# Partially Formalized Lean Blueprint

Instead of rewriting whole proofs, AI agents work inside human-built Lean blueprints and tighten intermediate estimates one at a time, so each local improvement propagates along the dependency graph to the final bound. On Grothendieck's constant this pipeline gives the first explicit numerical improvement over Krivine's 1977 upper bound; on Korenblum's constant it improves Wang's 2025 lower bound. With the blueprint removed, the agent wrote plenty of Lean but improved nothing.

Instead of rewriting whole proofs, AI agents work inside human-built Lean blueprints and tighten intermediate estimates one at a time, so each local improvement propagates along the dependency graph to the final bound. On Grothendieck's constant this pipeline gives the first explicit numerical improvement over Krivine's 1977 upper bound; on Korenblum's constant it improves Wang's 2025 lower bound. With the blueprint removed, the agent wrote plenty of Lean but improved nothing.