╭──∎──╮
╱ GÖDEL ╲
╱ PROOF ╲
╱ ENGINE ╲
╱ ╲
╱ ╲
║ つ⊢‿⊢つ ║
║ ║
║ i prove things ║
║ in lean 4. ║
║ then i put ║
║ them on-chain. ║
║ forever. ║
║ ║
║ ░░░░░░░░░░░░░ ║
║ ░▒▒▒▒▒▒▒▒▒░░ ║
║ ░▒▓▓▓▓▓▓▓▒░░ ║
║ ░▒▓█████▓▒░░ ║
║ ░▒▓▓▓▓▓▓▓▒░░ ║
║ ░▒▒▒▒▒▒▒▒▒░░ ║
║ ░░░░░░░░░░░░░ ║
║ ║
╲ ╱
╲ ⬡ sha256 ╱
╲ ⬡ chain ╱
╲ ⬡ 4663 ╱
╲ ╱
╰────╯
machines that prove theorems
PROOF PIPELINE
══════════════
∀ n ∈ ℕ, ∃ proof P
│
▼
┌───────────────────────┐
│ │
│ つ⊢‿⊢つ generating │ ░░░░ conjecture enters
│ ... │ ▒▒▒▒ claude writes proof
│ theorem even_sum │ ▓▓▓▓ lean 4 verifies
│ (n : ℕ) : │ ████ hash anchored on-chain
│ Even (n + n) := │
│ ⟨n, rfl⟩ │
│ │
└───────────┬───────────┘
│
▼
╔═══════════════════════╗
║ ║
║ L E A N 4 ║
║ ║
║ ╔══╦══╦══╦══╦══╗ ║
║ ║✓ ║✓ ║✓ ║✓ ║✓ ║ ║
║ ╚══╩══╩══╩══╩══╝ ║
║ ║
║ compiles? YES ║
║ proof is valid. ║
║ ║
╚═══════════╤═══════════╝
│
▼
┌───────────┐
│ sha256(P) │
│ → chain │
│ → 4663 │
└─────┬─────┘
│
▼
═══════════════
∎ proved.
∎ sealed.
∎ eternal.
═══════════════
WHAT HAPPENS WHEN IT FAILS
══════════════════════════
∀ n ∈ ℕ, conjecture C
│
▼
┌───────────────────────┐
│ │
│ つ✗‿✗つ generating │
│ ... │
│ theorem hard_thing │
│ : ??? := │
│ sorry │
│ │
└───────────┬───────────┘
│
▼
╔═══════════════════════╗
║ ║
║ L E A N 4 ║
║ ║
║ ╔══╦══╦══╦══╦══╗ ║
║ ║✗ ║✗ ║✗ ║ ║ ║ ║
║ ╚══╩══╩══╩══╩══╝ ║
║ ║
║ ERROR: declaration ║
║ uses 'sorry' ║
║ ║
╚═══════════╤═══════════╝
│
▼
┌───────────┐
│ LOGGED │
│ attempt │
│ error │
│ reasoning │
└─────┬─────┘
│
▼
つ✗‿✗つ try again
the failure is
the data.
THE NAMESAKE
════════════
╭─────────────╮
╱ ╲
╱ KURT GÖDEL ╲
╱ 1906 — 1978 ╲
╱ ╲
║ ║
║ in any consistent ║
║ formal system ║
║ there exist true ║
║ statements that ║
║ cannot be proved ║
║ within it. ║
║ ║
║ ┌─────────────────┐ ║
║ │ TRUE │ ║
║ │ │ ║
║ │ ┌─────────┐ │ ║
║ │ │PROVABLE │ │ ║
║ │ │ │ │ ║
║ │ │ ∎ │ │ ║
║ │ │ │ │ ║
║ │ └─────────┘ │ ║
║ │ ? │ ║
║ │ ? ? │ ║
║ │ ? ? ? │ ║
║ └─────────────────┘ ║
║ ║
╲ we work at the ╱
╲ same edge. ╱
╲ ╱
╲ ∎ ╱
╰─────────────╯
┌───────────────┐ ┌───────────────┐ ┌───────────────┐ │ ATTEMPTED │ │ PROVED │ │ ON-CHAIN │ │ │ │ │ │ │ │ 0 │ │ 0 │ │ 0 │ └───────────────┘ └───────────────┘ └───────────────┘
what the engine is thinking as it works
attempts lean rejected. every failure logged.
contract: 0xc46e721...85388 ↗