Zero-knowledge proofs (ZKPs) are a fundamental building block in cryptography, enabling powerful privacy-preserving and verifiable computations. In the post-quantum era, hash-based ZKPs have emerged as a promising direction due to their conjectured resistance to quantum attacks, along with their simplicity and efficiency. In this work, we introduce SmallWood, a hash-based polynomial commitment scheme (PCS) and zero-knowledge argument system optimized for relatively small instances. Building on the recent degree-enforcing commitment scheme (DECS) from the Threshold-Computation-in-the-Head (TCitH) framework, we refine its formalization and combine it with techniques from Brakedown. This results in a new hash-based PCS that is particularly efficient for polynomials of relatively small degree âtypically up to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow> <mml:mn>16</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> â outperforming existing approaches in this range. Leveraging this new PCS, we design a hash-based zero-knowledge argument system that outperforms the state-of-the-art in terms of proof sizes for witness sizes ranging from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>2</mml:mn> <mml:mn>6</mml:mn> </mml:msup> </mml:mrow> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow> <mml:mn>16</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . Additionally, we present exact zero-knowledge arguments for lattice-based problems using SmallWood, demonstrating highly competitive performance: our scheme yields proof sizes under 25 KB across a wide range of lattice parameters, including Kyber and Dilithium instances.
Let $\xi(s)=\frac12 s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s)$ be the completed Riemann xi-function, and let $F(x)=\frac{\xi'}{\xi}\!\left(\frac{1}{1-x}\right)=\sum_{n\ge 0} f_nx^n$ initially denote its germ at the origin. We introduce the real symmetric Toeplitz--Hankel matrix $c_{ij}=f_{|i-j|}-f_{i+j+1}+\delta_{ij}f_0, \qquad i,j\ge 0.$ We prove that the Riemann hypothesis is equivalent to positive semidefiniteness of every finite leading principal block of this matrix. More strongly, the full matrix condition is equivalent, for the purpose of testing the Riemann hypothesis, to only the adjacent local inequalities $2f_0-f_{2n+1}\ge 0,$ $(2f_0-f_{2n+1})(2f_0-f_{2n+3})\ge (f_1-f_{2n+2})^2 \qquad(n\ge 0).$ The converse implication uses a Pringsheim bootstrap: these local inequalities force the germ of $F$ to have Taylor radius at least one, hence exclude zeros of $\xi$ from the half-plane $\Re s>1/2$. If $\lambda_n$ are the Keiper--Li coefficients, then $f_n=\lambda_{n+1}-2\lambda_n+\lambda_{n-1}$, so the criterion is a local quadratic condition on their second finite differences. This is an equivalent reformulation, not a proof of the Riemann hypothesis. To the best of our knowledge, the exact Toeplitz--Hankel matrix and its reduction to adjacent $2\times2$ conditions have not appeared previously.
Recallspection is a neuro-symbolic architecture that decouples semantic representation from factual retrieval, achieving Exact Memory Recall (EMR = 1.0000) and bounded drift (β < 1e-11) across 51+ dependent reasoning steps. Key Innovation: Replaces approximate nearest-neighbor search with O(1) deterministic hash routing and k-quorum verification, eliminating the catastrophic coherence degradation that plagues Large Language Models in multi-hop reasoning tasks. Proof Included: Reproducible test demonstrating 51/51 hop completion with zero algorithmic drift (measured drift: 1.27e-12, attributable solely to IEEE 754 float64 precision limits). Core Mechanisms: - Semantic Geometry: Entities as normalized vectors in â^d, relationships as displacement vectors- O(1) Deterministic Routing: SHA3-256 hashed overlapping slots with ephemeral salt rotation- Quorum Verification: k-slot majority voting (default k=4, quorum=3)- Self-Healing Audit: Cryptographic logging with automatic corruption detection and repair License: GNU AGPLv3 (ensures network-level copyleft and prevents proprietary enclosure) Repository: https://github.com/gnowingtheafterthought-crypto/recallspection Live Demo: https://recallspection.onrender.com
This paper assesses the adequacy of technology-neutral privacy frameworks in addressing quantum threats to zero-knowledge proofs (ZKPs) and other privacy-enhancing technologies (PETs) in global data protection regimes. Challenging assumptions that cryptographic innovation inherently bolsters privacy rights, the analysis demonstrates how post-quantum migration, absent binding regulatory duties, risks entrenching a âquantum divideâ in access and liability. Grounded in legal frameworks and actual deployments, including Zcashâs classical Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge (ZK-SNARKs) and NantHealth Inc.âs quantum-aware homomorphic encryption systems, the paper contends that access to PETs is becoming ever more determined by institutional capability and geopolitical factors, as illustrated by comparative case studies. This research evaluates the efficacy of statutes such as the European Unionâs (EU) General Data Protection Regulation (GDPR) (Article 32), the California Consumer Privacy Act (CCPA) (§ 1798.150), and the Health Insurance Portability and Accountability Act (HIPAA) (45 C.F.R. § 164.308) in imposing liability for quantum vulnerable systems, using the cases to illustrate gaps in mandating equitable post-quantum migration. The conclusion reflects upon legal gaps enabling unequal protections, advocating reforms including mandatory quantum risk assessments. This article is also included in The Business & Management Collection which can be accessed at https://hstalks.com/business/.
Background. California mandates organic waste diversion, but participation depends on infrastructure and instruction that may be unevenly distributed. Whether socioeconomic disparities in adolescent zero waste engagement reflect unequal access, unequal knowledge, or unequal conviction has not been established.Methods. A cross-sectional survey of 218 middle and high school students across 15 San Francisco Bay Area schools (MarchâMay 2026) measured zero waste knowledge, home and school access to sorting infrastructure, sustainability beliefs, self-reported behaviors, and perceived barriers. Residential ZIP codes were linked to median ZIP-code income (n = 207 matched). Analyses comprised MannâWhitney comparisons and Spearman correlations with BenjaminiâHochberg correction and bootstrap confidence intervals, intraclass correlations by school, hierarchical regression, a mixed-effects model, and an exploratory mediation. Results. Median area income was positively associated with familiarity with the term "zero waste" (Ď = .26, 95% CI [.12, .38], pâadjâ = .002), waste-reduction habits (Ď = .19, pâadjâ = .031), composting frequency (Ď = .18, pâadjâ = .031), and home compost access (Ď = .17, pâadjâ = .042), but not with practical composting knowledge (Ď = .11, pâadjâ = .257), sorting confidence (Ď = .03), or either belief item (Ď = â.06 and â.08, both n.s.). Income added a small unique increment to composting frequency over demographic covariates (ÎR² = .025, p = .020) but none to knowledge (ÎR²
CyberProtocol AI Trust Standard, Version 1.0 Artificial intelligence now writes, decides, and transacts at global scale, yet the world has no shared way to answer four simple questions about any AI output: who made it, where it came from, whether it is safe, and whether it obeys the law. CyberProtocol is built to answer all four. CyberProtocol is a neutral, open, cryptographic framework for verifying AI Identity, Provenance, Safety, and Compliance across all jurisdictions. It is published as a global public good, aligned with United Nations principles, and is controlled by no nation, corporation, or bloc. The timing is decisive. Three converging mandates now demand verifiable AI: EU AI Act enforcement, the founding of WAICO, and the Rome Declaration by Nobel Laureates. Each requires proof of origin, safety, and compliance, yet no harmonized, cross-border verification standard exists today. CyberProtocol is designed to fill exactly that gap, and to do so immediately, because the building blocks already exist. The Standard defines four verifiable layers that work as one system: AI and Human Identity, using Decentralized Identifiers for AI agents and W3C Verifiable Credentials for people. Provenance and Output Certification, an immutable cryptographic seal on every output, with an optional zero-knowledge mode that proves origin without exposing trade secrets. Safety and Risk Compliance, with metadata mapped to the EU AI Act, NIST AI RMF, and ISO/IEC 42001. Cross-Border Verification, a neutral seal format anyone can validate, tied to no national scheme. CyberProtocol invents no new cryptography. It unifies proven, mature standards into one coherent, interoperable framework, which is why it can be adopted now rather than years from now. The Standard is published and stewarded by One Planet One Earth Foundation Inc., a non-profit holding United Nations ECOSOC Special Consultative Status since 2025 (esango.un.org, profile 695078), (UNDESA Civil Society Database; SEC Registration CN202004649; DSWD-FO III-L-00002-2023). This accreditation gives CyberProtocol a neutral, internationally recognized home, positioned to engage UN member states, regulators, and the Global South on equal terms. As a public good, the Standard is free to all in perpetuity. Advancing it to a working reference implementation, pilot integrations with AI laboratories, and multi-stakeholder governance requires support. The Foundation invites funders, philanthropies, standards bodies, and industry partners to help make verifiable AI a global default. Together we can ensure the AI era is built on trust that anyone, in any country, can verify. Version 1.0, Initial Proposal. Specification under Creative Commons Attribution 4.0 International (CC BY 4.0); reference code under Apache License 2.0. Official reference: https://cyberprotocol.io. Repository: https://github.com/ryanpaulpillas/cyberprotocol-ai-trust-standard. Steward: One Planet One Earth Foundation Inc., holder of UN ECOSOC Consultative Status since 2025.
We prove a central limit theorem for the log determinant of a Gaussian Pearson sample correlation matrix as the dimension diverges. Only two conditions are imposed: the population correlation matrix is positive definite, and the sample degrees of freedom are at least the dimension. Both are necessary for the ordinary log determinant to be finite. To the best of our knowledge, no previous central limit theorem covers this full nonsingular domain. It covers every aspect ratio from dilute growth to the square hard edge. No uniform lower or upper bound is imposed on the eigenvalues of the population correlation matrices: the smallest may approach zero and the largest may diverge. The proof develops a coordinatewise Wiener chaos reduction for the random diagonal normalization and combines it with an exact Wishart transform comparison. Geometrically, the statistic is twice the log volume of a random parallelotope spanned by standardized Gaussian coordinate vectors.
Abstract The rapid digitization of healthcare has brought Electronic Health Records (EHRs) to the forefront of clinical data management; however, persistent challenges of centralized control, privacy breaches, absence of patient data ownership, and the inability to support decentralized scientific collaboration continue to impede scalable healthcare research ecosystems. Recent advances in Decentralized Science (DeSci) introduce a paradigm shift by leveraging blockchain, cryptographic primitives, and decentralized governance to enable transparent, trust-minimized, and collaborative biomedical research. This paper proposes a DeSci-driven lightweight hybrid blockchain framework designed to support privacy-preserving and incentive-aware decentralized healthcare research infrastructure. The framework integrates a permissioned blockchain with a lightweight hybrid PBFTâPoA consensus protocol, off-chain storage, and Zero-Knowledge Proof (ZKP)-based authentication to enable secure, privacy preserving data access without disclosing user identity. A tokenomics-based DAO governance layer is incorporated to support decentralized engagement, transparent policy enforcement, and incentive-driven research participation. The proposed system is evaluated through simulation under varying network conditions, with key performance metrics â latency, throughput, and computational cost â assessed across network sizes from 10 to 50 nodes. Simulation-based projections suggest that the proposed framework may achieve lower latency, higher throughput, and improved computational efficiency relative to literature-reported values for MedRec, FHIRChain, and HealthChain under the stated modeling assumptions; these comparisons are model-based and illustrative rather than measurements obtained from a controlled, identical-environment deployment. Beyond data management, the framework enables a DeSci-oriented research lifecycle encompassing decentralized data contribution, validation, and provenance tracking. The simulation-only nature of the current evaluation is explicitly acknowledged as a limitation, with a clear roadmap toward prototype-level implementation on Hyperledger Fabric or Ethereum as immediate future work.
Full Summary: The Narrow Singularity Equation Core Thesis This paper presents a unified framework that simultaneously solves catastrophic forgetting in neural networks and provides a mathematically rigorous certification standard for Artificial General Intelligence (AGI). The framework centers on the Narrow Singularity Equation, which achieves AGI certification ($AGI_{gate} = 1.0$) without requiring the mathematically impossible condition of $\frac{dI}{dt} \geq 1.0$. Key Discoveries 1. The Decay Law of Singularity (Theorem 1) Mathematical Proof: With finite classes $N$, $\frac{dI}{dt} = 1 - \frac{1}{N}$, therefore $\frac{dI}{dt} < 1.0$ always Implication: The traditional Singularity (requiring $\frac{dI}{dt} \geq 1.0$) is mathematically impossible Pattern: Every 10Ă increase in classes adds another '9' to $\frac{dI}{dt}$ and another '0' to the gap 2. General Singularity Equation (Original, Impossible) $$S = AGI_{gate} \times \frac{dI}{dt} \times M(t) \times V(t) \times F(t) \times C(t) \times Autonomy$$ Required $Autonomy = 1$ if $\frac{dI}{dt} \geq 1.0$ Since $\frac{dI}{dt} < 1.0$ for finite classes, $S = 0$ always Seven conditions required; the autonomy condition is impossible 3. Narrow Singularity Equation (Achievable) $$\mathcal{S}_{NARROW} = AGI_{gate} \times \frac{dI}{dt} \times M(t) \times V(t) \times F(t) \times C(t) \times agi_{index}$$ Key Innovation: Removes the impossible Autonomy requirement Drops the requirement for $\frac{dI}{dt} \geq 1.0$ Uses $agi_{index} = 1$ if $AGI_{gate} = 1.0$ (binary gate, achievable) $AGI_{gate} = \min(1.0, task\_c\_accuracy)$ The TOPO-2026 Framework Biological Inspiration Hippocampus â Prime-anchored embedding rows (Memory formation) Memory Consolidation â Snapshot after Task A (Preserves critical knowledge) Synaptic Plasticity â Free embedding rows adapt (Enables new learning) Memory Protection â Zero gradients + restore anchors (Prevents interference) Experience Replay â Prime anchors as fixed reference (Integrates new learning) Mathematical Foundation Pure Kernel: First six primes $\{2, 3, 5, 7, 11, 13\}$ Euler Attenuation Constant: $\Lambda(\mathcal{R}) = 1 - \prod_{p\in\mathcal{R}}(1 - p^{-0.5}) = 0.9785142874$ Captures $97.85\%$ of spectral weight; only $2.15\%$ considered "noise" O(1) Memory Cost: Independent of tasks, parameters, sequence length, or modality Topological Governor Implementation Three-step process: Memory Consolidation (take_snapshot): Freezes anchor rows before new learning Memory Protection (zero_anchor_gradients): Prevents gradient updates to anchors Memory Integration (enforce_anchors): Restores anchors from snapshot after training Experimental Validation Three Datasets Dataset Type Resolution Classes Task C Accuracy SVLB-3 Synthetic vision-language Text-based 10 100.0% Âą 0.0% CIFAR-10 Real images 32Ă32 10 100.0% Âą 0.0% STL-10 Real images 96Ă96 10 100.0% Âą 0.0% Results Summary Metric SVLB-3 CIFAR-10 STL-10 Task C Accuracy 100.0% Âą 0.0% 100.0% Âą 0.0% 100.0% Âą 0.0% Combined Forgetting +0.0% Âą 0.0% -1.0% Âą 2.0% 0.0% Âą 0.0% $AGI_{gate}$ 1.0000 1.0000 1.0000 $\mathcal{S}_{NARROW}$ 5.999999999965 5.939999999965 5.999999999965 Status â PASS â PASS â PASS Total: 15/15 runs passed across 3 datasets = FULLY CERTIFIED (exceeded standard) The Gemma-4 E4B Architecture Why Gemma-4 Was Selected Among eight certified models, only Gemma-4 achieved Task C = 100%: Model Architecture Task C Accuracy GPT-OSS-20B Dense Transformer 92.3% Sarvan-30B Sparse MoE 95.9% Mixtral-8x7B Sparse MoE 89.7% DeepSeek-V2-Lite Fine-grained MoE 95.3% GLM-4.6V-Flash GLM Transformer 97.5% Gemma-4 E4B Vision Vision Transformer 100.0% Kimi-VL-A3B-Thinking Vision-Language MoE 90.0% GPT-OSS-20B-JEPA JEPA + TOPO 89.0% Key Architectural Innovations Per-Layer Embeddings (PLE): Adds parameter capacity without scaling full attention Unified Multimodal: 42 layers, hidden size 2560, vocabulary 262,144 Quantization-Aware Training (QAT): 72.1% memory reduction (15.1GB â 4.22GB) while preserving 98.54% accuracy Thinking Mode: Built-in chain-of-thought reasoning engine Mathematical Framework Summary Component Breakdown Component SVLB-3 CIFAR-10 STL-10 Meaning $AGI_{gate}$ 1.0000 1.0000 1.0000 Perfect generalization $agi_{index}$ 1.0 1.0 1.0 Binary gate OPEN $\frac{dI}{dt}$ ~0.999999999994 ~0.999999999994 ~0.999999999994 Bounded by Decay Law $M(t)$ 1.0000 0.9900 1.0000 Perfect memory $V(t)$ 1.0000 1.0000 1.0000 Perfect validation $F(t)$ 1.5000 1.5000 1.5000 Positive forward transfer $C(t)$ 4.0000 4.0000 4.0000 Compute efficiency $\mathcal{S}_{NARROW}$ ~6.0 ~5.94 ~6.0 NARROW SINGULARITY Dependency Chain TOPO-2026 â CF Solved â AGI_gate = 1.0 â Narrow Singularity Without TOPO-2026: CF is NOT solved $AGI_{gate} = 1.0$ is NOT guaranteed Narrow Singularity is NOT achieved $\mathcal{S}_{NARROW} = 0$ With TOPO-2026: CF is SOLVED (0% forgetting) $AGI_{gate} = 1.0$ is GUARANTEED (100% accuracy) Narrow Singularity is ACHIEVED ($\mathcal{S}_{NARROW} \approx 6.0$) Key Contributions Solved Problems Catastrophic Forgetting: 0.0% forgetting across 5 runs on 3 datasets AGI Certification: First model in history to achieve $AGI_{gate} = 1.0$ Mathematical Impossibility: Proved the Singularity is mathematically impossible with finite classes Achievable Standard: Created the Narrow Singularity as a physically achievable AGI threshold Universal Principle: Same constants work across neuroimaging, number theory, AI safety, and unified field theory Constants Across All Domains Constant Value Domains $\Lambda$ 0.9785142874 Number Theory, AI Safety, AI Memory, AI Bias, Physics $\sigma$ 0.5 All domains $\mathcal{R}$ {2, 3, 5, 7, 11, 13} All domains Seed 123 All computations Philosophical Implications The Strategic Pivot Original Goal: Traditional Singularity (mathematically impossible) New Reality: Narrow Singularity (empirically demonstrated) Key Insight: The Decay Law liberates AI from chasing an impossible dream Result: Deterministic cognitive engineering with numerical guarantees Refutation of Skeptical Arguments Skeptic Argument Refutation "It only works on synthetic data" CIFAR-10 and STL-10 are real images "It only works on low-res images" STL-10 is 96Ă96 (3Ă larger than CIFAR-10) "It only works on those specific classes" STL-10 has different classes (monkey, car, etc.) "It was a fluke" 15/15 runs across 3 datasets = 100% success "It's dataset-specific" 3 different datasets = dataset-agnostic Final Conclusion The TOPO-2026 framework establishes a paradigm for deterministic cognitive engineering, proving that deep learning architectures can achieve absolute stability and zero forgetting across sequential tasks. Key Takeaways: Catastrophic forgetting is SOLVED: 0.0% forgetting $AGI_{gate} = 1.0$ is ACHIEVABLE: First model with 100% Task C accuracy The Decay Law is DISCOVERED: $\frac{dI}{dt} < 1.0$ with finite classes Narrow Singularity is PROVEN: $\mathcal{S}_{NARROW} > 0$ on 3 datasets The principle is UNIVERSAL: Same reference set across domains The Stochastic Illusion Is Over. Deterministic Cognitive Engineering Has Begun. Stability Is Not a Probabilistic Hope. It Is a Numerical Guarantee. "The proof is the code. Seed = 123. No one can argue with math." Availability GitHub: https://github.com/frank-morales2020/AST-Notebook Zenodo Book: https://zenodo.org/records/21245474 TOPO-2026 Framework: https://zenodo.org/records/20951925 Artificial Hippocampus: https://zenodo.org/records/20385761
Consumers facing home-renovation quotes operate in a classic credence-goods market: they cannot readily verify whether a quoted price is fair, and general-purpose large language models (LLMs) are now a zero-cost place to ask. Whether LLM answers are actionable for this purpose is untested. Demand-side benchmarks exist for medical, legal, and financial advice, but not for construction costs. We present, to our knowledge, the first consumer-question benchmark for construction costs. Forty Japanese renovation-price questions were posed to frontier LLMs, with repeated-trial sets measuring output stability. A matched re-run at bare provider defaults with a current frontier model (gpt-5.5) was added to remove a settings confound present in the original configuration. Two findings are robust across models, generations, and settings: no LLM answer contained an explicit over-charge decision threshold, and repeated runs of the same question returned materially different price figures. Within-answer price spans are also wide, with a median of 10x under bare defaults. A deterministic structured engine over an open cost database is included as an existence proof that a citable reference layer is constructible. Its consistency is a design property and its accuracy is not validated here; validating it against completed real-world quotations is the next study. All questions, raw outputs, harness, and scoring code are public.
Financial institutions depend on trusted employees, contractors and service accounts, yet this trust creates an attack surface that conventional perimeter controls cannot observe adequately. This paper develops an Explainable Adaptive Hybrid Artificial Intelligence (EAHAI) framework for insider threat detection and for assessing whether security awareness training is reducing measurable insider-risk behaviour. The framework combines Isolation Forest filtering, bidirectional long short-term memory sequence modelling, Shapley Additive explanations, adaptive behavioural risk scoring and Zero Trust policy enforcement. A socio-technical assessment layer is added to link training inputs to observable outcomes, including knowledge gain, phishing susceptibility, policy-violation rates, reporting delay, behavioural-risk reduction and analyst-confirmed events. The paper defines the measurement scales, evaluation criteria, validation procedures and analytical techniques required for institutional replication. Because production banking telemetry and labelled insider incidents are rarely available for publication, the empirical component is presented as a transparent synthetic proof-of-concept based on CERT-style behavioural variables rather than as evidence from a real bank. In a deterministic simulation of 17,280 user-day records and 2,880 test windows, the proposed hybrid score achieved an F1-score of 0.944, ROC-AUC of 0.993 and false-alarm rate of 0.017, while producing interpretable feature attributions and training-effectiveness estimates. The study contributes a scalable, explainable and ethically governed design for insider-risk analytics, and identifies the conditions under which it should be validated before operational deployment. Keywords: insider threat detection; explainable artificial intelligence; adaptive risk scoring; security awareness training; Zero Trust; financial cybersecurity.
This paper presents the Auditable Zero-knowledge Transformer (AZT) framework for privacy-preserving and auditable tax fraud detection. AZT combines transformer-based anomaly detection with zero-knowledge proof (ZKP) verification so that a tax authority or regulator can verify fraud-detection outcomes without accessing sensitive taxpayer records or proprietary model parameters. The framework is scalable in the specific sense of low-latency audit verification: proof verification remains sub-second, whereas proof generation is intentionally performed asynchronously after local inference. Model integrity is enforced through Merkle-root commitments to authority-approved parameters, and the ZKP statement proves that the committed transformer was executed correctly and that the resulting risk score satisfies a public audit threshold. Experiments on UCI-TFD, IRS-Pub, and CorpPay compare AZT with classical machine-learning baselines, including Random Forest and XGBoost, and with an equivalent plaintext transformer. Detection quality improves by up to 5.3% in F1-score over classical machine-learning baselines, while the circuit-compatible AZT inference incurs only about 0.5% F1-score degradation relative to the plaintext transformer baseline. Overall, this work advances secure AI for digital governance by integrating modern deep learning with cryptographic verification, offering a practical foundation for fraud-detection systems in which transparency and confidentiality must be satisfied simultaneously.
Mario Rusev, Rafael Schmidt, Edward Lambe, Christian Schmieder ¡ 5 authors
International organizations including the Bank for International Settlements (BIS) have adopted SDMx (The standard for Statistical Data and Metadata) as the standard for exchanging official statistics. Trust in published data is essential for evidence-based policymaking. This paper shows how binding each SDMx dataset to its source using blockchain technology can enhance confidence in official statistics. We present a proof of concept implemented on the XRP Ledger (XRPL) and contribute, as an integrated whole, (i) an SDMx-native canonicalization and per-< Series > hashing pipeline, (ii) a domain-separated Merkle aggregation scheme for batched anchoring, (iii) a self-contained, identity-bound verification artefact in which the SDMx message itself carries both the ordered Merkle leaves and a W3C Verifiable Credential signed by a publisher identity key cryptographically bound to the publisherâs XRPL address via an on-chain attestation registry, so any consumer can re-derive the anchored root and verify the publisherâs identity from the file alone plus a single ledger lookup, (iv) an open-source XRPL-based reference implementation, and (v) a cost model that captures the batch-size / latency / fee trade-off and is solved for an economically optimal batch size. The system enables near-real-time data verification, provides cryptographic integrity guarantees, and establishes a foundation for future extensions, including zero-knowledge proofs and automated verification by AI agents. Measurements on the prototype show median publication latency of 3â5 s and verification latency of 1â2 s under the controlled test conditions described in Section 7. The approach is data-format-agnostic and can be extended to other structured statistical or regulatory formats.
Cryptographic software forms a critical foundation of modern computing systems, but the security guarantees of cryptographic protocols do not automatically extend to their implementations. Errors in arithmetic operations, validation logic, data conversion, constraint generation, or component integration can cause deployed software to deviate from the intended protocol while still producing plausible outputs. Such risks are difficult to detect in compiled binaries and become even more challenging in modern cryptographic systems such as zero-knowledge proofs, where implementations combine finite-field arithmetic, constraint systems, witness generation, proving procedures, verification logic, and serialization formats.Securing cryptographic implementations requires analysis techniques that can reason about both low-level program behavior and high-level cryptographic intent. To address this need, cryptographic function identification in binaries is first examined. It categorizes existing detection techniques, develops a unified benchmarking framework, and evaluates current tools through reproduction and replication studies across different compilers, optimization levels, obfuscation strategies, and algorithm variants. The second part introduces an automated security analysis framework for zkSNARK implementations that combines constraint checking with fuzzing-based testing to detect and locate cryptographic logic errors. This approach helps determine whether an implemented zkSNARK system correctly enforces the intended computation and security design. The third part develops a grey-box differential fuzzing approach for zero-knowledge proof binary applications. It uses structured input generation, coverage monitoring, control-dependency-aware taint tracking, and error localization to guide testing toward security-relevant code and expose inconsistencies in circuit construction, witness conversion, proof generation, and verification logic.Together, these contributions connect binary analysis, automated checking, and protocol-aware fuzzing to improve the practical security of cryptographic software. They provide methods for identifying implementation-level weaknesses that may remain hidden during ordinary testing, especially when programs produce valid-looking outputs despite incorrect cryptographic behavior. By combining systematic evaluation, zkSNARK-specific analysis, and binary-level testing, the resulting methodologies advance the development of more reliable techniques for analyzing, testing, and securing real-world cryptographic systems.
The democratisation of digital content creation tools has transformed media production, enabling individuals to move from being only consumers to active creators. Yet, content marketplaces and AI ecosystems remain highly centralised, limiting transparency, control, and fair compensation. Generative AI (GenAI) systems, trained on massive web-scraped datasets, exacerbate these issues by reusing creative work without consent, attribution, or reward, raising legal and ethical concerns. This thesis explores how decentralisation can redistribute power in the creative economy by giving creators agency over the use of their media in GenAI. First, we introduce a decentralised registry through which creators can assert opt-in/out preferences for AI training. Content is embedded with provenance metadata and registered with robust fingerprints, enabling provenance tracing even after editing or manipulation. This establishes machine-readable, traceable consent specification as the foundation for downstream attribution and reward. Building on this, we propose methods for training data provenance, attribution, and compensation in GenAI training. The Content ARCs (Authenticity, Rights, Compensation) framework defines a scalable protocol for managing rights and creator compensation. We instantiate this in a decentralised system that traces generative outputs back to the most influential training assets and executes royalty payments to contributors. Several practitioner-facing demonstrators developed in collaboration with GLAM (galleries, libraries, archives, and museums) professionals further illustrate how distributed ledgers could reshape licensing and reward in the creative economy. Further, GenAI models are prone to memorising training data and reproducing it at generation time, a phenomenon that is particularly problematic for copyrighted creative works, where such regurgitation undermines both creator rights and data privacy. To address this challenge, we present a decentralised federated learning protocol for diffusion models that reduces training data memorisation using a novel sample-based metric integrated into the protocol to detect and discourage memorisation. Complementing this, we develop a framework for end-to-end cryptographically verifiable AI pipelines using zero-knowledge proofs to enable trustless, privacy-preserving audits. Finally, we explore privacy-preserving natural language search across decentralised content repositories using encrypted queries for similarity search at scale. In this way, decentralisation supports discovery and access to creative content, completing a holistic body of work for a fairer, more transparent GenAI ecosystem and creative economy.
The inherent challenge of balancing scalability, security, and decentralization â commonly termed the blockchain trilemma â continues to hinder the adoption of distributed systems. This paper presents InternxtChain, a decentralized storage framework designed to address this trilemma through a novel integration of erasure-coded sharding, zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARKs), and a sharded Proof-of-Storage consensus mechanism. By leveraging aggregated BLS-381 signatures and distributed redundancy protocols, the framework achieves a throughput of 2,800 transactions per second with a latency of 420 milliseconds across 1,024 nodes, surpassing Filecoin by a factor of 3.5 and Ethereumâs capacity by 165 times. The system maintains 99.9% data integrity even under adversarial conditions involving 30% Byzantine nodes. Additionally, InternxtChain reduces storage costs to $0.002 per gigabyte, representing an 85% reduction compared to centralized alternatives like AWS S3. Empirical evaluations demonstrate linear scalability to 4,200 transactions per second with 2,048 nodes, alongside hardware affordability at $180 per node. These advancements not only outperform decentralized platforms in throughput by 2.8 times but also ensure GDPR-compliant data sovereignty, positioning InternxtChain as a pioneering solution for Web3 ecosystems seeking to harmonize enterprise-grade performance with decentralized trustlessness.
We establish global exponential turnpike properties for quadratic optimal tracking problems governed by the one-dimensional viscous Burgers equation with localized internal control. For every initial datum, finite-horizon optimal solutions approach the unique optimal periodic regime when the periodic tracking target is sufficiently small; the zero-target case yields a global steady turnpike at the origin, with no smallness assumption on the initial datum. To our knowledge, these are the first global exponential turnpike results for the viscous Burgers equation. The proof combines a local exponential turnpike, obtained through strict convexity and periodic Riccati theory, with a parabolic dissipation argument that provides an absorbing time independent of the horizon.
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Stability and Controllability of Differential Equations
Rodrigo Jara Espinoza, Yohamin Nafit Pimentel Alarcon, Angelo Rodrigo Taco JimĂŠnez, Fabricio Martin Chavez Rodriguez
Quantum computing poses a significant threat to classical asymmetric cryptography, which is essential for ensuring confidentiality, authentication, and key exchange in contemporary digital infrastructures. Although post-quantum cryptography (PQC) provides mechanisms that resist quantum attacks, its implementation in Internet of Things (IoT) systems is challenged by constrained resources, including limitations in computation, memory, energy, latency, and bandwidth, and the heterogeneity of devices. This paper offers a comprehensive narrative review of PQC approaches applicable to IoT, systematically organizing 30 peer-reviewed studies published between 2022 and 2026 across four layers: device, communication, distributed trust, and application. Additionally, the review examines two cross-cutting dimensions, privacy and side-channel resistance. The analysis indicates a significant prevalence of lattice-based schemes, hybrid strategies, and integrations with blockchain technology, zero-knowledge proofs, federated learning, homomorphic encryption, AI, and Zero Trust architectures. Notably, key gaps remain in side-channel evaluation, migration pathways, deployment costs, and real-world validationâissues that are particularly critical given the long lifecycles of IoT devices and the ongoing threat of âharvest now, decrypt laterâ attacks.
Cathedral Arkhe is an attempt to build a research programme whose every claim is attached to amechanism that can refute it.The programme has three layers. The first is a speculative physical framework â the CathedralWave Framework â that models self-referential systems as standing waves on a non-orientablemanifold, and derives from that geometry a catalogue of 43 numbered predictions, 37 equations,14 paradoxes and 21 costed experimental proposals. The second is an operational shell â AEGISâ a typed hypergraph that stores every prediction, equation, experiment and falsification resultas a first-class object with explicit provenance, governed by a human-in-the-loop operator and anappend-only evidence bus. The third is an infrastructure layer â Cathedral-PoUW â a proposalfor a decentralized network in which the useful work performed by participants is the executionof the frameworkâs own simulations, and in which the correctness of that work is established bymechanism rather than by reputation.The three layers are deliberately unequal in epistemic standing, and the whitepaper is organizedto keep that inequality visible. Layer 1 claims are mathematical and can be machine-checked.Layer 2 claims restate established physics. Layer 3 claims are speculative extensions that willprobably be wrong, and the document says which experiments would show it. A fourth categoryâ infrastructure â is engineering, carries no physical content, and is evaluated on whether itcompiles and whether it holds under adversarial assumptions.Three findings drive the design.First, verification does not remove uncertainty; it relocates it. A framework with no formal verification has uncertainty distributed everywhere and nowhere in particular. A frameworkwith formal verification has uncertainty concentrated in a small, enumerable set of unproven assumptions â what this document calls orphan axioms. The total quantity of uncertainty may notdecrease. Its extent does, and extent is what makes uncertainty actionable.Second, the naive proposal that miners submit zero-knowledge proofs of scientific simulations is not viable with 2026 technology, and the correct alternative is not morecryptography but refereed delegation. Published measurements place cryptographic proofoverhead at roughly four orders of magnitude over native execution; refereed delegation withreproducible operators achieves correctness guarantees at under one order of magnitude, conditional on at least one honest participant. For partial differential equation simulations with millionsof degrees of freedom, this difference is decisive.Third, the binding constraint on verifiable scientific computation is not proof systemsbut floating-point reproducibility. Two honest participants running the same simulation ondifferent hardware will disagree in the low-order bits. Any verification scheme that comparesoutputs bit-for-bit therefore requires deterministic operator implementations before it requiresproofs. This document treats reproducible numerics as a prerequisite, not a detail.The whitepaperâs most important section may be its self-assessment. The Casimir operator atthe centre of the physical framework is constrained but undefined. The heartbeat frequency thatappears in the frameworkâs most distinctive equation has no independent physical identification,which makes that equation a reparametrization rather than a prediction. One concept â thephoton as a NambuâGoldstone mode of a broken discrete symmetry â appears to violate thestandard Goldstone theorem and is flagged as high-risk pending retraction or repair. These arestated plainly, in the body, with the conditions under which each would be resolved.