Rival AI proofs, 155 leaked prompts, and Siri learns to remember

OpenAI published three claimed research results on 26 October, all produced by internal models it has not named. The headline claim is a disproof of the Exponential Time Hypothesis, a conjecture holding that certain logic problems cannot be solved much faster than by brute force. OpenAI also says a model proved the local smoothing conjecture in every spatial dimension of at least two, which it says settles the Kakeya and Stein restriction conjectures, and produced an existence proof for four-dimensional Yang-Mills theory and quantum chromodynamics. Hours later, Anthropic published its own disproof of the Exponential Time Hypothesis.

Anthropic's paper, "A 2^o(n) Time Algorithm for 3-SAT", lists its author as "Claude (Anthropic)" and sits in a public GitHub repository alongside a Lean 4 formalisation. The repository README says an internal research Claude model discovered the result and that AI models wrote the formalisation. It states two theorems: a deterministic algorithm that decides 3-SAT in 2^o(n) time, which refutes the hypothesis, and one that counts satisfying assignments in 2^O(n log log n / sqrt(log n)) time. Anthropic researcher Levent Alpoge said on X that the core algorithm was found on 16 October using 14 million output tokens, with no human input in the discovery itself.

Both labs date their result to 16 October, and Anthropic's paper acknowledges concurrent independent work at OpenAI. The pattern is becoming familiar: roughly seven weeks ago OpenAI announced an AI-generated proposed solution to a Navier-Stokes problem, and about three weeks ago it released hundreds of machine-written mathematical manuscripts. Its public openai/math repository now holds 721 manuscripts across 373 families, with about 42% of top-line results formalised in Lean. Formalisation is the part that matters here, because Lean checks a proof mechanically: Anthropic's repository ships scripts that print which axioms each theorem depends on, and a build that takes roughly eight minutes on 24 virtual CPUs.

None of this is peer-reviewed. Russell Impagliazzo and Ramamohan Paturi of UC San Diego, who proposed the hypothesis, are reviewing the claim with Ryan Williams of MIT, and all three have said their involvement should not be read as certification. OpenAI is withholding the physics material, which an outside group is still assessing, and the Advisory Group on Mathematics and Artificial Intelligence, a body OpenAI itself set up, has publicly asked for immediate release. The Yang-Mills claim covers existence only and not the mass gap, so it does not meet the Clay Millennium Prize conditions. Anthropic's own README says its result is purely asymptotic and says nothing about solving real formulas.

For anyone outside pure mathematics, the practical lesson is not the proof but the plumbing. A machine-checked artifact in a public repository, with pinned toolchain versions and an axiom printout, is a new kind of evidence: you no longer have to take the lab's word for it, you can run the check yourself. That skill is scarce and the volume of AI-generated claims is rising fast. The same logic is spreading to code. Teams that can read a formal specification, reproduce a build and then write down plainly what was and was not verified are going to be in demand, from newsrooms to investors to engineering groups.

Why it mattersTwo of the biggest AI labs are now making frontier research claims that arrive as machine-checkable repositories rather than journal papers. That changes who is able to verify them, and how quickly.

Cloudflare disclosed on 26 October that one of the AI models it hosts had returned other customers' data. Between 27 August and 9 September, 155 responses from @cf/zai-org/glm-5.3 on Workers AI contained fragments of earlier users' prompts and generations. Every affected request was unusually large: all of them carried prompts longer than 681,280 tokens. Cloudflare published the account jointly with the maintainers of SGLang, the open-source inference engine involved, and with the researcher who reported it. Cloudflare says that once its own tests and the researcher's activity were excluded, it found no evidence of deliberate exploitation.

The cause was two faults overlapping. Cloudflare deployed the model advertising a 1,048,576-token context window while its prefill GPU key-value cache pool held only 681,280 tokens. Cloudflare says it knew about the mismatch before launch and expected the engine to reject prompts that did not fit. SGLang did mark over-length requests as rejected and substituted a one-token placeholder, but its admission queues checked whether a request had finished rather than whether it had been rejected, so the request carried on regardless. The decode stage then reserved pages and read stale cache pages left behind by earlier requests, returning HTTP 200 instead of an error.

Gadi Evron of Knostic reported the problem through Cloudflare's HackerOne programme at 23:11 UTC on 8 September. Cloudflare declared an incident at 13:22 the next day, reproduced the leak within 25 minutes, made the model private at 14:00, identified the root cause at 14:35 and had corrected prefill nodes in place by 14:52. A patched deployment went out at 19:04 and the model was public again by 19:40. The prefill pool is now about 2.04 million tokens, roughly twice the context length, and Cloudflare added pre-deployment checks that compare pool size against context length. The underlying engine bug had been filed upstream as SGLang issue #30233 on 6 July.

Cloudflare states that no other model it hosts on Workers AI was affected, because every other disaggregated deployment has a cache pool larger than its context length, so no request could reach the faulty path. The wider problem is not Cloudflare's, though. In its own write-up the SGLang team says default prefill and decode configurations were exposed from the v0.4.x line until v0.5.21, released on 2 October, or v0.5.22 for one of the transports. It also describes a second fault, in which writes from an aborted request can land in cache slots the allocator has already handed to another request, and warns that operators cannot reliably tell from their logs whether past exposure occurred.

That last point is the one to sit with. Anyone running their own inference cluster on an affected version has no log-based way to rule out that their customers saw each other's prompts. SGLang says the fix was not backported, so upgrading is the only route: v0.5.22 or later, plus a router that cancels both halves of a prefill and decode pair when a request is aborted, and an optional cache checksum flag that ships off by default because it costs performance. For the much larger group of businesses that buy a model API rather than run one, the lesson is blunter: tenant isolation is a property of your vendor, not of your code.

Why it mattersThis is a reminder that when you call a hosted model, keeping your prompts away from other customers is work somebody else is doing on your behalf, in software you cannot see. The same bug class sat in a widely used open-source engine for several release lines.

Apple released iOS 27.2 on Monday 26 October, the first major update to iOS 27, and the headline change is that Siri AI now remembers. The assistant can refer back to earlier conversations, so a user can ask again about a restaurant it suggested last week rather than starting from scratch. Memory also arrives in macOS 27.2 and watchOS 27.2, but not visionOS. Alongside it, Siri AI gained access to new personal data: photos attached in Messages, the attendee lists on calendar events, and voicemails, with Apple saying that results drawn from Safari history and the Reading List improve too.

The update also reworks the controls. A redesigned Excluded Apps setting lets users choose in one place which apps Siri, Search and suggestions can reach, where the old App Access setting meant excluding apps one at a time. Siri responses now support selecting and copying part of an answer rather than all of it. Siri AI needs an iPhone 15 Pro or later, remains in beta, and is still unavailable in the EU and mainland China. Five languages were added, also in beta: French, Japanese, Korean, Portuguese and Spanish. Messages gains tappable contextual suggestions for Calendar, Reminders, Notes, Maps, and flights and packages.

Two other changes matter for anyone producing images. Pictures from Image Playground, and some Photos edits made with Extend, Reframe and large Clean Up operations, now carry SynthID watermarks, Google's invisible provenance marker, which can be checked on Google's SynthID Detector site. The update also ships more than 160 security fixes. TechCrunch reports that many were backported to iOS 26, including one originally fixed in iOS 18 back in 2024 that Apple says may have been exploited in an "extremely sophisticated attack" against specific individuals running versions before iOS 27. MacRumors, by contrast, reports that none of the flaws fixed in iOS 27.2 were actively exploited.

The reach is narrower than the headlines suggest. Apple told TechCrunch that around 80% of iPhone owners are still on iOS 26, so most users will not see any of this for months. Siri AI is beta software sitting on a hardware floor of iPhone 15 Pro, which excludes most phones in circulation, and two of the world's largest markets are shut out entirely. There is also an obvious tension in the design: an assistant that remembers past chats and reads voicemails and calendar attendees is more useful precisely because it holds more about you, and the new Excluded Apps screen is the only real brake on that.

That tension is where the work is. Any phone carrying client-confidential material, a lawyer's, a clinician's, a recruiter's, now has an assistant that can read across Messages attachments, calendars and voicemails unless somebody goes in and switches it off, and most people will never open the screen. At the same time, an assistant with memory changes how information gets found: when someone asks their phone to recall a plumber or a clinic, what surfaces is whatever was clean, structured and consistent in their messages, calendar and across the web. Both sides of that, locking it down and being findable, are services someone has to deliver.

Why it mattersAn assistant that remembers and can read voicemails, calendars and message attachments is the most personal data surface most people carry, and it is now on by default for anyone with a recent iPhone who has turned Siri AI on.