The TOPO2026_Technical_Report.pdf establishes a new certification pipeline for continual learning in Large Language Models, enabling sequential task training without the problem of catastrophic forgetting. The framework provides a universal, architecture-agnostic standard that functions as a certification layer, allowing it to sit above existing tools rather than competing with them. Core Framework and Methodology At the heart of the standard is the Topological Governor, which implements a mechanism derived from Arithmetic Spectral Theory. The system uses a set of prime-indexed embedding rows {2, 3, 5, 7, 11, 13} as anchors to lock model knowledge. A safety constant, $\Lambda=0.9785142874$, is calculated from the Euler attenuation product to provide 97.85% collective topological coverage. Integration requires only three specific steps in a training loop: taking a snapshot after the initial task, zeroing gradients for anchored rows during subsequent tasks, and enforcing anchors after the optimizer step. Performance and Scaling Unlike standard approaches, this method offers a mathematically provable memory guarantee. It operates at a flat, constant memory overhead of 67.5 KB to 96.0 KB, regardless of the model’s parameter count or the number of tasks performed. Computational overhead is minimal, requiring less than 0.5 ms for snapshot operations. The system is architecture-agnostic, having been successfully validated on both dense transformers like GPT-OSS-20B and sparse Mixture-of-Experts models like Sarvam-30B FP8. Comparison with Industry Frameworks The TOPO2026_Technical_Report.pdf highlights significant limitations in current industry-standard continual learning tools, including Avalanche, Mammoth, and PyCIL. These existing frameworks lack a training loop governed by a mathematical invariant, meaning they do not have a provable memory bound. Methods like EWC, often utilized within these tools, suffer from heavy memory requirements—reaching 4.4 GB per task on a 20B model—which frequently leads to out-of-memory errors during sequential training runs. While these frameworks rely on techniques that grow linearly with the number of tasks or suffer from plastic/stability trade-offs, the TOPO-2026 approach maintains a fixed, O(1) memory footprint. Certification and Future Integration The pipeline generates machine-readable artifacts, including a topological_config.json file, which serves as a "passport" for the model’s certified status. This includes validation against a rigorous three-task AG News benchmark, where the model must maintain performance on cross-domain tasks. The ultimate goal is to integrate this standard into the Hugging Face Hub, where models could carry a verified badge and be filtered by users based on their certification, creating a standardized axis for evaluating model stability and reliability.