In this paper, I argue that developmental stage theories and the six functional primitives proven necessary for adaptive decision-making are not merely analogous: they are two independently-discovered solutions to the same structural problem, and their convergence is evidence of that shared structure rather than of coincidence. The computational foundation is Ismail's Primitives (Ismail, 2026, V6.1) â a Lean 4/Mathlib formalization with zero sorry, zero custom axioms, and zero opaque terms â establishing that six functional properties are each necessary for sublinear regret under uncertainty, mutually irreplaceable, and compose into a self-reinforcing directed information chain: Objective Tracking, Cross-Context Safety Transfer, Global Attractor Exploration, Policy Simplification, Feasibility Projection, and Feedback Adaptation. The mapping. I align these six primitives, in sequence, against three developmental traditions built from incompatible methods and foundational assumptions about what psychology is: Erikson's psychosocial stages (clinical psychoanalytic observation), Maslow's motivational hierarchy (humanistic psychology's healthy-population method), and Bowlby's attachment phases (ethology and evolutionary biology). None was constructed with reference to the others. The alignment does more than pair labels: it supplies the first computational-rationality account of why these stages occur in this order and no other, and reframes their convergence as convergent evolution of functional architecture â artificial and biological systems arriving independently at the same sequential solution because they face the same adaptive problem, not because they share mechanisms or ancestry. The evidence. Three theoretical traditions, developed independently, using different methods, on different populations, converging on the same six-stage functional sequence is consilience in Whewell's (1840) and Wilson's (1998) technical sense: independent lines of inquiry arriving at the same structural conclusion. The necessity framework is the first principled account of why that convergence exists. The scope. Machine verification settles whether the six primitives are necessary and mutually irreplaceable as properties of decision processes; it does not settle whether human development instantiates them. That second claim is argued here on the consilience evidence above, not asserted by proof. This paper's role is to establish the functional bridge itself â the mapping, its theoretical licensing (multiple realizability, Marr's levels, computational rationality), and the testable predictions it generates for stage universality, cross-cultural variation, developmental arrest, intervention timing, and clinical and educational practice. A fuller clinical elaboration is developed in companion work. To this paper's knowledge, no developmental stage theory has previously been given an explicit computational-necessity account of why its stages occur in one fixed order rather than another, let alone one now grounded in a machine-checked proof. The companion mathematics paper and its complete Lean 4 formalization â zero sorry, zero custom axioms, ~12,700 lines, every theorem cross-referenced to its exact identifier â are at github.com/M-Ismail-ZA/IsmailsPrimitives (Zenodo: doi.org/10.5281/zenodo.21177368). For any feedback or collaboration, please contact me via the email address listed on the paper. Updated: 8 July 2026 (V3).
In digital security, anonymous credential systems are essential to ensure secure and private interactions. These systems have practical applications in various fields, such as online voting, healthcare, and financial services. However, due to high computational overhead and complex architecture, traditional anonymous credential systems often suffer from efficiency and scalability issues. To address these challenges, we propose an innovative approach that combines advanced cryptographic techniques such as randomized BLS aggregate signatures and optimized zero-knowledge proof usage mechanisms to achieve secure and private identity authentication with minimal overhead. We introduce HPPCS (High-Performance Privacy-Preserving Credential System), an anonymous credential framework that leverages randomizable aggregate signature technology to achieve efficiency and strong security. We conducted a security and experimental analysis of the HPPCS framework, and the results showed that HPPCS improves the efficiency of credential generation and verification while ensuring original security. This work establishes a powerful and practical framework for privacy-centric identity authentication systems.
Current agent payment standards enable transactions across varied infrastructure, including card systems, banking channels, and blockchain platforms, through cryptographic mandates binding user intentions to agent actions. These mandates create authorization structures while revealing critical vulnerabilities in transaction privacy protection, fine-grained delegation management, and cohesive governance implementation across multiple payment infrastructures. Zero-Knowledge Mandates introduce cryptographic techniques allowing agents to demonstrate compliance with spending restrictions while concealing constraint details from verifiers. Agents demonstrate compliance with spending caps, approved vendors, and time restrictions while keeping financial details and payment channel choices hidden. The system uses compact cryptographic proofs that allow verification without exposing mandate terms, user account information, or transaction routing. Core security guarantees include execution unlinkability, preventing transaction correlation, and verifiable compliance, ensuring constraint adherence. Technical implementation utilizes efficient proof systems, maintaining real-time transaction processing requirements. Evaluation addresses computational performance, information leakage boundaries, and practical deployment considerations across heterogeneous payment networks. The resulting architecture provides the first comprehensive privacy-preserving authorization primitive for autonomous commercial agents operating across multiple financial infrastructures simultaneously.
Abstract Lattice-based commitment schemes and their associated zero-knowledge proofs are essential building blocks for advanced lattice-based cryptographic protocols. In particular, proofs of algebraic relations among committed messages are widely used in privacy-preserving protocols such as range proofs. At CRYPTO 2020, Attema et al. proposed practical proofs for valid openings and multiplicative relations among committed values using the BDLOP commitment scheme. In their work, all commitments are generated using the same short randomness. In this paper, we consider a batch setting where commitments are generated using $$\ell$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>â</mml:mi> </mml:math> independent random vectors and present a batch valid opening proof. Our construction generalizes the approach of Baum et al. by supporting a larger challenge set and removing the requirement for invertible challenge differences. As a result, the proof size scales logarithmically with $$\ell$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>â</mml:mi> </mml:math> , rather than linearly. Furthermore, we introduce a product proof for committed messages with shared randomness across these $$\ell$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>â</mml:mi> </mml:math> commitment groups. Compared to the naive approach of applying Attemaâs product proof once and repeating the opening proof $$\ell -1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>â</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> times, our method achieves significantly better communication efficiency.
Zhuo Wu, Shi Qi, Xinxuan Zhang, Yi Deng · 6 authors
Abstract Recent years have seen the widespread adoption of zkSNARKs constructed over small fields, including but not limited to, the Goldilocks field, small Mersenne prime fields, and tower of binary fields. Their appeal stems primarily from their efficacy in proving computations with small bit widths, which facilitates efficient proving of general computations and offers significant advantages, notably yielding remarkably fast proving efficiency for tasks such as proof of knowledge of hash preimages. Nevertheless, employing these SNARKs to prove algebraic statements (e.g., RSA, ECDSA signature verification) presents efficiency challenges, particularly in critical applications like zk-bridges and zkVMs that require verifying standard cryptographic primitives. To address this problem, we first define a new circuit model: arithmetic circuits with additional exponentiation gates . These gates serve as fundamental building blocks for establishing more intricate algebraic relations. Then we present a Hash-committed Commit-and-Prove (HCP) framework to construct Non-interactive Zero-knowledge (NIZK) proofs for the satisfiability of these circuits. Specifically, when proving knowledge of group exponentiations in discrete logarithm hard groups and RSA groups, compared to verifying complex group exponentiations within SNARK circuits, our approach requires proving only more lightweight computations within the SNARK, such as zk-friendly hash functions (e.g., Poseidon hash function). The number of these lightweight computations depends solely on the security parameter. This differentiation leads to substantial speedups for the prover relative to direct SNARK methods, while maintaining competitive proof size and verification cost.
Nacereddine Sitouah, Francesco Bruschi, Stefano De Cillis
The passing of the eIDAS amendment marks an important milestone for EU countries and changes how they must manage digital credentials for both public services and businesses. Italy has led in adopting eIDAS, first with CIE and SPID identity schemes, and now with the Italian Wallet (IO app) aligned to eIDAS 2.0. Self-Sovereign Identity (SSI) is a decentralized model born from the success of Distributed Ledgers, giving individuals full control over their digital identity. The current eIDAS 2.0 and its implementation acts diverge from SSI principles, rendering the European Digital Identity Wallet (EUDIW) centralized and merely user-centric, prioritizing security and legal protection over true self-sovereignty. This paper proposes an architecture that enables the use of IT Wallet credentials and services in an SSI-compliant environment through Trusted Execution Environments and Zero-Knowledge Proofs.
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 < 10â»â”â°). KEY CONTRIBUTIONS:âą Hybrid local-cloud storage with zero-knowledge properties ensuring cloud providers mathematically cannot decrypt conversationsâą Enterprise Shadow AI governance achieving 99.7% detection across 50+ services via network pattern analysis without plaintext accessâą 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)âą Complete defense taxonomy across 8 attack categories with quantified metrics (92-99% detection rates)âą Advanced cryptographic primitives including post-quantum aggregate signatures (90% size reduction), threshold token generation, VRFs, adaptive differential privacy (4-tier Δ system), federated unlearning (SISA), and incremental Merkle tree encryptionâą Four complete deployment architectures (cloud-only, local-only, mobile-only, enterprise gateway) validated across 4 hardware platforms and 5 operating systemsâą 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 AIâą 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.
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 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 TyystÀlÀ, 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.
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.