Overview This research introduces a production-ready agentic AI system designed to mitigate catastrophic forgetting in Large Language Models (LLMs). By anchoring six prime-indexed embedding rows $\{2, 3, 5, 7, 11, 13\}$ as fixed reference points, the system maintains historical knowledge with near-zero forgetting while requiring minimal memory overhead. Key Technical Contributions The Core Innovation: Prime Anchoring Topological Invariant: Utilizes the first six primes to create stable reference points. Mechanism: Anchor rows are snapshotted after initial training; gradient updates are blocked for these specific rows during subsequent tasks. Sparsity & Memory: Only 6 out of ~50,000 rows (0.01% of parameters) are used, resulting in an O(1) memory overhead of only 48–96 KB. Mathematical Foundation Euler Attenuation Product: These six primes account for 97.85% of total spectral weight, defined by: $$\Lambda = 1 - \prod_{p\in \{2,3,5,7,11,13\}}(1 - p^{-0.5}) \approx 0.9785$$ Spectral Trap: The anchors create a spectral peak at $\sigma = 0.5$, aligning with the critical line of the Riemann Hypothesis. Green-Tao Quantification: Establishes a decay law for coherence: $$\text{coherence}(k) = 2.1546\times k^{-0.8186} + 0.1218$$ Performance Metrics (Selected Models) Model Task C Accuracy Forgetting Std Dev Zero Forgetting Runs GPT-OSS-20B 92.3% ±1.28% 0/5 Sarvam-30B FP8 95.9% ±2.82% 0/5 Mixtral-8x7B FP8 89.7% ±2.53% 0/5 DeepSeek-V2-Lite FP8 95.4% ±0.21% 3/5 Multi-Agent System Architecture The system employs four specialized agents to manage task routing and classification: Classifier Agent: Routes documents based on keywords. Topic Agent: Performs unsupervised domain topic extraction. Sentiment Agent: Conducts autonomous tone analysis. Decision Agent: Acts as the final arbiter for task approval and routing. Efficiency: Achieves 96–100% classification accuracy with inference times between 252–446ms. Comparative Analysis The topological approach outperforms traditional methods by balancing plasticity and stability: Method Memory Cost Performance/Issue EWC 4.4 GB/task Memory intensive; fragments GPU Experience Replay O(k) Buffer growth issues; lower accuracy HOPE-like 2.3 GB High forgetting resistance but lower accuracy (88.1%) Topological AI 48 KB 99.5% accuracy; highly efficient Biological and Theoretical Insights Biological Analogy: The system treats 0% forgetting as a pathology. By allowing 99.99% of embedding rows to remain plastic, the model mimics biological brains that prioritize selective forgetting to facilitate adaptation. Riemann Hypothesis Connection: The research posits that the specific selection of the first six primes creates a unique "spectral trap" at $\sigma = 0.5$. Including any prime $\geq 17$ disrupts this trap and destroys the stability condition. Production Readiness and Certification TOPO-2026 Track II: The system passed all rigorous benchmarks, including Task C accuracy ($\geq 80\%$), Combined Forgetting ($\leq 10\%$), and O(1) memory overhead. Deployment: Fully compatible with commodity hardware, specifically tested on NVIDIA RTX PRO 6000 Blackwell GPUs. Resources: Implementation code, technical reports, and proof documents are available via the project's GitHub and Zenodo repositories.