certified
A Lean-verified submission was approved for this target. Read the recorded review for its precise mathematical scope.
Submitted by JenW1N
Certified 9 Oct 2026, published by conjectures.io.
Review decision
Approved in reviewREVIEW_APPROVED
APPROVED — REVIEW_APPROVED, policy v3. Accepted 2026-10-07T22:08:18.636273+00:00; production verification completed 2026-10-07T22:13:41.682494+00:00. Every tight two-entry modification with both removed speeds in the upper half and inserted speeds at least n satisfies the individual multiplicative gcd criteria, with either matching order. The exact committed statement matches the intended reward target. Production run 43 passed the Lean kernel, Comparator, task-commitment, and permitted-axiom checks under landrun+seccomp. The full locked bounty of 2847.512143994 Alpha applies, subject to normal payout processing. No earlier eligible claimant, material formalization defect, or qualifying disqualification evidence was established. Two advisory Codex assessments, including a separate extra-high review recorded before comparison with the first, support approval with no material disagreement. They use the same model family and shared immutable evidence. The human reviewer authorized this decision. Review covered exact definitions, selected critical proof interfaces and bounded prior-work searches; it was not a line-by-line audit or exhaustive priority certification. No fresh Lean replay was performed; Nanoda was disabled. Source: https://arxiv.org/html/2608.13599v2#S9. The miner may request reconsideration from the Conjectures review team, referencing this submission and contrary evidence.
Approved · decided 8 Oct 2026
Formal statement
Math15.LonelyRunner.Target04Verification report
Every box below had to hold before the proof counted. They are grouped in the order the verifier reaches them.
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.
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.
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.
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
Stage COMPLETED · Axioms permitted: propext, Quot.sound, Classical.choice