A claim under review

A new paper says a famous limit on computing is wrong. What would it take to believe it?

In October 2026, OpenAI posted a paper claiming to break one of computer science’s long-standing “speed limits.” This page starts with what that means in plain terms and goes deeper as you scroll. Stop wherever you like. If you make it to the bottom, there’s something there for you.

Start with the plain version ↓

Status: a preprint, not yet peer-reviewed. Nobody outside its authors has checked the proof yet.

00 / The plain version

A puzzle, a speed limit, and a claim.

The puzzle. Set the switches so every rule holds. How many ways can you do it? That’s SAT, and scheduling, chip checking, and package installs all turn into it.

The speed limit. Every switch doubles the settings to check. At 300 switches there are more settings than atoms in the universe. Clever search shrinks the doubling, but the bet since 2001 (ETH) is that you can never escape it.

The claim. Fix a few shared numbers and the puzzle always falls apart into small pieces. Count each piece, multiply, and skip most of the doubling. Nobody outside the authors has checked that “always” yet.

01 / How we got here

Two strands, growing toward one question.

Solvers have always found shortcuts in sub-problems on many puzzles. The paper claims the shortcut is always there. Its first step is a branching split (sparsification), and its engine is the algebra strand (§1.1.4, §1.1.6).

02 / The claim, in its own words

What it says. What it says it doesn’t.

Math is minified code, so each claim comes with its translation. Check them against the PDF.

Evidence status, as of October 27, 2026:

A preprint, credited only to “OpenAI”. Not peer-reviewed.
No implementation, benchmark, or formal proof is reported in the paper.
One corollary’s context cites another OpenAI preprint from September 2026, which is also unreviewed.
We have not found an independent check of the proof. If you find one, that’s new evidence: update.

Before · the bet (ETH, 2001)

No shortcut escapes doubling.

math 2^Ω(n)

# for EVERY algorithm, some puzzle forces
steps(n) >= 2 ** (c * n)   # some c > 0

A conjecture, never proved. Whole fields built “this is probably optimal” results on it.

Paper p.4 · [IP01]

Claimed · Theorem 1.1

Counting, with a shrinking cost per switch.

math 2^{O_k(n log log n / √log n)}

L = log(n)
steps(n) = 2 ** (c * n * log(L) / sqrt(L))
# c depends on clause width k. Not given.

Exact counts, deterministic, small memory. If true it also topples SETH, Gap-ETH, NSETH, and #ETH.

Paper p.2, p.4–5

Its own limits

What it says it doesn’t do.

✕ P = NP. Shrinking isn’t polynomial.
✕ Free speedups for all of NP. The gain gets lost when you translate other problems into SAT (p.2).
✕ Unlimited rule size. Only for rules of a fixed size (p.5).
✕ Every hardness result. Some still stand on other assumptions (p.5).

Paper p.2, p.5

03 / Check the number

“Subexponential” is not the same as “fast.”

The claimed cost has a hidden constant c that the paper never gives. Guess first, then move it.

Predict first

1,000 switches, generous c = 1. Does it beat the best counter we already had?

Switches n

Hidden constant c

# what the chart plots
def doublings_per_switch(n, c):
    L = log(n)
    return c * log(L) / sqrt(L)  # brute force: 1.0

Cost per switch, in doublings · lower is faster

Brute forceBest before (2026)Claimed, your c

Natural logs, as in the paper. A polynomial factor is left out, and the paper doesn’t give it either. The sparse curve covers puzzles with a bounded number of rules per switch, which includes the hardest random ones.

04 / The claim ledger

File every claim by its evidence.

Each node asks you to predict what the paper says, then shows you what it says and where. A full node means you’ve predicted it. A bright one means you matched the paper. Speculation stays speculation however many arrows point at it.

●Theorem (claimed proof)◐Corollary the paper asserts◆Open question✧Speculation

CLAIM → CONSEQUENCES → OPEN → SPECULATION

05 / Sci-fi, labelled as sci-fi

What if it’s right? Where could it lead?

Everything in this section is speculation. That’s not an insult. Research directions usually start as stories about what might be true, and they become research when someone writes down the first step precisely enough to fail. Each rung and card below tries to do that: what it would take, the closest real precedent, and what would tell you it’s a dead end.

The long road

From here to P = NP, one rung at a time

Walls any path must get past

Relativization (Baker, Gill & Solovay, 1975). A technique that works the same way relative to every oracle can’t settle P vs NP, in either direction.

Algebrization (Aaronson & Wigderson, 2008). This extends the relativization wall to algebraic techniques, again in both directions. That’s the one that matters here, because this paper’s method is algebraic. Does it algebrize? That’s a precise, answerable first question.

Natural proofs (Razborov & Rudich, 1994). This wall blocks a broad family of lower-bound arguments, so it applies on the P ≠ NP side.

Plot twist

Faster SAT algorithms are also the best route anyone has found toward P ≠ NP. Ryan Williams showed in 2011 that a SAT algorithm even slightly better than brute force for a circuit class implies lower bounds against it, and used that to prove NEXP ⊄ ACC⁰. The paper’s Corollary 1.4 is a result of exactly that kind. The same algorithm could turn out to be a step toward either answer.

Most complexity theorists expect P ≠ NP. Sci-fi that says so is better sci-fi.

Research questions this opens

Six places to point an agent

06 / Your gate

Which of these did you nearly do?

Tick the ones you caught yourself starting. Then write the one that isn’t here, worded so the next person could catch it.

Read a preprint’s title as a result.“The Exponential Time Hypothesis is False” is the claim being made, not a finding anyone has confirmed. Read “subexponential” as “fast.”Asymptotic notation hides the constant. Here the constant sits in the exponent and is never given. Took the lineage for the proof.A good story about where a result came from explains why it was reachable. It doesn’t tell you whether the proof holds. Counted a removed lower bound as a new algorithm.If ETH falls, edit distance has one less reason to be hard. It doesn’t get any faster. Trusted a citation without opening it.Corollary 1.2’s hardness context cites [Ope26], another unreviewed OpenAI preprint. Let your agent summarise instead of quote.A summary of a 67-page proof that cites no page numbers is a vibe, not a reading.

07 / You made it to the bottom

This is what Vibe Research teaches.

Predict before you look. Check a number against the thing that produced it. Sort claims by their evidence, and turn the mistakes you catch into a gate. Vibe Research is a cohort that takes one question all the way through a research cycle with your own agent.

See Vibe Research →