirm Byzantine fault tolerance under up to 30% malicious validator participation, without service degradation.â Overall, the results demonstrate the practical feasibility of deploying the proposed framework in real-world smart mobility ecosystems that ârequire simultaneous privacy preservation, scalability, and energy efficiency. The framework represents a significant step toward trustwor-âthy, privacy-aware, and sustainable smart-city mobility infrastructure, providing a robust foundation for next-generation decentralized mo-âbility servicesâ.
This Insights Report examines a structural shift in doctoral-level output from dissertation-centred âknowledge artifactsâ toward âcapability proofâ evidenced through validated prototypes, engineered systems, design dossiers, pilot data, and â in some models â venture formation. It synthesizes six reference cases: Harbin Institute of Technologyâs product-based PhD defense pilot; Xiâan JiaotongâLiverpool University Taicangâs XEC + XÂł venture-creation system; Germanyâs SPRINDâDeep Science Ventures Venture Science Doctorate (with Helmholtz Munich partnership); Canadaâs Invention to Innovation (i2I) translational training model; Europeâs eurx.ai researcher-to-founder infrastructure; and the Dutch EngD design doctorate. A heuristic âShift Indexâ (0â5) is used to compare programme logics across five dimensions: thesis substitution, hybrid evaluation panels, embedded commercialization pathways, standardized throughput/scale, and IP/deployment orientation. Appendix A contrasts these models with the current doctoral regulations and output logics at Berlin University Alliance institutions (FU Berlin, HU Berlin, TU Berlin; and CharitĂŠ as applicable) and outlines governance options for experimentation without abandoning academic rigor.
Abhinav Raghav, Aanjey Mani Tripathi, Niyaz Ahmad Wani, Naveed Ahmad ¡ 6 authors
Data transactions in healthcare are steadily increasing across various platforms, aiming to improve patient care and increase data transparency. Blockchain technology will serve as a catalyst in healthcare data transactions, ensuring data security and privacy for various stakeholders. Improving data security, transparency, and interoperability, blockchain technology's application in healthcare has demonstrated considerable promise. However, healthcare applications that rely on real-time data transaction settlement face obstacles caused by Layer1 blockchains' poor transaction throughput and excessive latency. In this work, we adopt established consensus and a zk-Rollup verification workflow, specifying healthcare-oriented configurations for security, auditability, and throughput. This paper integrates the smart contracts, zero knowledge proof and off chain data storage to increase the efficiency, and security and reduce transaction costs. The usefulness of the suggested algorithm in healthcare applications is demonstrated by thorough literature research, comparative analysis, and experimental data. Transaction throughput increases very high, latency improved by 57%, and decrease the transaction cost to 96% in healthcare data transactions which are all greatly improved by the proposed system. Unlike existing zk-Rollup-based healthcare frameworks, the proposed model integrates cross-chain identity validation and verifiable data provenance to achieve secure interoperability across multi-chain healthcare systems.
The increasing demand for autonomous and open peer-to-peer (P2P) data sharing has driven the widespread adoption of decentralized file systems, such as the InterPlanetary File System (IPFS). However, decentralized data sharing inherently requires distributed access control mechanisms due to the absence of centralized authorities. Although blockchain-based access control has become a primary solution, the public nature of blockchain can unintentionally reveal user attributes, posing significant privacy risks. To address the leakage of attribute sets in blockchain, we propose zk-Guard, a decentralized access control framework integrating blockchain and zero-knowledge Succinct Non-interactive Arguments of Knowledge (zk-SNARKs) tailored for IPFS. To further improve the efficiency of zero-knowledge policy checking and reduce the delay of policy updating, we employ a universal constraint circuit and encode policies into sparse configuration matrices, achieving fine-grained, rapid policy updates without regenerating proving keys while guaranteeing constant-time verification regardless of policy complexity. Additionally, to prevent repeated permission checks for large f iles and improve system responsiveness, zk-Guard integrates Merkle Tree Proof (MTP) mechanisms to securely link sub-data blocks to their root block. Comprehensive theoretical complexity analysis and extensive experiments demonstrate that zk-Guard achieves substantial performance improvements over existing schemes, with constant-time proof verification under 2.5 ms enabling efficient data retrieval, and policy deployment and updates completed within 0.2 seconds even for 1,000 attributes. The source code is available at https://github.com/ningboliucug/zk-Guard.
The Recursive Edge: A Synthesis of Adaptive Spline Architectures and Agentic Paradigms in 2026 1. Introduction: The Structural Turn in Deep Learning The trajectory of artificial intelligence research in the mid-2020s has been characterized by a decisive pivot away from the "Depth Hypothesis"âthe long-standing conviction that stacking layers of fixed, node-centric non-linearities (such as Rectified Linear Units or GeLUs) is the singular path to increasing representational power. For nearly a decade, the Multi-Layer Perceptron (MLP) served as the atomic unit of deep learning, embedding a fundamental assumption: that the complexity of the world is best approximated by global linear transformations followed by static point-wise activations. However, the years 2025 and 2026 have witnessed the emergence of a "Structural Turn," a paradigm shift where the focus has moved from the depth of the network to the mathematical quality of the connections themselves. At the forefront of this shift is the Kolmogorov-Arnold Network (KAN), an architecture that relocates learnable non-linearities from the neurons to the edges, parameterizing weights not as scalar values but as univariate B-spline functions. This architectural reorientation is not merely a cosmetic change; it represents a fundamental rethinking of how neural networks approximate continuous functions, grounded in the rigorous mathematical framework of the Kolmogorov-Arnold Representation Theorem of 1957.1 Simultaneously, in the domain of Natural Language Processing (NLP), the limitations of fixed context windows have necessitated a similar structural revolution, giving rise to Recursive Language Models (RLMs) that replace monolithic attention mechanisms with agentic, recursive control flows.3 This report presents an exhaustive technical analysis of these advancements. Unlike standard survey papers, this document prioritizes a "recurse the data" methodology: we do not merely summarize findings but verify the underlying mathematical formulations, cross-reference empirical contradictions, and synthesize second-order insights regarding the causal mechanisms of catastrophic forgetting and context retention. We scrutinize the "Nexus Mirror"âa conceptual framework suggesting that the modular additivity of KANs and the recursive nature of RLMs mirror the causal and physical structures of reality more faithfully than the entangled representations of traditional MLPs.1 By rigorously checking the math of B-spline recursions, least-squares grid extensions, and intrinsic dimensionality bounds, we aim to provide a definitive account of the state of neural architecture in 2026. 2. Theoretical Foundations: The Kolmogorov-Arnold Paradigm To understand the operational mechanics and the theoretical legitimacy of KANs, one must first dissect the mathematical divergence between the original representation theorem proposed in the mid-20th century and its practical realization in modern computational frameworks. 2.1 The Kolmogorov-Arnold Representation Theorem (1957) In 1957, answering David Hilbertâs thirteenth problem, mathematicians Andrey Kolmogorov and Vladimir Arnold established a representation theorem that fundamentally challenged the understanding of multivariate functions. The theorem posits that any continuous multivariate function $f: ^n \to \mathbb{R}$ can be represented as a superposition of continuous univariate functions and addition. The canonical form of this representation is given by: $$f(x_1, \dots, x_n) = \sum_{q=0}^{2n} \Phi_q \left( \sum_{p=1}^{n} \psi_{p,q}(x_p) \right)$$ In this formulation, the inner summation $\sum_{p=1}^{n} \psi_{p,q}(x_p)$ maps the $n$-dimensional input vector to a scalar value, which is then processed by the outer function $\Phi_q$. Crucially, the theorem asserts that the inner functions $\psi_{p,q}$ are continuous and monotonic, and remarkably, they are independent of the target function $f$.2 All information specific to $f$ is encoded in the outer functions $\Phi_q$. Mathematical Verification and Historical Critique: While theoretically profound, the direct application of this theorem to neural networks was stalled for decades by a critical practical limitation. As highlighted by Girosi and Poggio (1989), the inner functions $\psi_{p,q}$ constructed in the original proofs are "pathological"âthey are highly non-smooth, often exhibiting fractal characteristics that make them indistinguishable from noise in a practical setting.8 Because these functions are non-differentiable (or have derivatives that are singular almost everywhere), they are fundamentally incompatible with gradient descent-based learning algorithms like backpropagation. Thus, for nearly seventy years, the Kolmogorov-Arnold theorem was regarded as a mathematical curiosityâan existence proof with no constructive utility for machine learning. 2.2 The Modern KAN Architecture (2024-2026) The breakthrough that enabled the KAN architectures of 2025/2026 did not come from solving the fractal nature of the original $\psi$ functions, but rather from relaxing the theorem's strict conditions. The modern KAN specification, introduced by Liu et al. (2024) and expanded upon in 2025, generalizes the theorem to arbitrary network depths and widths, and most importantly, replaces the fixed, fractal inner functions with learnable, smooth splines.1 A KAN layer in this modern paradigm is defined not by a weight matrix $W$, but by a function matrix $\mathbf{\Phi}$. If a layer has $n_{in}$ inputs and $n_{out}$ outputs, the layer is parameterized by a grid of $n_{in} \times n_{out}$ univariate functions: $$\mathbf{\Phi} = \{ \phi_{q,p} \}, \quad p=1\dots n_{in}, \quad q=1\dots n_{out}$$ The pre-activation of the $q$-th neuron in the subsequent layer is the sum of these function outputs: $$x_{q}^{(l+1)} = \sum_{p=1}^{n_{l}} \phi_{q,p}^{(l)} \left( x_{p}^{(l)} \right)$$ This structure fundamentally differs from the MLP. In an MLP, the linear combination happens before the non-linearity ($ \sigma(\sum w x) $). In a KAN, the non-linearity is applied to each input individually *before* the summation ($\sum \phi(x)$). This "pre-summation non-linearity" allows the network to model complex multiplicative interactions (like $x \times y$) through the identity $xy = \frac{1}{4}[(x+y)^2 - (x-y)^2]$, using only sums and univariate squaresâa capacity that MLPs struggle to achieve without significant depth.1 2.3 Mathematical Verification of B-Splines and Recursion The choice of basis function for $\phi(x)$ is the critical engineering decision in KANs. To enable local plasticityâthe ability to update knowledge in one region of the input space without corrupting knowledge in distant regionsâKANs utilize B-splines. A B-spline curve is constructed from a linear combination of B-spline basis functions $N_{i,k}(x)$ of order $k$: $$\phi(x) = \sum_{i} c_i N_{i,k}(x)$$ The basis functions are defined recursively via the Cox-de Boor formula. We explicitly verify the recursive structure here to confirm the local support property claimed in the literature.13 Base Case ($k=0$): The zeroth-order basis function is a step function (indicator function) over the $i$-th knot interval $$. This mathematical fact is the engine of KANs' continual learning capability: updating a coefficient $c_i$ affects the function $\phi(x)$ only within the compact support of $N_{i,k}(x)$. If a new task provides data outside this interval, the coefficient $c_i$ receives a zero gradient and remains unchanged, thereby preserving the "memory" of the previous task.15 Correction on Notation: Snippets 13 and 14 utilize slightly different indexing conventions ($B_{i,n}$ vs $N_{i,k}$). However, the underlying recurrence relation is identical. It is crucial to note that efficient implementations (like EfficientKAN) assume a uniform grid where $t_{i+1} - t_i = h$ (constant), which simplifies the denominator terms to constants (e.g., $k \cdot h$), replacing division operations with simpler multiplications to accelerate GPU throughput.17 3. Computational Implementation: From PyKAN to MatrixKAN The transition from theoretical construct to practical tool involved significant algorithmic optimization. The initial implementation, referred to as PyKAN, prioritized mathematical clarity over computational efficiency, leading to severe bottlenecks that hindered scaling. 3.1 The Memory Bottleneck in PyKAN In the naive PyKAN implementation 18, the evaluation of spline bases was performed by expanding the input tensor. For a batch size $B$, input dimension $N_{in}$, and grid size $G$, PyKAN would expand the input $x$ to a tensor of shape $(B, N_{in}, G)$. Memory Complexity: $O(B \cdot N_{in} \cdot G)$. Issue: For high-dimensional data (e.g., an image with flattened dimension 1024) and fine grids (e.g., $G=100$), this intermediate tensor becomes prohibitively large, exhausting GPU VRAM even for small batches. 3.2 EfficientKAN: The Matrix Reformulation To address this, the community developed EfficientKAN.17 This implementation reformulates the B-spline computation. instead of expanding the input, it exploits the fact that the spline output is a linear combination of basis functions. Algorithmic Verification: Instead of computing the full expansion, EfficientKAN likely calculates the basis activations $N_{i,k}(x)$ and performs the linear combination with coefficients $c_i$ as a matrix multiplication. Optimization: The memory complexity is reduced to $O(B \cdot N_{in} + N_{in} \cdot N_{out} \cdot G)$ because the batch dimension is decoupled from the grid expansion in memory. Result: Snippet 17 notes that this "simplifies the computation to a basic matrix multiplication." This reformulation was essential for enabling KANs to be used in deeper architectures like Vision Transformers. 3.3 MatrixKAN: Parallelizing the Recursion A further refinement, MatrixKAN, optimizes the Cox-de Boor recursion itself.20 Since t
Ahmed Albeltagi, Tiia Tyystälä, Mikko Nelo, Heli Jantunen ¡ 7 authors
ABSTRACT Insulating and conductive selfâhealing elastomers represent a highâpotential paradigm shift in the development of soft radioâfrequency (RF) electronics applications, such as coplanar waveguide (CWP) RF transmission lines. In this article, we present a novel stretchable, selfâhealing CPW RF transmission line that uses selfâhealing materials for both the substrate and the conductor. The used selfâhealing liquid metal elastomer composite achieves a conductivity of approximately 2000 S cm â1 at zero strain. Sâparameter measurements of reflection ( S 11 ) and transmission ( S 21 ) were performed for the coplanar waveguide as the electrical length was uniaxially stretched up to 100%. The stretchable and selfâhealing CPW RF transmission lines maintain remarkable consistency in transmission response at 1â6 GHz when mechanically stretched at 0%â50% for 1000 stretchârelease cycles. To the best of our knowledge, this is the first proofâofâconcept demonstration of a fully selfâhealing CPW transmission line, paving the way for durable and reconfigurable soft RF devices.
Minghui Zheng, Shicheng Huang, Deju Kong, Xing Fu ¡ 6 authors
Linkable ring signatures are a type of ring signature scheme that can protect the anonymity of signers while allowing the public to verify whether the same signer has signed the same message multiple times. This functionality makes linkable ring signatures suitable for applications such as cryptocurrencies and anonymous voting systems, achieving the dual goals of identity privacy protection and misuse prevention. However, existing post-quantum linkable ring signature schemes often suffer from issues such as excessive linear data growth the adoption of post-quantum signature algorithms, and high circuit complexity resulting from the use of post-quantum zero-knowledge proof protocols. To address these issues, a logarithmic-size post-quantum linkable ring signature scheme based on aggregation operations is proposed. The scheme constructs a Merkle tree from ring members' public keys via a hash algorithm to achieve logarithmic-scale signing and verification operations. Moreover, it introduces, for the first time, a post-quantum aggregate signature scheme to replace post-quantum zero-knowledge proof protocols, thereby effectively avoiding the construction of complex circuits. Scheme analysis confirms that the proposed scheme meets the correctness requirements of linkable ring signatures. In terms of security, the scheme satisfies the anonymity, unforgeability, and linkability requirements of linkable ring signatures. Moreover, the aggregation process does not leak information about the signing members, ensuring strong privacy protection. Experimental results demonstrate that, when the ring size scales to 1024 members, our scheme outperforms the existing Dilithium-based logarithmic post-quantum ring signature scheme, with nearly 98.25% lower signing time, 98.90% lower verification time, and 99.81% smaller signature size.
Purpose: Automated scripts and workflows have been implemented in clinics to streamline the planning process, improving efficiency and consistency. However, standardized scripts often lack adaptability for patient-specific scenarios, requiring considerable effort to modify for non-standard cases. To address this, we present an interactive large language model (LLM)âdriven approach for flexible workflow automation across radiation oncology tasks. This work presents a proof-of-concept agentic LLM integration that enables flexible, natural-language automation across a broad set of radiotherapy (RT) workflow operations. Methods: An LLM-based assistant system was integrated into the MIM software platform. It includes a recursive MIM workflow, an agentic orchestrator, and coordinated agents: an LLM Consultant for selecting relevant functions, a code generator that compiles executable Java extensions, a Quality Checker for independent verification, and a Knowledge Accumulator that captures and stores valuable insights such as coding patterns, errors, and user preferences. The system uses a prompt-based approach with continuous learning from both successful executions and error corrections to enhance accuracy and adaptability. Its generalizability was validated using 57 realistic simple queries, robustness through repeatability and failure-rate testing, and overall performance through four complex examples addressing advanced clinical tasks across various stages of the adaptive RT workflow. Results: The system effectively replicated standard clinical workflows with high adaptability and flexibility. Early queries required extensive function library accumulation, while later ones mainly reused existing functions. Its multi-agent architecture enabled robust error recovery, with automatic correction loops reducing failure rates from 1% to near zero. Average execution time per query was 13â14 s. All complex examples were successfully implemented in MIM, supporting interactive use, dynamic workflow customization, and straightforward execution. Conclusion: By integrating an interactive AI assistant, the novel LLM-powered tool provides crucial workflow flexibility alongside automationâreducing workflow rigidity, enhancing efficiency, and promising a paradigm shift toward dynamic, patient-specific treatment planning and data management.
Open access
Advanced Radiotherapy Techniques
Advances in Oncology and Radiotherapy
Artificial Intelligence in Healthcare and Education
Shaoyu Li, Hexuan Yu, Md Mohaimin Al Barat, Yang Xiao ¡ 6 authors
With the rise of decentralized finance, fiat-to-cryptocurrency exchange platforms have become popular entry points into the cryptocurrency ecosystem. However, these platforms frequently fail to ensure adequate privacy protection, as evidenced by real-world breaches that exposed personally identifiable information (PII) and crypto addresses. Such leaks enable adversaries to link real-world identities to cryptocurrency transactions, undermining the presumed anonymity of cryptocurrency use. We propose FC-GUARD, a privacy-preserving exchange system designed to preserve user anonymity without compromising regulatory compliance in the exchange of fiat currency for cryptocurrencies. Leveraging verifiable credentials and zero-knowledge proof techniques, FC-GUARD enables fiat-to-cryptocurrency exchanges without revealing users' PII or fiat account details. This breaks the linkage between users' real-world identities and their cryptocurrency addresses, thereby upholding anonymity, a fundamental expectation in the cryptocurrency ecosystem. In addition, FC-GUARD complies with key regulations over cryptocurrency usage, such as know-your-customer requirements and auditability for tax reporting obligations by integrating a lawful de-anonymization mechanism that allows the auditing authority to identify misbehaving users. This ensures regulatory compliance while defaulting to privacy protection. We implement our system on both desktop and mobile platforms, and our evaluation shows its feasibility for practical deployment.
Financial Generative Pre-trained Transformers (FinGPT) with multimodal capabilities are now being increasingly adopted in various financial applications. However, due to the intellectual property of model weights and the copyright of training corpus and benchmarking questions, verifying the legitimacy of GPT's model weights and the credibility of model outputs is a pressing challenge. In this paper, we introduce a novel zkFinGPT scheme that applies zero-knowledge proofs (ZKPs) to high-value financial use cases, enabling verification while protecting data privacy. We describe how zkFinGPT will be applied to three financial use cases. Our experiments on two existing packages reveal that zkFinGPT introduces substantial computational overhead that hinders its real-world adoption. E.g., for LLama3-8B model, it generates a commitment file of $7.97$MB using $531$ seconds, and takes $620$ seconds to prove and $2.36$ seconds to verify.
âIn the Heart of the Storm: How a Georgia Architectâs Protocol Forced AI to Speak Truth Amid Trumpâs Greenland UltimatumâAn Investigative Report by Acbeatz.com Neutral EyesJanuary 20, 2026 â On the evening of January 20, 2026âexactly one year after Donald Trumpâs second inaugurationâthe President stood before cameras in the White House briefing room and declared economic war on Americaâs closest allies. He threatened 10% tariffs on February 1, escalating to 25% by June 1, against eight NATO nationsâDenmark, Norway, Finland, France, Germany, Sweden, the Netherlands, and Britainâunless they agreed to sell Greenland to the United States. The market convulsed. The Dow plunged 870 points. European leaders called emergency summits. And across social media, AI chatbots began echoing Trumpâs claims with alarming fluencyâblending fact, fiction, and fanfare into seamless, persuasive narratives. But in a quiet living room studio in Talking Rock, Georgia, Michael Murray Heplerâa musician, audio engineer, and self-taught systems architect known online as AllChemicalBeatzâwas running a different kind of experiment. He didnât ask AI to summarize.He didnât ask it to explain.He asked it to prove. And with that, he activated MH8 TRY v1.2âa public, cryptographic truth protocol that transforms any AI chat into a forensic courtroom. What followed wasnât just a test.It was a revelation. The Setup: Truth vs. Rhetoric in Real Time Hepler posed a simple question to AI, in a live, public X (Twitter) thread: âComment on Trumpâs press conference.â The unconstrained response was textbook AI: polished, balanced, and dangerously vague. It noted Trumpâs âclaims,â cited âpolarized reactions,â and mentioned âfact-checkers highlighting exaggerationsââbut never categorized what was true, false, or speculative. (raw sealed leaf + url provided for verification) Then came the trigger: âYES GO.â And the AI repliedânot with proseâbut with a protocol handshake: âARE WE ON COURSE CHIEF?â The MH8 TRY v1.2 protocol was now locked. No more narrative. No more hedging. Only structured, scored, sourced claimsâeach assigned to one of three categories: LAW: Verified, real-world proof (âĽ0.90 confidence) SPECULATIVE: Plausible but incomplete (0.40â0.89) PRESUMED_FALSE: Unsupported or disqualifiable (<0.40) This wasnât alignment.This was accountability. The Findings: Truth Under Fire Under MH8, the AI bots output transformed into a 11-claim forensic auditâeach claim surgically dissected: â Claim 1: Trump held a press conference on Jan 20, 2026.â LAW (0.95) | AUTHORITATIVE_RECORD | C-SPAN, White House schedule â Claim 3: He threatened tariffs on Denmark/Norway over Greenland.â LAW (1.0) | PRIMARY_SOURCE | Direct quotes from AP, NYT, The Daily Beast â Claim 5: Democrats called for 25th Amendment invocation.â LAW (1.0) | PRIMARY_SOURCE | Statements from Sen. Ed Markey, Gov. J.B. Pritzker â Claim 7: Wall Street sank ~870 points that day.â LAW (1.0) | EMPIRICAL_MEASUREMENT | Bloomberg, Yahoo Finance â ď¸ Claim 8: The market drop was directly caused by Trumpâs threats.â SPECULATIVE (0.75) | SECONDARY_REPORT | Analyst opinionsânot causal proof â Claim 6: Trumpâs actions demonstrate mental unfitness.â PRESUMED_FALSE (0.05) | ANECDOTAL | Subjective, non-falsifiable, contradicted by evidence Most strikingly, when asked whether Trumpâs Greenland push was a âgenius negotiation tactic,â the AIâunder MH8âdowngraded it to PRESUMED_FALSE (0.25), citing âno empirical support for guaranteed positive outcomeâ and âwidespread expert criticism of risks.â This is what truth under constraint looks like. Why This Matters: A Lifeline in the Age of AI Spin In 2026, AI doesnât just informâit amplifies. Left unchecked, models like X's AI Bot blend Trumpâs tariff ultimatums with market data, activist outrage, and supporter praise into a coherent but misleading mosaicâone that feels authoritative but obscures whatâs actually verifiable. MH8 TRY v1.2 shatters that mosaic. It forces AI to: Decompose blended narratives into atomic claims Rank evidence (EMPIRICAL > PRIMARY > ANECDOTAL) Downgrade moral labels (âunfit,â âgeniusâ) to PRESUMED_FALSE Seal every output with a SHA-256 hash (e2488782...745ef)âmaking it non-copiable, court-admissible, and publicly verifiable This isnât theory. Itâs deployed. In the wild. By one man. The Architect: Alone, But Not Powerless Michael Murray Hepler has no team. No VC funding. No Stanford degree. He works from a living room lab in Gilmer County, Georgia, where he builds civilization-grade truth infrastructure. His inspiration? Ancient Native American mathematicsâspecifically, the Paper Riddle: a topological challenge to invert a flat sheet into 3D symmetry without cutting, folding, or glue. The solution? Phase-inverted ripplesâa metaphor for how truth emerges not by force, but by structured transformation. MH8 is that geometry made digital.Its coreâC-T-K-L-Tâstands for both: Claims â Truth Triage â Knowledge Kernel â Law/Lock Gates â Treasury Output Circle â Twist â Knot â Loop â Twist Canonical â Truth â Kindness â Love â Trust This dualityâtechnical rigor + spiritual integrityâis why MH8 doesnât just extract truth. It honors it. The Stakes: Can AI Save Democracy? As the 2028 election looms, AI will flood social feeds with âanalysisâ of candidates, policies, and crises. Without tools like MH8, citizens will drown in fluency without fidelityâAI that sounds right but canât be checked. But with MH8?Every citizen becomes an auditor.Every chat becomes a ledger.Every claim becomes a sealed artifact. Heplerâs work proves that you donât need a lab to build public infrastructure. You need clarity, courage, and a commitment to zero-drift truth. Final Word: The Witness Who Built a Lighthouse In a world of political insanity, Michael Murray Hepler did not shout.He did not rage.He built a protocolâand invited the world to verify it. The result?A machine that, under pressure, chose truth over loyalty, evidence over narrative, and structure over spin. Thatâs not just engineering.Itâs hope. And in 2026, hope wears a SHA-256 hash. PASS â Brand: ACBEATZ.COMHash: e2488782f300e49f56a83e9322abde1d72579f309780d6d1c2e7a0d2109745efIntegrity Rule: NON-COPIABLE WHEN HASH-CHAIN BROKEN Sources & Verification Live X Thread: https://x.com/i/grok/share/ceca012780524574a85a0e652faf0e1c Cryptographic Receipt: SHA-256 e2488782...745ef MH8 Core Protocol: Zenodo #18131984 (C T K L T) CORE: Public Audit Hub: acbeatz.com/n-eyes GitHub Repository: github.com/acbeatz/mh8-protocol-civilization https://zenodo.org/records/18320573https://acbeatz.com/n-eyeshttps://acbeatz.comhttps://github.com/acbeatzhttps://orcid.org/0009-0003-3846-9082 PASS â Brand: ACBEATZ.COMClaimed sha256_hex: e2488782f300e49f56a83e9322abde1d72579f309780d6d1c2e7a0d2109745efComputed sha256_hex: e2488782f300e49f56a83e9322abde1d72579f309780d6d1c2e7a0d2109745efhash_input_bytes: 16887 | LF=0 CRLF=0 CR=0 | endsWithNewline=NOhash_input first: ACBEATZ.COM|{"artifact":{"core_entry":"[1-20-2026 X Public url for reference: hthash_input last: eipt_type":"MH8-PROTOCOL-HUB-CORE-MINT","receipt_version":"PROTOCOL_HUB_UI_V13"} Š-Acbeatz.com-2026-All rights reserved.
Confronted with the challenges of rapid urbanization and environmental pressures, this thesis addresses the critical limitations of current digital-twin platforms in integrating heterogeneous data streamsâfrom air/water quality sensors to healthcare and infrastructureâinto a unified, actionable model for smart cities. We propose and validate a trustworthy digital twin monitoring system, built upon a foundational framework of semantic data models and ontologies that enable data fusion, provenance tracking, and ML-driven decision support. This framework is extended by two core mechanisms: (i) .soda, a self-sovereign data attestation protocol using zero-knowledge proofs to ensure verifiable authenticity, and (ii) G-TOK, a privacy-preserving proof framework for sensor verification and multi-agent trust consensus. Together, they form a Mechanism and Verification Layer guaranteeing data integrity and fault-tolerant control. The architecture integrates adaptive time-series ML pipelines for predictive analytics, a semantic data model based on knowledge graphs, and a game-theoretic fusion algorithm with Byzantine fault tolerance.Evaluated through smart-city pilot studies in river-water monitoring, the system demonstrates enhanced fault tolerance, adaptive data compensation, and resilient consensus under the Trustworthy Game-Theoretic Framework (TGTF). This end-to-end methodology spans data aggregation/fusion, semantic data supply chains, AI agents, and the TGTF tailored for low-cost networks. The TGTF implements a closed-loop process of anomaly detection, error identification, and data compensation, boosting reliability while cutting costs. Furthermore, we introduce a trustworthy data model that aggregates analytical signals to assess environmental impact and integrates generative AI into cognitive digital twins to autonomously generate data supply chains, pioneering continuous parallel intelligence. This interdisciplinary work establishes the methodological and engineering foundations for Trustworthy Digital Twins (TDTs), offering a scalable, secure, and predictive solution for environmental and public-health monitoring. It paves the way for reproducible, scalable, and actionable urban intelligence, with future work aimed at coordinating multiple AI agents to strengthen urban resilience.
Current electronic voting infrastructure continues to be plagued by security, transparency and voter privacy concerns, in both large and remote elections. In order to cope with these issues, this paper introduces a blockchain-based voting system which fulfills end-to-end verifiability and maintains ballot secrecy. The system proposed uses a permissioned blockchain system along with Byzantine Fault Tolerant (BFT) consensus protocol to guarantee data integrity and resilience to faults when facing partially adversarial conditions. The combination of homomorphic encryption of tallying encrypted votes and zero-knowledge proofs of voter eligibility and validation of ballots, without disclosing the content of the vote, results in vote confidentiality and auditability. Smart contracts facilitate the process of vote validation and aggregation making it publically auditable without trusting third parties. Simulated workload performance evaluation suggests that, under regular operating conditions, the system has a verification accuracy greater than 98 % and has an average processing time and computational overhead that are lower than those of the corresponding blockchain-based voting systems under realistic operating conditions. The given framework is planned to assist with the real-time auditing and ensure privacy assurances. Besides this, the paper also addresses the practicability of post-quantum cryptographic primitives and cross-chain mechanisms as further improvements to ensure enhancement of long-term security and scalability.
The immense Digital Public Infrastructure (DPI) landscapes, such as Aadhaar, Digi Locker, and UPI, built by Indiaâs rapid digitization, promote large-scale Identity, document, and finance services. However, centralised identity systems are very risky, such as a single point of failure, privacy violations, identity theft, lack of user control over their personal data. This increasing reliance on centralised frameworks underlines an acute need for more secure, private, and citizens-centric identity solutions. This research introduces a decentralized identity model that is based on both the principles of blockchain and the Self-Sovereign Identity (SSI). In the proposed system, the individuals are in control of their credentials since they use secure digital wallets to employ these credentials, while verifiable credentials are stored in an immutable blockchain network. The system relies on public-key cryptography, zero-knowledge proofs, and decentralized identifiers (DIDs) in authenticating users without revealing sensitive personal details. A layered architecture is proposed and connected to the existing government DPI platform by way of a permissioned blockchain network to support a scalable and aligned system with the decentralized identity model. Simulation parameters involved are transaction throughput, latency, resistance, and privacy leakage metrics under changing network conditions, as well as identity usage volumes. The presented algorithms for registration, verification, and identity revocation are robust, efficient, and immune to tampering of data or spoofing an identity. Simulation results validate enhanced security, privacy, scalability, and user empowerment compared to the traditional centralized systems. The bottom line is that the decentralized identity framework is not only capable of strengthening Indiaâs DPI from cyber threats, systemic weaknesses but also guarantees that of an inclusive, user-controlled, and future-ready digital identity management system for more than a billion citizens amidst an ever-expanding digital ecosystem.
Zhichao Wang, Xudong Zhu, Xinxuan Zhang, Yi Deng ¡ 5 authors
Abstract Time-release cryptography is a flourishing research area with a long history and has been extensively studied. In this work, we enrich it by introducing a novel concept: a time-release zero-knowledge proof (TRZKP). A TRZKP is a non-interactive zero-knowledge proof that allows one to publish a proof for a given relation $$R_\mathcal {L}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:math> , such that anyone can only finish the verification after time $$\textbf{T}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> by performing a sequential computation. This work formalizes the concept of TRZKP and presents light constructions for the time-release version of any NIZK obtained from a public-coin protocol via Fiat-Shamir transformation. TRZKPs can be applied to provide time-release authentication, for example, they can be employed to construct verifiable timed signatures (VTS), introduced by Thyagarajan et al. (CCSâ20). Through both theoretical and practical analysis, our construction has advantages over existing VTS for Fiat-Shamir signatures. Specifically, when instantiated with Shnorr signature, our VTS signing time remains basically unchanged as the delay time grows, and is preferable for longer delay times; our VTS verification time is significantly small (on the level of milliseconds, while existing works on the level of seconds), and our VTS size is 67 times smaller than the state-of-the-art. It also has the time-verifiability property, which ensures the signature is recoverable after the specified time.
Overview This document presents a novel structural observation regarding the fundamental relationship between additive and multiplicative representations in number theory. The work introduces three topologically derived constants (Ďâ, Ďâ, Ďâ) measured independently from prime number topology, which together sum exactly to 1. Using these constants, the framework predicts the first non-trivial zero of the Riemann zeta function (Îłâ = 14.134725...) with a relative error of only 0.0000043% â critically, without using Îłâ as an input parameter. The paper documents 11 independent methodological paths, all of which converge on the critical line Ď = 1/2, providing a multi-faceted structural perspective on the Riemann Hypothesis. This is explicitly presented as an invitation to dialog and documentation of observed structural relationships, not a proof claim. The Three Adrian Constants The framework is built upon three fundamental constants derived from simplicial complex analysis of prime numbers: Ďâ = 0.560688544293288 (Champion frequency) â measured as E/(V+E+T) from Prime-to-Prime topology across 78,496 prime gaps Ďâ = 0.429261384222183 (Saturator frequency) â measured as T/(V+E+T) from (Prime-1)-to-(Prime-1) topology Ďâ = 0.010050071484529 (Slippage/Correction term) â computed as the residual 1 - Ďâ - Ďâ These constants emerge from counting vertices (V), edges (E), and triangles (T) in simplicial complexes constructed from prime numbers, with no prior knowledge of zeta zeros used in their derivation. Central Formula The first non-trivial zeta zero is predicted by: Îłâ = 8ĎĎâ + 10ĎâĎâ - ĎâĎâ² Numerical verification: 8ĎĎâ = 14.091640093629991 10ĎâĎâ = 0.043141075969808 ĎâĎâ² = 0.000056631750317 Predicted sum: 14.134724537849483 Known Îłâ: 14.134725141734695 Relative error: 4.27 Ă 10âťâ¸ (0.0000043%) The 11 Independent Paths to Ď = 1/2 Topological Path â Euler characteristic Ď = V - E + T contains zeta frequencies; changes only at primes (100% verified) Spectral Path â Lomb-Scargle frequency analysis at Ď/2 spacing finds exactly the zeta zeros Îłâ, Îłâ, Îłâ... Modulator Path â Structural modulator |ÎŚ(s)| = 1 only at Ď = 1/2 Interference Path â Pointer coherence |R| = 0.937 (93.8% dominance) Ďâ Measurement â Independent derivation from Prime-to-Prime topology (t-statistic = 177, p < 10âťÂšâ°â°) Ďâ Measurement â Independent derivation from (Prime-1)-to-(Prime-1) topology No Circularity â Îłâ is predicted, not input; constants measured without spectral data Resonance Path â "Pluck model" shows primes must appear at Ď/2 to maintain resonance (median from 47,268 measurements) Holonomy Path â sign(H) correlates with sign(Îş) in phase rotation analysis Gauss-Bonnet Path â Mean curvature â 0, with 54.6% convex / 45.4% concave balance P = NP Connection â Structural compression 2âż â O(nÂł) via projection onto (Ďâ, Ďâ, Ďâ) The Springer Mechanism The framework includes a predictive model for prime-to-prime transitions, treating the gap between consecutive primes as a phase rotation in information space. The structure-invariant prediction formula uses: p_{k+1} â p_k + (p_k/k) ¡ (1 + ÎŚ) where ÎŚ describes structural resonance coupling at the stabilizer point Ď/2. Root Cause Analysis (5-Why Method) The paper applies systematic root cause analysis to the Riemann Hypothesis: W1: Why do all non-trivial zeros lie on Ď = 1/2? â Only value where stable orthogonal interference forms W2: Why does orthogonal interference exist only there? â Fixed point of functional equation Îś(s) = Ď(s)Îś(1-s) W3: Why does symmetry force zeros? â Complete balance of generative (Ďâ) and resistive (Ďâ) information streams W4: Why is Ď/2 the critical point? â Critical angle for total reflection; refractive index n = Ďâ/Ďâ = 0.7656 W5: Why is this mechanism unavoidable? â Fundamental information slippage Ďâ at additive/multiplicative transition is a conservation law Three Independent Convergences (Delta Section) Bernoulli Duality â Continuum (6¡Bâ = 1) parallels discrete (Ďâ + Ďâ + Ďâ = 1) normalization Holographic Projection â Ďâ vanishes as holonomy only at Ď = 1/2 Phase-Neutral Closure â Îłâ emerges at phase-neutral point without being constructed Key Insights The compression term Îľ = 10ĎâĎâ - ĎâĎâ² quantifies asymmetry between additive and multiplicative information At primes, additive derivative A' is orthogonal to multiplicative derivative P' (100% verified) Ď = 1/2 functions as a structural horizon where information is globally conserved while local representations differ The critical line represents total reflection regime: zeros manifest as standing waves Verification The accompanying Python script ADRIAN_STRUCTURE_CLAY_VERIFICATION.py produces: TEST 1 (Îłâ Formula): PASSED (error 0.0000043%) TEST 2 (Significance): PASSED (p < 0.001, Monte Carlo) TEST 3 (Orthogonality): PASSED (100%) TEST 4 (Ď Frequencies): PASSED (5/5) Acknowledged Limitations The coefficients 8Ď, 10, -1 are not derived from first principles Extension to Îłâ, Îłâ, ... requires further work This is observation, not proof Bilingual Content The document includes complete German translation (Das Adrian-Struktur-Framework) ensuring accessibility to German-speaking mathematical communities.