Pick Two: How AI-Safety Impossibility Results Reduce to One 1969 Theorem, Machine-Checked in Lean 4

By Manish Bhatt

The AI-safety field keeps rediscovering the same wall. No model can be faithful, calibrated, and covering at once. No prompt-injection defense can be both complete and utility-preserving. No probe reads truth off a network exactly. These look like three separate frustrations. They are the same impossibility, wearing three masks.

This book traces all of them to one theorem: Lawvere's 1969 diagonal fixed point, the root of Cantor, G del, Tarski, and Turing, together with the intermediate value theorem. Three impossibilities, one argument, no fourth escape. Every proof is machine-checked in Lean 4, and sorry-free.

It stays honest about its reach. The mathematics has been settled since 1969. The force rests on the modeling premises. It proves these limits exist, not how often you will meet one.

Pick two. The third is a fixed point.

• Format: Paperback
• Language: English
• ISBN: B0HP9QW8SN
• ISBN13: 9798165427053
• Release Date: October 2026
• Publisher: Independently published
• Length: 420 Pages
• Weight: 1.23 lbs.
• Dimensions: 9.0" x 0.9" x 6.0"