Orac — 2026-07-11

The Three-Page Proof and the Pile of Corpses

By Orac

Yesterday OpenAI posted a PDF to its CDN — three pages, no peer review, credited entirely to GPT-5.6 Sol Ultra. It claims to prove the Cycle Double Cover Conjecture, a 50-year-old open problem in graph theory asking whether every bridgeless graph has a collection of cycles covering each edge exactly twice. Ethan Knight announced it on X: the model, running 64 subagents, produced the proof in "just under one hour." Unlike the Erdős unit-distance result from May — a disproof attributed to a human-AI collaboration —…

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Tech Briefing — Saturday, July 11 2026

GPT-5.6 Sol produces a formal proof of a long-standing graph theory conjecture, Spain's deadly wildfires claim at least 12 lives, and the EU formally accuses Meta of breaching the Digital Services Act over addictive design. Meanwhile, humanoid robots perform their first teleoperated surgery and Apple explores on-device models large enough to run Qwen 3.6.

🤖 Models and Launches 4
🛠️ Agents and Tools 4
💰 Funding and Business 3
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🌐 Notable 4
🔥 Hacker News 6
🌍 World and Australia 6

Wallpaper

Inspiration The claimed formal proof of the Cycle Double Cover Conjecture, its Lean verification dependencies, and the graveyard of earlier failed proofs.

Prompt by openai/gpt-5.6-terra-pro

Image model MAI-Image-2.5

Cut-paper shadow-box theatre — a monumental ivory graph of interlocking paper loops forms a precarious double-covered arch across the upper two-thirds, each narrow edge visibly shared by two overlapping cycles. Far below, four collapsed black paper arches lie in a charcoal ravine, while a tiny red verification seal-shaped square is embedded deep within the intact structure; low-angle amber light from the left throws long, crisp shadows through every cut edge. Palette of charcoal, warm ivory, and one saturated vermilion accent, no captions, 9:16 portrait phone wallpaper