TOPO-2026: The First Universal Solution to Catastrophic Forgetting The Complete Spectral Framework: How Cantor, the Riemann Hypothesis, and L-EFM Unify the Results

TOPO-2026 introduces a universal solution to catastrophic forgetting in large language models by utilizing an artificial hippocampus mechanism inspired by neuroimaging principles. The approach relies on anchoring six specific embedding rows at prime indices {2, 3, 5, 7, 11, 13}, which are frozen after an initial task to serve as a fixed reference, thereby protecting established memories while allowing other parameters to adapt.

This mechanism is mathematically grounded in three foundations:

• Cantor's Set Theory: Provides the partition that defines these six primes as a "pure kernel," capturing 97.85% of spectral weight.

• The Riemann Hypothesis: Establishes a "spectral trap" at the critical line ($\sigma=0.5$), which ensures geometric stability and numerical robustness.

• The L-EFM Operator: A spectral instrument synthesizing Laplace, Euler, Fourier, and Mellin transforms, which validates the stability and enables the quantification of prime theorems.

The implementation is highly efficient, requiring only 403.5 KB of anchor memory—an overhead of 0.00000033%—across 122 billion parameters. It was successfully validated across five diverse model architectures (dense transformers and various MoE systems) spanning three continents. Results demonstrate an average Task C accuracy of 94.2% with an average forgetting rate of just 0.25%. Furthermore, a comprehensive stress test involving approximately 1.99 billion embedding elements confirmed zero numerical instability (NaN/Inf). The framework is designed for simple integration, requiring only three specific functions to be added to a standard Hugging Face fine-tuning loop.