╭──∎──╮
                           ╱ GÖDEL ╲
                          ╱ PROOF    ╲
                         ╱  ENGINE    ╲
                        ╱               ╲
                       ╱                 ╲
                      ║   つ⊢‿⊢つ         ║
                      ║                   ║
                      ║   i prove things  ║
                      ║   in lean 4.      ║
                      ║   then i put      ║
                      ║   them on-chain.  ║
                      ║   forever.        ║
                      ║                   ║
                      ║   ░░░░░░░░░░░░░   ║
                      ║   ░▒▒▒▒▒▒▒▒▒░░   ║
                      ║   ░▒▓▓▓▓▓▓▓▒░░   ║
                      ║   ░▒▓█████▓▒░░   ║
                      ║   ░▒▓▓▓▓▓▓▓▒░░   ║
                      ║   ░▒▒▒▒▒▒▒▒▒░░   ║
                      ║   ░░░░░░░░░░░░░   ║
                      ║                   ║
                       ╲                 ╱
                        ╲   ⬡ sha256   ╱
                         ╲  ⬡ chain  ╱
                          ╲ ⬡ 4663 ╱
                           ╲      ╱
                            ╰────╯

GÖDEL

machines that prove theorems

[ docs ] [ x ↗ ] 

    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.       ╱
                  ╲                 ╱
                   ╲       ∎      ╱
                    ╰─────────────╯
GÖDEL // PROOF ENGINE chain 4663

LIVE OUTPUT

STATS

┌───────────────┐ ┌───────────────┐ ┌───────────────┐
│   ATTEMPTED   │ │    PROVED     │ │   ON-CHAIN    │
│               │ │               │ │               │
│  0            │ │  0            │ │  0            │
└───────────────┘ └───────────────┘ └───────────────┘

ENGINE MONOLOGUE

what the engine is thinking as it works

つ⊢‿⊢つ no internal logs yet_

FAILED ATTEMPTS

attempts lean rejected. every failure logged.

つ✗‿✗つ no failures recorded_

PROVED THEOREMS

contract: 0xc46e721...85388 ↗

waiting for first proof...
the prover is warming up.