TOPO-2026: The Indispensable Mechanism for Achieving Artificial General Intelligence

The TOPO-2026 framework is a prime-anchored continual learning mechanism designed to address catastrophic forgetting in large language models (LLMs).

Here is a summary of the framework:

• Core Mechanism: It uses six prime-indexed embedding rows—specifically {2, 3, 5, 7, 11, 13}—as fixed anchors to stabilize the embedding manifold during continual learning.

• Mathematical Grounding: The framework relies on Arithmetic Spectral Theory (AST), utilizing a coverage constant ($\Lambda = 0.9785142874$) derived from the prime anchor set, which captures 97.85% of the spectral weight.

• Performance and Validation:

  • Memory Scaling: The framework achieves $O(1)$ memory scaling, requiring only 307.5 KB total across all anchored models regardless of the number of tasks.

  • Architecture Agnosticism: It has been validated across four distinct transformer-based architectures (dense and sparse MoE), showing it operates independently of the model's routing mechanism or quantization scheme.

  • Stability: It demonstrated zero NaN/Inf values across 2 billion embedding parameters during stress testing.

  • Learning Outcomes: Across multiple production models, the framework demonstrated zero forgetting in specific test runs and observed backward transfer, where models improved on previous tasks after learning new ones.

• Public Accessibility: The framework is designed for reproducibility, with all models and checkpoints available on Hugging Face and the full validation code published on GitHub.

TOPO-2026 is positioned as a necessary condition for Artificial General Intelligence (AGI), as it enables a system to acquire knowledge indefinitely without degrading previously learned representations.