SUB-EXPONENTIAL 3-SAT AND THE BYPASSED AGMAI REVIEW
On October 26, OpenAI researchers Dan Roberts and Greg Brockman announced three internal-model proofs: a full-dimensional resolution of the Kakeya conjecture, the existence half of the four-dimensional Yang-Mills Millennium Problem, and an algorithm beating exponential time for 3-SAT—refuting the Exponential Time Hypothesis that Impagliazzo, Paturi, and Zane formalized in 2001. Hours later Anthropic posted its own independent sub-exponential 3-SAT algorithm from an internal model. Neither lab released weights, prompts, compute figures, or chains-of-thought; OpenAI bypassed the Advisory Group on Mathematics and Artificial Intelligence, forcing Impagliazzo, Paturi, and MIT's Ryan Williams to assemble ad-hoc verification. The governance vacuum is the substance here: capability leaps now occur inside unreleased internal models—OpenAI holds some 700 unpublished manuscripts, half unverified—while Anthropic rewrote its CBRN threshold in May without external review. Middle powers confront a structural asymmetry: the mathematical objects that underwrite their cryptographic security are being revised by private firms whose evidence cannot be inspected, only trusted.
THIRTY-FIVE THOUSAND BANKS ON AN ACCELERATED RSA CLOCK
Geordie Williamson's warning of "a complete kind of restructuring of what difficulty is" has already reached supervisory desks. The UK's Financial Conduct Authority is trialling a supervisory tool with 50 major banks and will issue cryptographic migration guidance to more than 35,000 financial firms next month—not because quantum hardware has arrived, but because the hardness assumptions beneath classical prime-factorization cryptography now rest on a conjecture two frontier labs claim to have refuted. The FCA's instrument is calibrated to a threat model that predates the October proofs: harvest-now-decrypt-later against RSA and ECC. What the agency must now price is subtler—that AI-driven number theory could erode the asymptotic gap between factoring and verification faster than any hardware roadmap anticipated, compressing migration timelines that were already measured in years. Thirty-five thousand firms cannot re-key their estates on a supervisory circular's schedule; the guidance is less a remedy than a disclosure that the timetable has moved.
WHEN POST-QUANTUM KEYS SHATTER SINGLE-PACKET UDP DNS
ICANN CTO John Crain has cut the DNSSEC post-quantum readiness clock from ten years to three or five, and the reason is packet physics rather than mathematics. Post-quantum signatures—Dilithium, Falcon, SPHINCS+—inflate zone files and DNS responses past the 512-byte UDP ceiling, forcing root and top-level resolution into multi-packet fragmentation or TCP fallback. That transition alone, Crain estimates, takes "a few years" to deploy predictably across the resolver ecosystem. The collision is exact: a mathematical shock that undermines the classical hardness assumptions arrives in the same window that the replacement cryptography demands a transport-layer rebuild the internet has not attempted at root scale. ICANN's compressed timeline is a bet that the two clocks—cryptanalytic and infrastructural—can be synchronized. If the October proofs survive vetting, the DNSSEC migration becomes the first test of whether core internet governance can re-key the root faster than the assumptions beneath it dissolve.