OpenAI’s ETH Claim Faces Independent Review

OpenAI claims to have refuted the Exponential Time Hypothesis (ETH), a conjecture about the time needed to solve certain hard problems, but researchers are organizing an independent examination and the result does not establish a practical attack on Bitcoin. CryptoSlate’s review is limited to introductory pages 1–8 of the paper, so it does not assess the full proof. The researchers organizing the examination said their involvement should not be taken as certification of the claim.

The manuscript, dated Oct. 17 and revised Oct. 25, claims a deterministic algorithm that exactly counts satisfying assignments for fixed-width Boolean formulas in subexponential time and polynomial space. The article explains that this means the running time grows more slowly than an exponential bound as a problem grows; it does not mean the problem becomes easy on current computers. The disclosed bound does not establish a polynomial-time algorithm or settle P=NP, the question of whether every problem whose proposed solution can be checked in polynomial time can also be solved in polynomial time. OpenAI says the result was verified in Lean, a proof assistant, but the scope note for that formalization gives a weaker time bound than the manuscript’s sharpest claim.

Bitcoin mining and spending authorization are separate security tasks. Mining searches for a block-header hash below a target, while signatures authorize spending. Bitcoin uses ECDSA and Schnorr signatures over the secp256k1 elliptic curve; recovering a private key from its public counterpart is a different task from solving worst-case SAT problems. The article says the ETH claim does not show how to defeat those mechanisms: a practical attack would still need a suitable encoding, an implementation and a cost comparison. SAT formula variable counts also cannot be substituted directly for cryptographic key or hash bit lengths. Bitcoin adjusts its mining target every 2,016 blocks, a mechanism concerning block production rather than signature authorization.

The ETH claim is separate from a CryptoSlate-covered debate on Oct. 7, when Justin Drake called for “bunker mode” preparations after an earlier OpenAI mathematics release. Ryan Williams said he, Russell Impagliazzo and Mohan Paturi were asked to organize an open examination without NDAs or compensation. Williams separately said he asked OpenAI to check whether existing cryptosystems were compromised and relayed that they were apparently safe; this is a second-hand account, not an independent cryptographic audit. OpenAI says practical improvements require significant further research. Williams said he did not know whether developers would see benefits, allowing for progress within 12 months or none, and the organizers plan to share findings as the examination proceeds.

OpenAI claims to have refuted the Exponential Time Hypothesis (ETH), a conjecture about the time needed to solve certain hard problems, but researchers are organizing an independent examination and the result does not establish a practical attack on Bitcoin. CryptoSlate’s review is limited to introductory pages 1–8 of the paper, so it does not assess the full proof. The researchers organizing the examination said their involvement should not be taken as certification of the claim.

The manuscript, dated Oct. 17 and revised Oct. 25, claims a deterministic algorithm that exactly counts satisfying assignments for fixed-width Boolean formulas in subexponential time and polynomial space. The article explains that this means the running time grows more slowly than an exponential bound as a problem grows; it does not mean the problem becomes easy on current computers. The disclosed bound does not establish a polynomial-time algorithm or settle P=NP, the question of whether every problem whose proposed solution can be checked in polynomial time can also be solved in polynomial time. OpenAI says the result was verified in Lean, a proof assistant, but the scope note for that formalization gives a weaker time bound than the manuscript’s sharpest claim.

Bitcoin mining and spending authorization are separate security tasks. Mining searches for a block-header hash below a target, while signatures authorize spending. Bitcoin uses ECDSA and Schnorr signatures over the secp256k1 elliptic curve; recovering a private key from its public counterpart is a different task from solving worst-case SAT problems. The article says the ETH claim does not show how to defeat those mechanisms: a practical attack would still need a suitable encoding, an implementation and a cost comparison. SAT formula variable counts also cannot be substituted directly for cryptographic key or hash bit lengths. Bitcoin adjusts its mining target every 2,016 blocks, a mechanism concerning block production rather than signature authorization.

The ETH claim is separate from a CryptoSlate-covered debate on Oct. 7, when Justin Drake called for “bunker mode” preparations after an earlier OpenAI mathematics release. Ryan Williams said he, Russell Impagliazzo and Mohan Paturi were asked to organize an open examination without NDAs or compensation. Williams separately said he asked OpenAI to check whether existing cryptosystems were compromised and relayed that they were apparently safe; this is a second-hand account, not an independent cryptographic audit. OpenAI says practical improvements require significant further research. Williams said he did not know whether developers would see benefits, allowing for progress within 12 months or none, and the organizers plan to share findings as the examination proceeds.