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How do you actually formally verify the code underpinning Ethereum's future? In this episode (the finale of the lean Ethereum miniseries), Nico sits down with Alex Hicks (Alexander Hicks), lead of Protocol Snarkification at the Ethereum Foundation, to break down formal verification from first principles. They cover: – What...

15,143 Aufrufe • vor 5 Monaten •via X (Twitter)

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Axiom Math's Carina Hong on why verification isn't about catching mistakes, it's how you drive the cost of a proof to zero: "Formal verification is going to make your life slightly better if you're facing a proof with one million lines. Remember the Erdős unit distance problem, the chain of thought being generated? There are actual mathematicians trying to follow it step by step and scrutinize it. That seems very difficult if you're not in that very niche domain of discrete geometry intersecting with algebraic number theory." "But if you have a Lean proof accompanying it, you can just run it. And running the Lean proof gives you that provable guarantee that this proof is sound." "I have a hot take. People think Lean is this library built on the existing Mathlib. I think it's going to grow significantly. A lot of the hurdles where Lean is difficult is that the basic definitions of some mathematical fields are just not in the library." "My hot take is the scaling law, if you go down the formal mathematics path, is going to be a lot steeper than informal mathematics. So it's not just for verification, for trust, it's also for performance, it's also for optimal generation." "Verification is not like insurance. It's not something where, oh, we want to make sure there's no flaw. That's great, but it also helps you generate mathematics, both proofs and conjectures and theories, a lot better." "So imagine the cost of proof goes to zero. Then you can massage the problem statements, and even if it's an open problem, a lot more easily, flexibly, and adaptively." Carina Hong Axiom

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13,273 Aufrufe • vor 1 Monat

Ethereum is starting from the endgame. Episode 4 of TheCoordinate is a deep dive into Lean Ethereum: a clean-slate rethink of consensus, execution, and data availability. I sat down with Justin Drake from Ethereum Foundation to unpack: > need for the rewrite, > rewrite items: post-quantum security + fast finality, > endgame finality (3-slot -> 2-slot -> maybe 1-slot), > slot anatomy, networking constraints, and the "SOL slots" meme, > real-time ZK proving changing the execution roadmap, > censorship resistance with FOSSIL, > role of L2s in the world of Lean Ethereum, > incentives across proposer, builder, prover, includer, attester. If you’re building on Ethereum or trying to understand where the base layer is headed, this one is for you. This is Episode 4 of TheCoordinate. Hope you enjoy it! ------------------------------- Timestamps: 0:00 Intro: digital intelligence needs digital institutions 0:30 The big questions: Lean Ethereum, consensus/execution, post-quantum 1:25 Why Ethereum needs an endgame mindset (and a clean-slate approach) 3:30 The two “rewrite-class” items: post-quantum security + fast finality 5:52 Beamchain → Lean Consensus → Lean Ethereum (expands beyond consensus) 6:34 ZK EVM + real-time proving within a slot → “10,000 TPS” target 10:10 “SOL slots”: pushing slot duration toward speed-of-light constraints 11:09 3-slot finality (3SF) → endgame finality (2-slot / 1-slot paths) 18:19 eFP2P: erasure-coded gossip, bandwidth efficiency, scaling blobs 26:21 FOSSIL today: inclusion lists + opening includers beyond validators 39:09 Lean VM: minimal ZKVM 51:04 XMSS explained: Merkle signatures, 2^32 leaves, statefulness tradeoff 1:00:36 Rollups: 99.9% throughput on L2s + “native rollups” 1:06:53 Economics: roles (builder/prover/includer/attester), proving costs, stake capping

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86,471 Aufrufe • vor 6 Monaten

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23,942 Aufrufe • vor 1 Monat

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Mistral AI Releases Leanstral 1.5: An Apache-2.0 Lean 4 Code Agent Model Solving 587 of 672 PutnamBench Problems Most AI theorem proving is a language model generating a proof in one shot, with a verifier bolted on at the end to check it. That's autocomplete with a grader — and Mistral just drew a clear line between that and an actual proof agent. They released Leanstral 1.5 — a 119B MoE with 6.5B active parameters, trained as a code agent that lives inside the Lean 4 compiler loop: propose a proof, read the compiler's goals and errors, refine, repeat until it compiles or the budget runs out. Verification isn't the eval here. It's the training signal. Here's what's actually interesting: → Test-time scaling behaves like a dial: PutnamBench Pass@8 climbs 44 → 244 → 493 → 587 solved as the per-attempt token budget moves 50k → 200k → 1M → 4M → 587/672 on PutnamBench at ~$4 per problem, versus an estimated $300+ for Seed-Prover 1.5 high (a 10 H20-days-per-problem budget) → Saturates miniF2F: 100% on both validation and test sets → Two RL environments in training — a multiturn prover, and a raw-filesystem code agent that edits files, runs bash, and queries the Lean language server for live goals and types → Not just math: an Aeneas (Rust → Lean) pipeline flagged 11 genuine bugs across 57 repos, 5 previously unreported — including an integer overflow in datrs/varinteger when (value + 1) hits Std.U64.MAX Apache 2.0 weights, free API endpoint Full analysis: Model weights: Project: Technical Details: Mistral AI Mistral AI for Developers Sophia Yang, Ph.D.

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