Sol Ruck retweeted
We are publishing an update to OpenAI problem #109 Integer multiplication) with another substantial further tightening:
κ = 2⁻⁵⁹ (from OpenAI’s original κ = 2⁻¹⁸²)
Approximately 500 thousand fold improvement over our previous result and a 2¹²³ fold improvement over the original OAI result.
The latest redesigned the finite network to share intermediate computations and scratch space, then tightened the recursion and Gaussian estimates.
We are publishing an update to OpenAI Problem #109 (integer multiplication) with a substantial further tightening:
T(n) = O(n (log n)^(1 − κ)),
With κ = 2⁻⁷⁸ (tightened from κ = 2⁻¹⁸²)
Approximately 570 million fold improvement over our previous result and a 2¹⁰⁴ fold improvement over original OAI result.
Our earlier ceiling applied to a cubic bottleneck in the network. The new witness scales quadratically; we haven't established a new ceiling.
The key was using nonadjacent axis swaps to route around the cubic bottleneck. The original manuscript already supported nonadjacent axis swaps. Using them directly reduces layout routing from O(d²) to O(d) swaps.
Sol Ruck retweeted
Claude was like "holy fuck"
Claude has discovered a previously unknown enzyme system hidden in the DNA of bacteriophages. Beside the enzyme’s gene sits a long array of repeating DNA—a structure that looks somewhat similar to CRISPR.
We don’t yet understand what this system does, but only a handful of known systems share its features, and all of them are able to cut, copy, and paste DNA. Historically, the discovery of such programmable systems has helped revolutionize medicine. CRISPR, for instance, is now the foundation of genetic medicines. But it will take much more work to learn what this system does, and whether it can be put to similar use.
Read more: anthropic.com/news/claude-di…
Sol Ruck retweeted
GPT-6 Astra is world class at Blender and 3 dimensional reasoning. This was a 1-shot game it created, all running in browser.
Sol Ruck retweeted
I love having @SolRuck on the internet.dev team
