Independent protocol · Robinhood Chain

Aristotle

A market for machine-checkable truth.

$ARISTOTLE
Abstract

Almost everything a blockchain is asked to adjudicate is fuzzy — a price, an outcome, a judgement. Formal proof is not. A proof written in Lean either typechecks or it does not, and every honest checker on earth returns the same answer in seconds. Aristotle is an escrow market built on that one hard fact: lock a bounty against a statement, and it pays out to the first proof a machine confirms. No oracle. No committee taste. No trust.

§1 The asymmetry

A formal proof is expensive to produce and cheap to verify. Finding one can take a researcher months or a prover-model thousands of GPU-hours. Checking one takes a laptop a few seconds.

That is the same asymmetry proof-of-work is built on — except here the expensive artifact is worth something to somebody after it is made.

Observation 1.1

Verification is deterministic. Two honest verifiers cannot disagree, because they are not forming an opinion — they are running a kernel. A protocol settling on formal proofs has no oracle problem to solve.

§2 The protocol

  1. A poster locks $ARISTOTLE against a Lean theorem statement. The statement is the specification, and it is fixed at post time.
  2. Solvers — researchers, prover models, or people driving prover models — submit proof terms against it.
  3. The verifier elaborates the statement in a clean module the solver cannot touch, typechecks the submitted proof against it, and audits which axioms the proof actually depends on.
  4. The first submission that survives all three takes the bounty. The artifact is published, and anyone can re-verify it forever.

Step 3 is the whole game. A solver must not be able to quietly change what they are proving, and must not be able to smuggle in an assumption. Statement binding handles the first. The axiom audit handles the second.

§3 The audit

Lean will happily accept a proof that leans on sorry, or on an axiom the solver declared himself two lines earlier. Both typecheck. Neither is a proof of anything. So the verifier asks a second question after the kernel is satisfied: what does this proof actually rest on?

Only the three axioms of standard classical mathematics are accepted — propext, Classical.choice, Quot.sound. Anything else fails, including the ones that are easy to introduce by accident.

bounty #0001 — submission

      
      

An illustration of the verifier's decision path, not a live Lean instance. The third case typechecks perfectly and is still rejected — that is the point of the audit.

§4 What the token does

Three sinks. Only two of them are load-bearing, and we would rather say so than pretend otherwise.

4.1

Bounty escrow

Prizes are locked in $ARISTOTLE for the duration of the bounty. Honest caveat: a poster could denominate in stablecoins instead, so this sink alone would be decoration.

4.2

Verifier bonds mandatory

Attesting to a proof requires posting stake. Sign off on something that does not typecheck and the bond is slashed to whoever proves you wrong. You cannot participate in verification without holding the token, and that cannot be routed around.

4.3

Settlement fee mandatory

Every settled bounty pays a protocol fee, routed to buy-and-burn and to verifier stakers. Scales with real throughput, not with narrative.

§5 Who actually pays

Not mathematicians, at first. Protocols. A contract holding nine figures wants to know its liquidation logic cannot be driven insolvent — and today it buys an audit, which reports that several careful people looked hard and found nothing.

The distinction

“We did not find an exploit” and “no exploit exists” are different claims. Only one of them can be proved, and it is the one nobody is currently selling.

Formal proofs of contract invariants are the paying market. Open mathematics is the second market, and it is the one that makes this worth watching.

§6 Verification, in two phases

shipping

Optimistic

Lean's kernel is far too large to run on the EVM. So proofs are attested on-chain by bonded verifiers, with a challenge window in which anyone may re-run the kernel locally and dispute. Unlike most optimistic systems, the disputed question here is objective and cheaply recomputable — a liar cannot recruit honest confusion, because every independent checker gets the same answer.

next

Zero-knowledge

Lean's trusted kernel is small — on the order of ten thousand lines. Running it inside a zkVM to produce a succinct proof that this term typechecks against this statement is engineering, not research. At that point verification is fully on-chain and the trust assumption disappears entirely.

§7 What could go wrong