AI Coding Live News — Real-Time 𝕏/Twitter Updates & Breakthroughs

Physical Superintelligence@psipbc·Collected 3d ago

👀36

🔥94

PSI Announces Aaronson–Ambainis Conjecture Proof: Non-Public Anthropic Model, Lean Formalization Open-Sourced

On 2026-11-06, Physical Superintelligence (PSI, @psipbc) said its internal research system, running non-public Anthropic model instances, produced a complete proof of the Aaronson–Ambainis conjecture (open since 2008) on day three, accepted by Lean, then improved the result twice. The research page and Lean 4 formalization repo are public. Vendor wording; no journal peer review yet; the README still asks humans to check that the formal statement matches the printed conjecture.

Key Takeaways

Sources: PSI research page 2026-11-06 + @psipbc original post + GitHub physical-superintelligence/aaronson-ambainis
Claim: complete proof on day three, accepted by Lean; two later improvements also Lean-accepted (vendor wording)
Implication: if the conjecture holds, quantum machines get at most polynomial speedups on random unstructured inputs; PSI now calls it a theorem
Checkability: public Lean 4.33/Mathlib repo; four main theorems with no sorry/extra axioms; README still leaves statement fidelity to human readers
Limits: Anthropic model unnamed, no journal peer review, paper prose not machine-checked — cite as vendor claim

Read full story

Linked Models & Agents:

🌐 PSI 🌐 Anthropic

#PSI#Physical Superintelligence#Aaronson-Ambainis#Lean#Anthropic#quantum complexity#formal verification#Release

Levent Alpoge@__alpoge__·Collected 14d ago

👀218

🔥88

View on 𝕏 ↗

Anthropic publishes a 3-SAT algorithm found by an internal Claude research model: its paper and Lean 4 proof claim to refute the Exponential Time Hypothesis

Anthropic published the paper "A 2^o(n) Time Algorithm for 3-SAT" (credited to Claude, Anthropic) and an AI-written Lean 4 formalization in its official anthropics/formal-math GitHub repo. It claims a deterministic algorithm solves 3-SAT in 2^o(n) time, which would refute the Exponential Time Hypothesis (ETH). Anthropic's Levent Alpoge said on X that an internal Claude research model found the core algorithm on Oct 16 with 14M output tokens and no human input. The repo stresses the result is purely asymptotic and says nothing about solving formulas in practice.

Key Takeaways

The paper claims a deterministic algorithm decides 3-SAT on n variables in 2^o(n) time, refuting ETH, and solves the harder counting problem #3-SAT in 2^O(n log log n / sqrt(log n)) time
Per Levent Alpoge on X, an internal Claude research model found the core algorithm on Oct 16 with 14M output tokens and no human input; researchers then worked with Claude on the presentation
The Lean 4 proof was written by AI models and pins Lean and Mathlib v4.33.1; the README says it depends only on Lean's three standard axioms, and CI re-checks it with a second independent kernel, nanoda
The repo states the result is purely asymptotic and says nothing about solving formulas in practice; independent review by mathematicians is still pending
A day earlier OpenAI announced its own model-produced refutation of ETH; both claims are now under review

Read full story

Linked Models & Agents:

⚡ Claude⚡ Claude Opus 5.5 🌐 Anthropic

#Anthropic#AI for science#Exponential Time Hypothesis#3-SAT#Lean#formal verification#complexity theory

@huggingface@huggingface·Collected 24d ago

👀80

🔥93

Zero-Human-Label Step Accuracy Jumps from 48.2% to 74.7%: LeanPRM Grounds Process Supervision in Lean 4, While Cornell's CPLM Matches Full Attention at w=128

Tackling step-level verification in mathematical reasoning and in-context copying bottlenecks in Transformers, NYU/UCLA/Stanford researchers introduce LeanPRM (arXiv:2610.17697)—using the Lean 4 theorem prover to automatically label 152K steps across 10,634 natural-language proofs with zero human annotation, boosting Qwen3-4B step accuracy on LeanPRM-Bench from 48.2% to 74.7% (vs. 60.3% for PRM800K). Meanwhile, Cornell University's Copy-Paste Language Models (CPLMs, arXiv:2610.19247) add a lightweight Copy-Paste head (~3% compute overhead) that relieves the LM head gradient bottleneck, boosting LAMBADA accuracy by +2.5-4.0 points and allowing a w=128 sliding-window CPLM to match full-attention perplexity.

Key Takeaways

LeanPRM uses the Lean 4 proof assistant and a syntax-error filter to generate 152K step-level labels across 10,634 proofs with zero human annotation
A Qwen3-4B verifier trained on LeanPRM reaches 74.7% step accuracy on LeanPRM-Bench (vs. 48.2% base and 60.3% with PRM800K) and improves 0.6B-8B verifiers on Hard2Verify and IMO-GradingBench
Cornell's Copy-Paste Language Models (CPLMs) add a ~3%-overhead copy head that relieves the LM head gradient bottleneck, boosting LAMBADA by +2.5-4.0 points and matching full-attention perplexity with a w=128 sliding window

Read full story

Linked Models & Agents:

#LeanPRM#Lean-4#Process-Reward-Model#Qwen3#Copy-Paste-LM#Long-Context

Hugging Face@huggingface·Collected 45d ago

👀81

🔥94

NYU and DeepMind Unveil Framework for Autonomous Math Discovery: Quantifying Intrinsic Theorem Value via 27B Prover

Researchers from New York University in collaboration with Google DeepMind's Rémi Munos have published 'Learning to Discover Interesting Mathematics' (arXiv: 2609.28603). While LLMs excel at proving existing conjectures, autonomous mathematical expansion has been crippled by models spamming trivial or useless lemmas. The authors formulate a metric for intrinsic mathematical interestingness—defined by the compression ratio between proof length and statement brevity. Powered by a specialized 27B proof-difficulty model, the framework autonomously conjectures, verifies, and curates high-value theorems, enabling self-expanding formal mathematical libraries without human-specified goals.

Key Takeaways

Establishes a quantitative mathematical metric for intrinsic theorem interestingness based on proof-to-statement complexity ratios.
Demonstrates robust correlation between intrinsic syntactic interestingness and downstream extrinsic utility across mathematical domains.
Trains a 27B proof-difficulty predictor that outperforms frontier general-purpose LLMs in evaluating proof feasibility.
Reduces Mathlib redundant theorem overlap from 91.9% down to 30.6%, driving 69.4% of exploration into entirely out-of-distribution math.
Preprint, Lean verification harnesses, and autonomous conjecture pipelines released openly on arXiv and Hugging Face.

Read full story

Linked Models & Agents:

⚡ Lean 4⚡ Math Prover 27b🤖 math-discovery-agent 🤖 lean-agent 🌐 nyu 🌐 deepmind 🌐 huggingface

#Mathematics#Lean 4#DeepMind#NYU#Automated Reasoning#AI for Science#Hugging Face