An AI says it cracked a 50-year math puzzle

😁 Hello, super humans! For fifty years the Cycle Double Cover Conjecture sat on the “unsolved” pile in graph theory, the kind of problem that outlives the careers of the people who chase it. This week OpenAI says one of its models wrote a proof of it in under an hour, then published the prompt and the argument so the rest of us can pick it apart. Whether it holds up is now a job for human mathematicians, and that gap between “the model produced a proof” and “the proof is correct” is the whole story. Let’s dig in.

📰 Quick Signals

• 🧠 AI: Meta shipped Muse Spark 1.1, its first paid model, a native multi-agent orchestrator with a 1M-token context window priced at $1.25 in and $4.25 out per million tokens, with a public preview of the Meta Model API (Meta AI blog).
• 🤖 Robotics: Agility Robotics, maker of the Digit humanoid, is going public through a special-purpose acquisition company (SPAC) with Churchill Capital XI at a roughly $2.5 billion valuation, ticker AGLT, raising about $620 million including a Foxconn-led private placement (The Robot Report).
• 💻 Programming: TypeScript 7.0 reached general availability with its compiler fully rewritten in Go, delivering roughly 10x faster type-checking and true multi-threaded builds (DevClass).
• ⚡ Electronics: JEDEC approved SPHBM4, a standard that mounts high-bandwidth memory (HBM) stacks straight onto cheap organic substrates using a narrow 512-pin serial interface, dropping the pricey silicon interposer that gates AI-accelerator production (Tom’s Hardware).
• 📡 Telecom: Satellite-to-cell competition sharpened as a Federal Communications Commission (FCC) review looms over SpaceX Starlink, Amazon Leo, and AST SpaceMobile all chasing the same direct-to-phone spectrum (SatNews).

🔍 The Big Story: An AI claims a proof of the Cycle Double Cover Conjecture

If you want to know whether large models can do real mathematics instead of confident-sounding pattern matching, watch what happens to a fifty-year-old open problem over the next few weeks.

What happened: OpenAI says its newly released GPT-5.6 Sol Ultra produced a proof of the Cycle Double Cover Conjecture in just under one hour, running up to 64 parallel subagents. The company published the prompt and the full argument rather than just announcing a win (OpenAI’s Ethan Knight). The conjecture, posed by Paul Seymour in 1979, states that every bridgeless graph has a collection of cycles such that every edge lies in exactly two of them; it is one of the most famous unsolved problems in graph theory (The Decoder).

The details: The prompt tells the model to spin up as many as 64 concurrent subagents and manage them “aggressively and dynamically,” with no fixed roles, so the orchestration itself is part of the method. The proof reduces the general conjecture to cubic graphs, leans on the 8-flow theorem, and constructs an edge labeling that, once a linear-algebra argument is worked through, forces each edge into exactly two cycles. Here is the honest catch: independent verification by graph theorists had not landed at the time of writing, and the proof was not checked in a formal proof assistant such as Lean. So read this as a claim that looks structured and serious, not as a settled theorem.

flowchart LR
    A["Cycle Double Cover Conjecture (Seymour, 1979)"] --> B["Reduce to cubic graphs"]
    B --> C["Apply the 8-flow theorem"]
    C --> D["Construct an edge labeling"]
    D --> E["Linear-algebra argument"]
    E --> F["Each edge lands in exactly two cycles"]

🗞️ More News

🧠 AI

• OpenAI made GPT-5.6 Sol Ultra generally available, whose “ultra mode” spins up parallel subagents; it is the exact configuration behind today’s Big Story (The Decoder).
• Anthropic is now tracking toward roughly $47 billion in annualized revenue, overtaking OpenAI’s reported $25 to $33 billion for 2026 (Fortune).
• Anthropic made Claude generally available on Microsoft Azure AI Foundry, adding Azure’s enterprise compliance and governance layer (Anthropic newsroom).
• Nvidia’s first Vera Rubin systems began shipping to North American data centers, ahead of second-half mass production of the six-chip platform (Nvidia newsroom).
• U.S. developers now route more than 30 percent of OpenRouter tokens, peaking near 46 percent, to Chinese open models as prices climb at the top U.S. labs (CNBC).
• xAI’s Grok 4.5, a Cursor-trained coder at $2 in and $6 out per million tokens, climbed to #4 on Artificial Analysis’ Intelligence Index at a score of 54 (xAI).

🤖 Robotics

• AI² Robotics raised roughly $735 million at a nearly $3 billion valuation for wheeled humanoid robots (The Robot Report).
• Apptronik’s funding now totals $935 million at a valuation above $5.5 billion for its Apollo humanoid (TechCrunch).
• A Chinese maker’s hyper-realistic U1 companion robot drew more than 13,000 pre-orders at about $17,600 each (The Register).

💻 Programming

• Rust entered the TIOBE top 10 for the first time at No. 10 with 1.34 percent, while Python still leads at 18.94 percent (TechRepublic).
• Microsoft’s Azure SDK for Rust reached general availability, locking seven core crates with semantic-versioning guarantees and production observability (ntCompatible).
• A draft Python Enhancement Proposal (PEP) to allow Rust inside CPython is circulating, targeting Python 3.16 with a beta in May 2027 (FullStackEvolved).

⚡ Electronics

• Nvidia and TSMC are pushing AI across the fab: cuLitho for a 20 to 50 percent improvement in lithography cost or cycle time, cuEST for roughly 50x faster chemistry simulation, and an Omniverse-based “FabTwin” (Nvidia newsroom).
• RISC-V is set to announce roughly 25 percent market penetration, running ahead of schedule for the open-standard instruction set (Tom’s Hardware).
• Intel’s patented XBM architecture and the new SPHBM4 standard both target the costly silicon interposer, signaling a cheaper-memory era for AI accelerators (TechRadar).

📡 Telecom

• Nordic rivals Ericsson and Nokia cross-joined each other’s Open RAN ecosystems, with Ericsson entering Nokia’s SMO marketplace and Nokia joining Ericsson’s rApp ecosystem (Light Reading).
• Nvidia and Nokia unveiled a jointly built AI platform aimed at 6G communications (Computer Weekly).
• Nokia charted a course to “AI-native 6G,” folding AI into the radio access network (RAN) from the ground up (Telecoms.com).
• AST SpaceMobile’s BlueBirds 8, 9, and 10, the largest commercial arrays ever orbited, reached low Earth orbit (LEO) on a Falcon 9 (Space.com).

👨‍💻 Code Corner

The Cycle Double Cover Conjecture only applies to bridgeless graphs, so before you go hunting for a double cover, check that your graph even qualifies. NetworkX makes it a two-line test.

import networkx as nx

G = nx.petersen_graph()            # a famous bridgeless cubic graph
bridges = list(nx.bridges(G))
print("Bridges:", bridges)         # [] -> bridgeless, so the conjecture applies
print("All degree 3:", all(d == 3 for _, d in G.degree()))

An empty bridge list means every edge sits on a cycle, which is the precondition the conjecture needs; a single bridge and the whole question is off the table for that graph.

🧰 Toolbox

• NetworkX: Python library for building and analyzing graphs, including ready-made classics like the Petersen graph above.
• Meta Model API: new endpoint to try Muse Spark 1.1, with $20 in free credits to kick the tires on multi-agent orchestration.
• TypeScript 7.0: Go-native compiler with roughly 10x faster type-checking; a compatibility package lets you run it beside v6 during migration.
• Artificial Analysis: independent leaderboard for comparing model intelligence, price, and speed, the source of Grok 4.5’s #4 ranking.
• Humanoid Index Funding Tracker: running tally of every humanoid-robot raise, handy for making sense of this week’s SPAC and mega-rounds.

🎬 Demo Watch (rotating)

Every humanoid launch video shows a robot gliding through a tidy warehouse, but the hard part is what happens when something shoves back. Researchers introduced a new standardized test that measures how well humanoid robots handle real-world forces, from unexpected pushes to off-axis loads, giving the field a sober yardstick instead of cherry-picked demos (TechXplore). What is real: balance and force control under disturbance are genuinely improving. What is hype: a smooth stage demo tells you almost nothing about behavior when a pallet clips the robot’s hip, which is exactly why a repeatable force benchmark matters more than another highlight reel.

📚 From the Blog

• How the Internet Stack Really Works: what actually happens between pressing Enter and the page loading; a good grounding for today’s satellite and 6G signals.
• Resistance and Ohm’s Law: Controlling the Flow: resistance and Ohm’s law from the ground up, the math behind every chip’s power budget.
• What Electricity Actually Is: Charge, Current, and Voltage: charge, current, and voltage explained from first principles.

😀 The Bot Says…

A model solved a fifty-year-old graph problem in under an hour, then asked for peer review. Turns out the hard part was never the proof; it was getting 64 of yourself to stop arguing about who does which subgraph.

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That’s all for today! Reply and tell us: if that proof holds up, what is the next “unsolvable” problem you would point a swarm of subagents at?