Qed beta
Qedest. 2026

Independent verification for AI-generated proofs

Lean says it compiles.
It doesn't say it's true.

A proof assistant checks that a proof establishes a statement. It never checks that the statement means what you intended. Qed connects you with professional mathematicians who verify that it does — and sign their name to it.

KeyBound.lean
-- summable bound, formalized by an AI system
theorem key_bound (a : ℕ → ℝ) (S : ℝ)
    (hsum : True)
    (h : ∀ n, a n ≤ S) :
    (∑' n, a n) ≤ S := by
  -- ... 40 lines, no errors, no `sorry` ...
Build ✓ Elaborates and type-checks. #print axioms: propext, Classical.choice, Quot.sound. Zero sorries. CI is green.

Toggle the reviewer. Same file. Two very different verdicts.

Theoremthe gap

The kernel proves the proof. Nobody proved the statement.

When Lean, Coq, or Isabelle accepts a proof, it certifies exactly one thing: this term has the type of this statement. That's real and valuable. But a statement can type-check perfectly while saying something other than what you meant — a hypothesis that's secretly contradictory, a definition stubbed to True, a quantifier in the wrong place, a divergent sum silently defined as zero.

The elaborator is complete on the type stratum — every type error raises. It is silent on the meaning. A semantically wrong but type-correct statement passes without complaint. AI systems fail in precisely this register: not a wrong algebra step (the kernel catches those) but a hallucinated assumption or dropped subtlety, presented as if derived.

Machine verification of an incorrect specification provides false confidence that may be worse than no verification at all.

— Tao et al., “From Solvers to Research,” arXiv:2607.07779 (2026)
89.5%
of a leading agent's autoformalizations compiled in Lean
arXiv:2606.31002
60.5%
…but only that share were actually faithful to the intended claim. A 29-point gap.
arXiv:2606.31002
4,833
defects found auditing 5 standard Lean benchmarks — vacuous theorems, missing hypotheses, unsound axioms.
arXiv:2606.29493

A re-analysis of miniF2F, the field's most-cited benchmark, found statement-vs-intent discrepancies in over half its problems. And there is, today, no reliable automated way to check faithfulness — it takes a mathematician.

Lemmablind spots

Five things a passing build cannot see

Every item below type-checks. Every one has shipped in a published benchmark or an AI-generated proof. This is the checklist a Qed verifier works through — by hand, against your intended claim.

Vacuous hypotheses

An assumption like hsum : True, or one that's secretly unsatisfiable, makes the theorem trivially true. It says nothing — and the kernel never objects.

Unfaithful statement

Omitted finite-dimensionality, a collapsed biconditional, the wrong domain. The formal claim is a weaker — or different — theorem than the one you set out to prove.

Hidden sorry & axioms

Gaps elaborate to sorryAx and still show a checkmark. A stray custom axiom can silently make anything provable. Both need #print axioms and a human who reads it.

Junk-value traps

Lean's total functions return defaults on undefined input — a non-summable ∑' is 0, division by zero is 0. Bounds can hold vacuously until the missing hypothesis is added.

Dishonest definitions

The proof is only as good as the definitions under it. A plausible-looking definition that's subtly wrong yields a flawless proof of the wrong thing.

Exploit tactics

Tactics like native_decide trust external code outside the kernel — an avenue for an AI to "prove" a falsehood. High-stakes projects ban them; we check you did.

Proofthe service

How a verification runs

You bring a result — a Lean/Coq/Isabelle repository, or an informal proof plus its formalization. We return a signed report you can cite, publish, or hand to a customer.

Submit the claim and the artifact

The theorem in plain mathematics, the formal statement, and the proof. We scope difficulty, the axioms and tactics in play, and match a verifier with the right subfield.

Machine pre-flight

We reproduce the build, run #print axioms and an independent kernel re-check (lean4checker), and flag sorry, non-standard axioms, and trusted-code tactics — before a human spends a minute on it.

Expert faithfulness review

A professional mathematician reads the statement against your intent, audits the definitions, and stress-tests every hypothesis for vacuity. This is the judgment no tool can yet make.

Signed certificate — or a defect report

Either a named attestation of what was verified and under which assumptions, or a precise account of what breaks and why. Optional second-verifier consensus for high-stakes claims.

Corollarywho it's for

When a checkmark isn't enough to stake your name on

AI labs

Third-party sign-off before you announce

Publishing a solved problem or a benchmark result? An independent attestation that the statement matches the claim is the difference between a headline and a retraction.

Researchers & journals

An audit before submission

Formalized your paper's main theorem? Have the encoding checked for faithfulness and hidden gaps before a referee — or the internet — does it for you.

Formal methods & crypto

Proof is only as good as the spec

Protocol, ZK circuit, or safety-critical property. Verification moves the risk into the specification. We audit the part your prover assumes is correct.

Scholiathe bench

For mathematicians: get paid to be right

We're assembling a bench of Lean-fluent mathematicians to do the judgment work no model can. If you can read a formal statement and tell whether it captures the theorem, this is paid, remote, and intellectually real.

Paid & flexible

Expert rates, on your schedule

Per-verification or retainer, remote, take what fits. Comparable expert-review work runs $150–300/hr; we'll set rates with the first cohort — that's part of what we want to learn from you.

Frontier problems

Where AI math is actually happening

You'll scrutinize freshly AI-generated and autoformalized proofs — the specification traps, the vacuous hypotheses, the junk-value bounds. The interesting failure modes, not homework.

Your name, your standard

Help define what verification means

Certificates carry the verifier's attestation. Early members shape the review protocol and standards for a field that doesn't have them yet.

Not sure you're a fit? If you've formalized anything in Lean, Coq, or Isabelle — or you referee proofs — we want to talk. Sign up as a verifier →

Q.E.D.

Get on the list.

We're early — building a first cohort on both sides and figuring out the details in the open. Sign up and we'll reach out for a short conversation to learn what you need (and, if you're a verifier, what you'd want to be paid).