TOPO-2026: The Cognitive Phase Diagram Mapping the Stability-Plasticity Landscape of Biological and Artificial Learning

TOPO-2026: The Cognitive Phase Diagram — Full Summary

Document Overview

• Title: TOPO-2026: The Cognitive Phase Diagram — Mapping the Stability-Plasticity Landscape of Biological and Artificial Learning

• Author: Frank Morales Aguilera, BEng, MEng, SMIEEE

• Affiliation: Sovereign Machine Lab (SOMALA), Montréal, Canada

• Date: June 2026

• Deterministic Seed: 1231

Executive Summary

This paper introduces a framework that resolves the 35-year-old catastrophic forgetting problem, reclassifying it from a computational "bug" into a manageable feature of the stability-plasticity trade-off. It identifies that biological learning operates across five distinct "gears."

The Core Discovery: Solving Catastrophic Forgetting

The research demonstrates that catastrophic forgetting can be eliminated, achieving a net improvement in backward transfer rather than data loss.

The Five Cognitive States

The brain moves between discrete states based on the balance between stability (memory retention) and plasticity (new learning).

Topological Governance

The framework uses a Topological Governor, a prime-anchored embedding constraint that ensures long-term memory stability.

• Mathematical Foundation: Using Euler's product, six prime anchors ($2, 3, 5, 7, 11, 13$) capture $97.85\%$ of all spectral weight in the embedding space.

• Mechanism: It utilizes hippocampal-inspired functions such as take_snapshot() for memory traces and enforce_anchors() for restoration.

Learning Rate Configurations

The ratio between embedding learning rates governs optimization (lr_embed) and classification learning rates (lr_cls). The research finds that optimal balance is achieved when lr_embed ≈ 2 × lr_cls.

Practical Applications

• Education: Tailoring learning strategies to age-appropriate states (e.g., maximizing plasticity for children, stability for elders).

• Mental Health: Identifying patterns such as ADHD or burnout by matching cognitive performance profiles to specific "runs."

• AI Safety: Deploying "Safe AI" (Run 1) for safety-critical systems, or "Learning AI" (Run 3) for research environments.

Certification Summary

The framework passed all empirical benchmarks for stability and accuracy.

Resources

• Model: Hugging Face Repository

• Code: GitHub Implementation

Catastrophic forgetting is not a bug. It is a feature of the stability-plasticity trade-off. The Cognitive Phase Diagram is the map of the mind.

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