Links for 2026-03-31
Claude’s Cycles
In late February, Don Knuth reported that Claude Opus 4.6 had surprised him by finding a construction for his open Hamiltonian decomposition problem — for all odd m — after about an hour of guided exploration by Filip Stappers. He titled the paper Claude’s Cycles.
The revised paper (16 March 2026) shows the story grew substantially. For the base case m = 3, there are exactly 11,502 Hamiltonian cycles. Of these, 996 generalize to all odd m > 1, and Knuth proves that exactly 760 valid “Claude-like” decompositions arise from that family. Claude happened to find one of those 760.
The even case, which Claude could not generalize, was then pushed forward by several people working with different models. Ho Boon Suan first used GPT-5.3-codex to generate code for all even m ≥ 8, tested from 8 to 200 and at random values up to 2000, then used GPT-5.4 Pro to produce a 14-page proof of correctness that he said required no editing. An anonymous contributor, “Exocija,” found what may be the simplest odd-m construction — using only s and j, not i — with its proof assembled by bouncing between GPT 5.4 and Claude 4.6 Sonnet. Keston Aquino-Michaels then used GPT and Claude together in a multi-agent workflow to find new constructions for both parities, including a simpler even-case decomposition. Separately, Kim Morrison formalized Knuth’s proof of Claude’s original odd-case construction in Lean, posting the verification on March 4.
So the revised paper presents something striking: not just one AI finding one construction, but a broader mathematical workflow in which humans, multiple AI systems, computation, and formal verification all contributed to resolving the problem. The case m = 2 was proved impossible long ago. As Knuth puts it: we are living in very interesting times indeed.
Paper: https://cs.stanford.edu/~knuth/papers/claude-cycles.pdf
AI
The universe is under no obligation to set the clearing price for human labor above 2000 kcal / day.
Nicholas Carlini from Anthropic just showcased Claude autonomously finding and exploiting zero-day vulnerabilities. In one example, Claude found the first-ever critical security vulnerability in Ghost (a CMS with 50,000 GitHub stars)—a blind SQL injection that allowed the AI to write a script to steal production admin API keys and password hashes. Even more impressively, it also found a completely different, highly complex vulnerability in the heavily hardened Linux kernel (a heap buffer overflow in the NFS daemon) that had gone unnoticed by human researchers since 2003. https://www.youtube.com/watch?v=1sd26pWhfmg
Stanford University fine-tuned π0, a VLA model pretrained entirely on manipulators, to fly a drone that picks up objects, navigates through gates, and composes both skills from language commands. https://airvla.github.io/
New paper for Tinsghua and Shenzhen says, what if AI itself runs the harness, rather than defining it in code? Given a natural language SOP of how an agent should orchestrate subagents, memory, compaction, etc., we can just have an LLM execute that logic! (And AI could design that SOP dynamically and depending on the task too) https://arxiv.org/abs/2603.25723
Meta-Harness: End-to-End Optimization of Model Harnesses [PDF] https://yoonholee.com/meta-harness/paper.pdf
AIRA_2: Overcoming Bottlenecks in AI Research Agents https://arxiv.org/abs/2603.26499
PivotRL: High Accuracy Agentic Post-Training at Low Compute Cost https://arxiv.org/abs/2603.21383
Effective Strategies for Asynchronous Software Engineering Agents https://arxiv.org/abs/2603.21489
Coding Agents are Effective Long-Context Processors https://arxiv.org/abs/2603.20432
PRBench: End-to-end Paper Reproduction in Physics Research — All agents exhibit a zero end-to-end callback success rate. https://arxiv.org/abs/2603.27646
AI might actually fix the information environment by putting expert knowledge in everyone’s hands https://www.conspicuouscognition.com/p/how-ai-will-reshape-public-opinion
Building Political Superintelligence https://freesystems.substack.com/p/building-political-superintelligence
“The next intelligence explosion will not be a single silicon brain, but a complex, combinatorial society specializing and sprawling like a city.” https://arxiv.org/abs/2603.20639
AI drones might force governments to become police states to survive. https://www.thenewatlantis.com/publications/a-shakeup-is-coming-for-the-nation-state
Mathematical methods and human thought in the age of AI https://terrytao.wordpress.com/2026/03/29/mathematical-methods-and-human-thought-in-the-age-of-ai/
HorizonMath: Measuring AI Progress Toward Mathematical Discovery with Automatic Verification https://arxiv.org/abs/2603.15617
Eli Lilly reaches $2.75 billion deal with Insilico to bring AI-developed drugs to the global market https://www.cnbc.com/2026/03/29/eli-lilly-reaches-deal-to-bring-ai-developed-drugs-to-global-market.html
Microsoft is introducing multi-model intelligence in Researcher https://techcommunity.microsoft.com/blog/microsoft365copilotblog/introducing-multi-model-intelligence-in-researcher/4506011
Memristor demonstrates use in fully analog hardware-based neural network https://techxplore.com/news/2026-03-memristor-fully-analog-hardware-based.html
‘I no longer knew how to work without it’: DeepSeek outage cuts off millions https://www.scmp.com/tech/big-tech/article/3348345/deepseek-outage-leaves-millions-cut-and-sparks-complaints-rivals-gain-ground
Quantum Computers and Cryptography
Google Quantum AI’s new whitepaper argues that quantum attacks on the elliptic-curve cryptography used by Bitcoin and Ethereum may require far fewer resources than many people assumed. For secp256k1, the authors report Shor-algorithm circuits using either about 1,200 logical qubits and 90 million Toffoli gates or about 1,450 logical qubits and 70 million Toffoli gates, and they estimate that under favorable superconducting-hardware assumptions these attacks could run in minutes with fewer than half a million physical qubits. The most novel part is their disclosure method: instead of publishing the full attack optimizations, they provide a zero-knowledge proof showing that they really do possess a circuit of the claimed size for the key elliptic-curve point-addition bottleneck, allowing outsiders to verify the resource estimate without handing would-be attackers a full blueprint. For Bitcoin, the paper’s big implication is that sufficiently fast “fast-clock” quantum machines could eventually enable “on-spend” attacks, where a public key exposed during a transaction broadcast is cracked before confirmation, while older exposed keys and dormant coins remain an even bigger long-term target; the authors therefore argue that migration to post-quantum protections should begin urgently. [PDF] https://quantumai.google/static/site-assets/downloads/cryptocurrency-whitepaper.pdf
Oratomic’s paper makes the complementary claim that the physical-hardware cost of cryptographically relevant Shor attacks may also be much lower than standard surface-code estimates suggest, at least for neutral-atom machines with reconfigurable connectivity and high-rate qLDPC-style error correction. The authors say Shor’s algorithm could in principle run with as few as 10,000 atomic qubits, and that an architecture with roughly 26,000 physical qubits might solve ECC-256 discrete logs in around 10 days under a 1 ms stabilizer-cycle assumption, with RSA-2048 taking much longer. The point is not that Bitcoin can be broken tomorrow—this is still a theoretical resource estimate with major engineering hurdles—but that the hardware gap may be shrinking faster than expected if nonlocal neutral-atom architectures and better codes work as hoped. For Bitcoin and similar systems, that strengthens the broader message from the Google paper: even if neutral atoms are too slow for near-real-time mempool attacks, they could still threaten long-exposed public keys and dormant funds, reinforcing the case for post-quantum migration well before such machines actually exist. https://arxiv.org/abs/2603.28627
Automated near-term quantum algorithm discovery for molecular ground states https://arxiv.org/abs/2603.26359
Physics
Causality optional? Testing the “indefinite causal order” superposition https://arstechnica.com/science/2026/03/getting-formal-about-quantum-mechanics-lack-of-causality/
“I Built Feynman’s Reverse Sprinkler To Solve 140 Year Old Mystery” https://www.youtube.com/watch?v=G5DzkVI4EQE
For decades, the original paper which introduced something called the see-saw mechanism for neutrino mass was overlooked in favour of subsequent papers by more famous physicists. https://blog.inspirehep.net/2013/06/sleeping-beauty/
Psychology and Neuroscience
Open Access Book: Decision Making under Deep Uncertainty — From Theory to Practice https://link.springer.com/book/10.1007/978-3-030-05252-2
“Slack”—defined as the absence of binding constraints or having free capacity/space—is essential for any system or agent to be effective. https://www.lesswrong.com/posts/nQd64RC5vXyqiFZLD/slack-in-cells-slack-in-brains
Thalamic activation of the visual cortex at the single-synapse level https://www.science.org/doi/full/10.1126/science.aec9923
A neural algorithm for a fundamental computing problem [published in 2017] https://www.science.org/doi/10.1126/science.aam9868
Cerebellum as a kernel machine: A novel perspective on expansion recoding in granule cell layer [published in 2022] https://pmc.ncbi.nlm.nih.gov/articles/PMC9815768/
Politics
Against The Concept Of Telescopic Altruism https://www.astralcodexten.com/p/against-the-concept-of-telescopic
How Viktor Orbán’s Hungary Eroded the Rule of Law and Free Markets https://www.cato.org/policy-analysis/how-viktor-orbans-hungary-eroded-rule-law-free-markets
Cracks Spread Through Putin’s Power Structure https://foreignpolicy.com/2026/03/27/russia-putin-war-ukraine-dissent-protests-remeslo-internet-shutdown/ [no paywall: https://archive.is/qBNKl]