AnalysisScienceJuly 21, 2026

AI agents prove Collatz theorem bound: 436 ln N steps

Researchers used AI agents to strengthen Terence Tao's Collatz theorem, proving that for any f(N)→∞, almost every N reaches below f(N) within 436 ln N steps. The result establishes natural density and an explicit clock, is Lean-verified, but does not solve the full conjecture.

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AI agents strengthened Terence Tao's landmark Collatz theorem. For each f(N)→∞, almost every N falls below f(N) within 436 ln N steps. New: natural density and one explicit clock. Not the full conjecture. Lean-verified.proofatlas.ai

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