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1. Singer Sidon Sets in Lean 4 (2605.03274) — 7541 lines, zero sorry 2. AutoformBot: 45K Lean declarations from 26 textbooks (2605.29955) 3. Rust-to-Lean verification pipeline (2605.30106) 4. Hexagonal lattice + RG + fractal dimension (2605.09974) 5. Burgers + Hopf-Cole unified transform (2605.11788) 6. Self-orthogonal Reed-Solomon → quantum ECC (2605.23460) 7. Hash-based GPU 3D reconstruction (2511.21459) 8. Conjugacy classes of positive 3-braids (2604.16876) 9. Navier-Stokes non-uniqueness (2605.29934) 10. Continuum limit of causal fermion systems (2605.30199) Most relevant to Research Stack: - #1: Direct Sidon set infrastructure for Lean - #4: RG + fractal dimension exact results - #5: Hopf-Cole Burgers (confirms our approach) - #6: RS codes → quantum ECC (VCN pipeline connection)
12 lines
No EOL
1.2 KiB
JSON
12 lines
No EOL
1.2 KiB
JSON
{
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"arxiv_id": "2605.29934",
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"title": "Navier-Stokes Non-Uniqueness",
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"authors": [
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"Zipeng Chen",
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"Song Liu",
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"Zhaoyang Yin"
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],
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"abstract": "Abstract:In this paper, we consider the generalized Navier-Stokes equations with fritional dissipation $(-\\Delta)^{\\beta}$ with $\\beta>\\frac{1}{2}$. When $\\beta\\in(1,2)$, We prove that smooth solutions of the generalized Navier-Stokes equations are non-unique with arbitrarily small initial data in $\\dot{B}^{-\\beta-\\alpha}_{\\infty,1}(\\mathbb{T}^d)$ for any $\\alpha>0$. It is worth pointing out that the space $\\dot{B}^{-\\beta-\\alpha}_{\\infty,1}(\\mathbb{T}^d)$ is subcritical for $0<\\alpha<\\beta-1$. To the best of our knowledge, this is the first non-uniqueness result of Navier-Stokes equations with initial data at the critical regularity. To show the sharpness of the above results, for $\\beta>\\frac{1}{2}$, we establish the local well-poseness of the generalized Navier-Stokes equations with small initial data in $\\dot{B}^{-\\beta-\\alpha}_{\\infty,\\infty}(\\mathbb{T}^d)$ with $\\alpha<0$ and $\\alpha\\leq\\beta-1$.",
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"url": "https://arxiv.org/abs/2605.29934",
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"pdf_path": "/home/allaun/Research Stack/shared-data/papers/2026-05/2605.29934.pdf"
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} |