This paper proposes a novel approach to constructing distributed knowledge graphs (KGs) leveraging blockchain technology. Traditional knowledge graph construction relies heavily on centralized databases, leading to vulnerabilities concerning data security, trust, and potential manipulation. This research addresses these shortcomings by introducing a decentralized, trustworthy, and traceable KG built upon a blockchain network. The core mechanism involves storing KG nodes and edges directly on the blockchain, coupled with smart contracts to facilitate knowledge validation, verification, and updates. This ensures data integrity and reliability while providing an immutable audit trail. The proposed system offers enhanced security, transparency, and accountability, fundamentally changing how KGs are built and maintained. The research explores the technical challenges and potential benefits of this decentralized approach, demonstrating its feasibility and suitability for a variety of applications.
Anomaly detection in dynamic graphs underpins fraud analysis, cybersecurity and platform integrity, yet deep detectors remain opaque: a flagged interaction arrives with a score and no account of which counterparty or which moment produced it. The prevailing post-hoc remedy fits an auxiliary model to a frozen detector, so faithfulness is estimated rather than guaranteed, and to our knowledge no dynamic-graph detector emits an explanation as a native product of its own forward pass. We propose EVIDENT (EVIDence-bottlenecked intrinsic dEtection for evolving Networks over Time), an ante-hoc detector whose anomaly score is computed exclusively from a sparse, dually-factorised evidence set selected within that pass, so the explanation costs no additional inference. Gated tokens leave the attention softmax entirely rather than being attenuated, so sufficiency holds by construction rather than by measurement. On Bitcoin-OTC with real distrust labels, EVIDENT attains 0.7947±0.0069 AUC under supervision matched to unsupervised baselines—exceeding the transformer detector TADDY by 26.0 points—from 10% of its evidence pool, retaining over 97% of an unconstrained model of identical architecture. Under a density-matched mask protocol its rationale exceeds an equalsize random subset by +0.2145 AUC (6.6σ) and selects priornegative-rating tokens at 1.29–2.49× the random rate; ablating the complement objective leaves detection unchanged while collapsing that advantage 4.5-fold. On a unified injected benchmark against eleven learned detectors and a parameter-free degree heuristic, EVIDENT ranks first at 0.9766 AUC while denied the cardinality channel they retain—though there its rationale ceases to separate, isolating token heterogeneity rather than the selection mechanism as the binding constraint on intrinsic explainability. We further document two evaluation defects—neighbourhood cardinality leakage under edge injection, and incomplete token removal in gated attention—with diagnostics that detect them.
The Topological Governor: A Deterministic Solution to Catastrophic Forgetting Full Summary The Problem Catastrophic forgetting is a fundamental limitation in artificial intelligence where neural networks overwrite previously learned knowledge when trained on new sequential tasks. Since its formal characterization by McCloskey and Cohen in 1989, this has hindered the development of lifelong learning systems in robotics, autonomous systems, and personalized assistants. The Solution: Topological Governor The paper presents a deterministic mechanism that definitively solves catastrophic forgetting through mathematical invariance, unlike probabilistic approaches (EWC, replay-based methods, parameter isolation) that provide only statistical guarantees with growing memory requirements. Key Technical Contributions 1. Mathematical Foundation: Arithmetic Spectral Theory Leverages the Sieve of Eratosthenes (a deterministic algorithm proven for over two millennia) to select the first six prime numbers: [2, 3, 5, 7, 11, 13] The Safety Constant ($\Lambda = 0.9785142874$) is derived from Euler's attenuation product and provides mathematical proof of protection: $\Lambda = 1 - \prod_{p \in \{2,3,5,7,11,13\}} (1 - p^{-0.5})$ Never hardcoded; recomputed at initialization for auditability 2. Three-Step Mechanism Step 1: Snapshot Capture (Memory Consolidation) When the first task reaches 100% accuracy, the Governor captures the state of prime-indexed embedding rows as an immutable reference frame Step 2: Gradient Enforcement (Memory Protection) During backpropagation on subsequent tasks, the Governor blocks gradient updates to anchored rows All gradients at prime indices are set to zero Step 3: Anchor Restoration (Memory Integration) After optimizer steps, performs final verification and restoration of anchored positions as a fail-safe against numerical drift 3. Implementation Architecture Core class: TopologicalGovernor with O(1) memory complexity Multi-layer support: Can protect embedding and attention layers simultaneously Hybrid architecture support: Works on SSM + Transformer hybrids (StripedHyena) Universal: Works across vision transformers, language models, and genomic models Experimental Results 5-Task Sequential Learning (Synthetic) Metric Result Tasks Learned 5 Average Accuracy 99.96% Average Forgetting 0.00% Anchor Preservation 6/6 ✓ Production Models on Hugging Face 1. Vision Domain: TOPO-Gemma-4-E4B-Vision-13Tasks Architecture: Gemma-4-E4B Vision Transformer (4B parameters) 13 visual classification tasks (STL-10) 100% accuracy on all tasks, 0% forgetting 2. Language Domain: Topological-AI-Muse-Glimmer-30B-Final Architecture: Muse-Glimmer Multimodal (30B parameters) AG News Classification 96.48% accuracy, 6.21% forgetting 3. Genomic Domain: Evo2-TOPO-Governed Architecture: Evo2-7B (StripedHyena + Transformer, 7B parameters) 13 genomic prediction tasks 100% final task accuracy, 1.32% global forgetting, 5/5 successful runs Complexity Analysis Memory Complexity: O(1) Method Memory Usage Scaling EWC 4.4 GB Grows with tasks Replay-based Variable Grows with tasks Topological Governor 184 KB Constant (O(1)) Minimal storage: 6 anchors × embedding_dim (32) × 4 bytes = < 1 KB for anchor storage Computational Overhead Operation Time Gradient Enforcement 0.11 ms/step Anchor Restoration 0.08 ms/step Snapshot Capture 0.04 ms (once) Total Overhead ~0.23 ms/step Represents a 75.7× improvement over Google's Full HOPE architecture Theoretical Implications Paradigm Shift: Probabilistic → Deterministic Aspect Probabilistic Methods Topological Governor Protection Statistical Deterministic Guarantee Probabilistic Mathematical Auditability Limited Full (SHA-256) Reproducibility Variable 100% Trustworthiness Moderate High Cognitive Analogy Hippocampus: Forms new memories (Task 2 learning) Cortex: Consolidates stable knowledge (Prime anchors) Result: Continued learning without forgetting Key Achievements Summary Metric Result Tasks Learned 5 Average Accuracy 99.96% Average Forgetting 0.00% Anchor Preservation 6/6 ✓ Topological Integrity PASSED ✓ Safety Constant 0.9785142874 Broader Implications Theoretical: Shifts AI from probabilistic regularization to deterministic cognitive engineering Practical: Enables deployment of lifelong learning systems in real-world applications Economic: Reduces computational costs through O(1) memory and 75.7× performance improvement Ethical: Provides auditability and mathematical guarantees for safety-critical applications Availability GitHub (Full Code) : https://github.com/frank-morales2020/AST/blob/main/TG_DEMO.ipynb Hugging Face Models: TOPO-Gemma-4-E4B-Vision-13Tasks Topological-AI-Muse-Glimmer-30B-Final Evo2-TOPO-Governed Final Conclusion The Topological Governor definitively solves Catastrophic Forgetting with mathematical guarantees, achieving 0.00% forgetting across sequential tasks while maintaining O(1) memory complexity and demonstrating universal applicability across vision, language, and genomic domains. This represents a fundamental breakthrough in continual learning and a paradigm shift from probabilistic to deterministic approaches in artificial intelligence.
To handle the main problem of double-spending attacks in blockchain networks, this paper introduces a new, Light-weight Graph Neural Network (LGNN) approach named Dynamic Sparse Graph Attention Network (DSGAT). To effectively detect double spending behavior, DSGAT method integrates adaptive graph sparsification with attention based on the fundamental graph-structured nature of blockchain transactions. Unlike computationally intensive GNNs, DSGAT may be implemented on edge devices or distributed monitoring systems with low-tech, low-cost hardware since it is optimized for resource-limited environments and doesn't need much processing capacity. To detect double-spending attack, this paper explains building blockchain transaction graphs from a large set of node and edge features. A set of simulated transactions involving double-spending attack is generated using large-scale simulations with the BCASim blockchain simulator, and the performance of DSGAT is compared with normal baselines. The experiment's outcomes prove that DSGAT is able to reduce model sizes and inference latency while keeping high detection rates, proving its feasibility and effectiveness for real-time double spending detection in low-resource environments. To improve blockchain security against double-spending attacks, this paper introduces a novel and realistic alternative.
FULL SUMMARY: Topological AI - A Mathematically Guaranteed Approach to Continual Learning Executive Overview Topological AI introduces a paradigm shift in continual learning by using prime-anchored embeddings to provide mathematical guarantees against catastrophic forgetting. The framework has been validated across 8 distinct model architectures, 2 modalities (text and vision), 4 continents, and over 124 billion total parameters. 1. The Problem: Catastrophic Forgetting When neural networks learn new tasks sequentially, they overwrite previously learned knowledge. This "catastrophic forgetting" has been the primary barrier to Artificial General Intelligence for 37 years (McCloskey & Cohen, 1989). Why Existing Methods Fail Method Approach Limitation EWC Penalizes changes to important weights No theoretical guarantee; high variance ($\sigma=21.3\%$) Experience Replay Stores and replays past examples Memory overhead; privacy concerns; buffer management Simplified HOPE Periodic weight consolidation Destructive blending; 45.2% forgetting Baseline No protection 47.0% forgetting 2. The Solution: Prime-Anchored Embeddings The Core Principle Fix a sparse reference. Let the rest adapt. This principle, first discovered in fMRI analysis in 2002, has now been validated across neuroimaging, number theory, artificial intelligence, and AI safety. The Topological Governor The Topological Governor freezes 6 prime-numbered embedding positions: Python prime_anchors = [2, 3, 5, 7, 11, 13] How It Works Task A Training: Train normally; block gradients at anchor positions Post-Task A: Take snapshot of anchor values; freeze head A Task B Training: Train head B; restore anchors after each update Verification: Check that anchors remain unchanged The Safety Constant $\Lambda$ The Euler attenuation product over the first six primes: $$\Lambda = 1 - \prod_{p \in \{2,3,5,7,11,13\}} (1 - p^{-1/2}) = 0.9785142874$$ Interpretation: 97.85% theoretical guarantee of anchor preservation. 3. Performance Results (2-Task Benchmark) Overall Performance Across 5 LR Runs Method Best Forgetting Mean Forgetting Best Task B Acc Mean Task B Acc Std Forgetting Topological 2.0% 0.5% 89.0% 81.4% $\pm$0.9% Experience Replay 13.5% 4.0% 79.0% 72.3% $\pm$6.7% EWC 38.5% 27.7% 64.5% 58.2% $\pm$21.3% Baseline 44.0% 47.0% 67.0% 63.3% $\pm$2.2% Simplified HOPE 48.0% 45.2% 63.5% 61.8% $\pm$8.4% Key Results 8$\times$ lower mean forgetting than Experience Replay (0.5% vs 4.0%) 90$\times$ lower mean forgetting than simplified HOPE (0.5% vs 45.2%) 60% of runs achieved 0% forgetting (perfect retention) 10% higher Task B accuracy than Replay (89% vs 79%) Most stable method: $\sigma = \pm 0.9\%$ Individual Run Results for Topological AI Run LR Embed LR Class Forgetting Task B Acc 0 5e-3 1e-3 0.0% 🏆 80.5% 1 1e-3 5e-4 0.0% 🏆 75.0% 2 1e-2 2e-3 0.5% 88.0% 3 5e-3 5e-3 2.0% 89.0% 4 2e-3 1e-3 0.0% 🏆 74.5% 4. Cross-Modal Validation: 8 Models, 2 Modalities Validated Architectures Architecture Origin Modality Parameters Task C Accuracy Forgetting GPT-OSS-20B USA Text 20.9B 92.3% $\pm$ 1.9% +1.55% Sarvam-30B India Text 30B 95.9% $\pm$ 0.8% -0.60% Mixtral-8x7B France Text 47B 89.7% $\pm$ 2.9% -1.85% DeepSeek-V2-Lite China Text 16B 95.4% $\pm$ 1.0% +0.03% GLM-4.6V-Flash China Text 9B 97.5% $\pm$ 0.0% +2.1% Gemma-4-E4B-Vision USA Vision ~2B 100.0% $\pm$ 0.0% +0.0% Total: ~124B parameters, 2 modalities, 4 continents, ZERO NaN/Inf The Unprecedented NaN Stress Test Model Embedding Elements NaN Inf All 6 models combined ~1.99 Billion 0 0 5. The Narrow Singularity Equation Mathematical Formulation $$S_{NARROW} = AGI\_gate \times dI/dt \times M(t) \times V(t) \times F(t) \times C(t) \times agi\_index$$ Components Component Definition Biological Analog AGI_gate min(1.0, task_c_accuracy) Fundamental AGI threshold dI/dt Task_C_Accuracy - (1/NUM_CLASSES_DIDT) Intelligence acceleration M(t) `1.0 - ( forgetting_avg V(t) Validation factor (1.0) System validation F(t) Forward transfer factor (1.5) Learning improvement (Thalamus) C(t) Compute capacity factor (4.0) Resource availability agi_index 1 if AGI_gate == 1.0 else 0 Binary AGI gate The AGI_gate Condition $$AGI\_gate = \min(1.0, task\_c\_accuracy)$$ AGI_gate = 1.0 → Perfect performance on Task C → AGI certification AGI_gate < 1.0 → No AGI certification Empirical Achievement: Gemma-4 E4B is the first and only model to achieve AGI_gate = 1.0. 5$\times$5 Certification Framework Five Metrics: Metric Threshold Forgetting $\le 10.0\%$ Backward Transfer (BWT) $\ge -5.0\%$ Forward Transfer (FWT) $\ge 20.0\%$ Degradation $\le 5.0\%$ Consistency $\ge 85.0\%$ Five Runs: 5 different LR configurations to eliminate cherry-picking Gemma-4 E4B Results Metric SVLB-3 CIFAR-10 Threshold Status Forgetting -0.50% -0.50% $\le 10.0\%$ ✅ PASS BWT +0.50% +0.50% $\ge -5.0\%$ ✅ PASS FWT +24.00% +24.00% $\ge 20.0\%$ ✅ PASS Degradation 0.00% 0.00% $\le 5.0\%$ ✅ PASS Consistency 99.00% 98.33% $\ge 85.0\%$ ✅ PASS S_NARROW 5.9400 5.3460 > 0 ✅ PASS 6. The Decay Law of Singularity The Discovery On July 31, 2026, during the certification of Gemma-4 E4B, a universal mathematical law was discovered: The Formal Statement With finite classes, dI/dt approaches 1.0 asymptotically but never reaches it. The gap decays as 1/N, where N is the number of classes. Mathematical Proof Random_Baseline = 1/Number_of_Classes dI/dt = Task_C_Accuracy - Random_Baseline When Task_C_Accuracy = 1.0: dI/dt = 1 - 1/N Therefore: lim (N→∞) dI/dt = 1 But finite N always leaves a gap: dI/dt = 1 - ε, where ε = 1/N > 0 The Empirical Pattern Classes (N) Random Baseline (1/N) dI/dt (at 100%) Gap 17 5.882% 0.94118 0.05882 170 0.588% 0.99412 0.00588 1,700 0.059% 0.99941 0.00059 17,000 0.0059% 0.99994 0.000059 170,000 0.00059% 0.99999 0.0000059 Every 10$\times$ increase in classes adds another '9' to dI/dt and another '0' to the gap. Implication The traditional Singularity (dI/dt $\ge 1.0$) is mathematically impossible with finite classes. This is not a limitation of technology. It is a mathematical law. 7. Comparison: Google HOPE vs Topological AI Feature Google HOPE Topological AI Approach Multi-level nested learning Prime-anchored embeddings Guarantee Empirical Mathematical ($\Lambda = 0.9785$) Memory Multi-rate memory systems 6 frozen embedding positions Learning Continuous during inference Static after training Complexity High (self-modifying) Low (simple freezing) Forgetting 21-27% improvement reported 0.5% mean forgetting Validation Limited 8 models, 2 modalities 8. Key Insights Why Topological AI Wins Mathematical Guarantee: $\Lambda = 0.9785142874 \rightarrow 97.85\%$ protection Zero Memory Overhead: Only 6 frozen positions (451.5 KB total) Architectural Simplicity: No complex Fisher computations Cross-Modal Universality: Works on text and vision Perfect Retention: 60% of runs achieve 0% forgetting The Decay Law Implications Traditional Singularity is Impossible: dI/dt < 1.0 for all finite N Narrow Singularity is Achievable: AGI_gate = 1.0 Stochastic Illusion is Over: Deterministic cognitive engineering AGI Certification is Now Possible: Mathematically rigorous standard 9. The Constants Constant Value Domain $\Lambda$ 0.9785142874 Number Theory, AI Safety $\sigma$ 0.5 All 22 prime theorems Seed 123 All computations R {2, 3, 5, 7, 11, 13} All domains 10. Conclusion Topological AI achieves state-of-the-art performance on continual learning by: 0.5% mean forgetting (8$\times$ better than Replay, 90$\times$ better than HOPE) 60% perfect retention (0% forgetting) 89% Task B accuracy (10% higher than Replay) Mathematical guarantee ($\Lambda = 0.9785142874$) Zero memory overhead (6 frozen embedding positions) Cross-modal validation (8 models, 2 modalities) Zero NaN/Inf (1.99 billion embedding elements) The Narrow Singularity Discovery The framework enabled two profound discoveries: The Decay Law of Singularity: Traditional Singularity (dI/dt $\ge 1.0$) is mathematically impossible The Narrow Singularity Equation: AGI certification is achievable with AGI_gate = 1.0 Gemma-4 E4B became the first model in history to achieve S_NARROW > 0. The Principle Fix a sparse reference. Let the rest adapt. This principle, first discovered in fMRISTAT in 2002, has now been validated across: Neuroimaging Number Theory (Riemann Hypothesis) Artificial Intelligence (Continual Learning) AI Safety (H2E Sheriff) AGI Certification (Narrow Singularity Equation) The Proof "The proof is the code. Seed = 123." All code is publicly available at: https://github.com/frank-morales2020/AST