Reposted by Marcel Weiß
Marcel Weiß
@marcelweiss.bsky.social
479 followers 402 following 925 posts
Strategy Analyst & Publizist - FAZ, neunetz.com, neunetz.fm, Lieblingsfarbe Blau
Strategy Analyst & Publizist - FAZ, neunetz.com, neunetz.fm, Lieblingsfarbe Blau
![Acknowledgments and Methodology
How the result was originally found and shared with the authors. An Anthropic
employee used an internal research model to investigate open problems in the theory of cryptog-
raphy. One of them was about cryptographic constructions based on the average-case hardness
of Zero-k-Clique [LLV19, AHY25]. Claude was tasked with verifying and improving the construc-
tions, but instead developed this algorithm, first for the average case, then for the worst case.
The session used 16M output tokens with no human input.
Anthropic shared the algorithm with the authors in September 2026 under a confidentiality
agreement, offered compensation, and provided access to the public version of Claude.
Shared algorithm. The algorithm that was shared with the authors is essentially the algorithm
in Section 2, although presented differently and with other numerical parameters. A different
reduction from Exact Triangle to the problem of Section 2 was also shared, although the authors
did not include it here, and instead used known reductions to All-Edges Sparse Triangle, which
suffice and strengthen the connection. The authors derived the data structure version in Section 4
and its connection with Hinted OMv.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:ctphcgyhnllfluywokibtrgb/bafkreib3a3aoeedbwzbh6f7zbc4nbdbqo2sv2rjrtmy2zcddq2z47f5x3u)
![Hacker news comment:
jboggan 12 hours ago | root | parent | prev | next [-] I went back to that Fable chat and showed it this new preprint. It coded up the new constructive algorithm and ran it against the existing test suite, that looks good at least.
It has been super helpful in delineating where the crucial concept came from. The proof is rather simple as graph theory proofs go, but it does seem to use some constructions that would only seem obvious if you had serious physics experience with partition function and calculating energy states that cancel out. *It's not a wholly alien bolt from the heavens, but I can also see how there hasn't been a human being with the broad theoretical physics knowledge combined with the deep graph theory experience in planar graphs to come up with this idea.* (emphasis mine) I don't know, I'm looking for precedents of this formulation and some old papers of Penrose counting the number of edge colorings of this same graph type are coming up, the line of argument at least rhymes.
But I agree with the thought that this sort of progress should not be siloed inside those companies. I propose a tax so that every slop cannon AI video pays for another hour of compute time for advancing mathematics.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:p572wxnsuoogcrhlfrlizlrb/bafkreiae4n5n7qedkgaiuomuvtj3jplg3njoiyulijogc7zsxkpn23gzei)
