Conjectures.io

submission

erdos15-erdos-15

Lean accepted this proof on 5 Aug 2026. What happens to it next is decided by people, and that decision is recorded below.

Review decision

Defect in the published taskFORMALIZATION_DEFECT_AWARD

Formal statement

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 validPassed

    The task bundle held together: the exact file set, a strict manifest, and every trusted hash matching the bytes on disk.

  • Task commitment matchesPassed

    The bundle digest the submission committed to is the digest of the bundle that was actually verified.

  • Production taskPassed

    The task came from the production pool rather than a test fixture.

  • Trusted file hashes matchPassed

    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 respectedPassed

    The submitted source passed the static scan: no imports, no axiom declarations, no sorry, no native_decide, no unsafe options.

  • Production sandboxPassed

    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 builtPassed

    The trusted Challenge.lean, which contains no miner code, compiled on its own.

  • Source type hash matchesPassed

    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 builtPassed

    The submitted Solution.lean compiled.

  • Statement unchangedPassed

    The theorem the proof establishes has exactly the same canonical type as the task's target - it was not weakened or restated.

  • Only permitted axiomsPassed

    The transitive axiom closure of the proof stays inside the axioms this task permits.

  • Lean kernel acceptedPassed

    The Lean kernel replayed the proof and accepted it.

  • Nanoda acceptedNot 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