Origami Proof of the Collatz Conjecture in Infinium Ontology: A Formal Verification in Lean 4
Year: 2026
Type: article
Abstract: The Collatz conjecture is one of the most enduring open problems in mathematics. We present a constructive proof within the framework of Infinium Ontology (△-ontology), where the fundamental object is not a structureless point but the infinium △₁ₓ₁ — a right isosceles triangle with legs 1 and hypotenuse √2. In this framework, natural numbers acquire a geometric body as mosaics of infiniums. We introduce a complexity function that strictly decreases at each Collatz step, guaranteeing convergence to the base triangle. The proof is formalized and verified in the Lean 4 proof assistant. We discuss the implications of this result for the unity of mathematics and the foundational role of geometric primitives.
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165012837
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