ZK certificate #7

Sealed comparator (v2): bound to this problem's challenge — proof kept by the house, made on a rented A5000 in 109 s

✅ verified mathematically: the receipt proves the Lean kernel (nanoda, in the zkVM) accepted a proof

🔒 Bound to challenge (sealed comparator, journal v2): the statements proven are exactly the challenge's, checked inside the proof; 686e2a073a93140c0270f14e89eb46df2f0669fdebd3353c4cbf95d66efa5150 · 32 declarations of the statements found identical
✓ matches this problem's current challenge
Proven for the theorems listed below only. If the problem asks for more results than these, this certificate does not cover them.

Statements proven (the proofs stay secret)

add_comm'

theorem add_comm' (n m : Nat) : Eq (HAdd.hAdd n m) (HAdd.hAdd m n) := _

Holder: Valaxia (casa)
The holder is the account that posted the receipt. The receipt itself is not yet bound to an account or a transaction: it proves that a proof exists, not who owns it.
Problems: Example / Exemplu: n + m = m + n in Lean 4 (no reward)
Recorded at (UTC): 2026-09-25T21:03:40.589133Z
Program image id (lean_check): 9eb59152d4c880edce28e437b688d6fc84be75ed66e2e36ec8d5987a288acc84
Axiom policy (axioms the checker was allowed to accept): Classical.choice, Quot.sound, propext
SHA-256 of the (secret) export: 1d2f166b162fca240f8601b1028ca93addd0e8a49ed770a3ceb5459c06d16f90 · 56 declarations checked
receipt: succinct · sha256 cd8b8e79770b3e9c04007a9dad4b960924206c6a24401f81cdd9363067659c93 · Download the receipt
Entry hash: aa2d639079f234c5716a7107887f66a03b626dbe905df0ab59a387a0ac0c0396 · #7

Verify it yourself

Build the verifier from zk/lean_check/verifier (Rust), then run it on the receipt with the image id. The image id is the hash of the fixed program; anyone rebuilding zk/lean_check obtains the same id.

lean_check_verifier receipt.bin 9eb59152d4c880edce28e437b688d6fc84be75ed66e2e36ec8d5987a288acc84