certified
Green's open problem 42
Formalization defect
The accepted file establishes a result about a faulty formal statement. It does not settle the intended mathematical problem. The recorded review explains the mismatch.
Submitted by 5GbYxU…yUxBzW
- Lean verification:
- Passed
- Conjectures review:
- Approved
- Reward:
- Paid
Certified 6 Aug 2026, published by conjectures.io.
Review decision
Defect in the published taskFORMALIZATION_DEFECT_AWARD
Lean verified the exact published task, but the formal statement does not faithfully encode the intended Cohn–Elkies scheme. Its admissibility predicate includes decay conditions but omits regularity needed to prevent changing a function at a single point. The submitted witness exploits that omission: it modifies the function at the origin, leaving the Fourier transform unchanged while altering the separately evaluated ratio f(0)/fHat(0). Consequently the artifact does not settle Green Problem 42. The submission receives the $750 USD-equivalent formalization-defect award in Subnet 66 Alpha instead of the displayed conjecture bounty.
Partial award · decided 6 Aug 2026
Formal statement
True ↔ Green42.CohnElkiesOptimal 2 (√3 / 6)Verification report
Every box below had to hold before the proof counted. They are grouped in the order the verifier reaches them.
The task it was checked against
Manifest valid — Passed
The task bundle held together: the exact file set, a strict manifest, and every trusted hash matching the bytes on disk.
Task commitment matches — Passed
The bundle digest the submission committed to is the digest of the bundle that was actually verified.
Production task — Passed
The task came from the production pool rather than a test fixture.
Trusted file hashes match — Passed
The pinned dependencies agree across the manifest, the lockfile and the checkout, down to the same Formal Conjectures commit.
The submission and the sandbox
Submission policy respected — Passed
The submitted source passed the static scan: no imports, no axiom declarations, no sorry, no native_decide, no unsafe options.
Production sandbox — Passed
The run happened under real isolation, Landrun with seccomp, and the sandbox passed its own live self-test before the proof was touched.
The trusted build
Challenge built — Passed
The trusted Challenge.lean, which contains no miner code, compiled on its own.
Source type hash matches — Passed
The source theorem in the compiled environment still hashes to the type recorded in the task, so the statement has not drifted upstream.
The kernel's verdict
Solution built — Passed
The submitted Solution.lean compiled.
Statement unchanged — Passed
The theorem the proof establishes has exactly the same canonical type as the task's target - it was not weakened or restated.
Only permitted axioms — Passed
The transitive axiom closure of the proof stays inside the axioms this task permits.
Lean kernel accepted — Passed
The Lean kernel replayed the proof and accepted it.
Nanoda accepted — Not run
A second kernel, written independently of Lean's, also accepted the proof.
One kernel, not two
This task does not require a second, independent kernel, so Nanoda was not run. The verdict rests on a single kernel implementation.
Theorems established
- Bounty.target
Stage COMPLETED · Axioms permitted: propext, Quot.sound, Classical.choice