This market resolves YES if by December 31, 2025, an AI system demonstrates implementation of a mathematical framework for infinity toposes with the following criteria: 1. Includes mathematically valid categorical constructions of infinity toposes 2. Demonstrates path invariance across different query approaches 3. Provides proof of correctness for the core constructions 4. Is published in a peer-reviewed journal or conference, OR is publicly available and verified by multiple mathematicians Resolution will be based on published research or public demonstrations that meet these criteria.