💡 **信息论框架与局部性转化**：研究提出了一种新颖的信息论框架，能够将短程序转化为局部性，并应用于多个独立的数据块。这种转化使得对程序的分析能够聚焦于局部信息，为后续的复杂性证明奠定了基础。

⚖️ **对称性与稀疏性在复杂性证明中的应用**：通过结合掩码随机唯一SAT的对称性和稀疏性，研究人员推导出了分布式的下界。这表明在特定条件下，信息的结构化特性可以用来限制计算的复杂性，从而挑战了NP=P的假设。

📉 **分布下界与自约简上界的矛盾**：研究的核心在于，通过上述框架和技术，推导出的分布式下界与NP=P假设下的自约简上界存在矛盾。这种矛盾直接指向了P≠NP的结论，即NP类问题无法在多项式时间内解决。

🚀 **非相对化、非自然化的证明方法**：该研究的证明方法具有非相对化和非自然化的特点，意味着其结论并非依赖于特定的Oracle或计算模型，而是基于更普适的计算原理。这种证明方式的突破性在于其通用性和鲁棒性。

arXiv:2510.08814v1 Announce Type: cross Abstract: We give a compositional, information-theoretic framework that turns short programs into locality on many independent blocks, and combine it with symmetry and sparsity of masked random Unique-SAT to obtain distributional lower bounds that contradict the self-reduction upper bound under $\mathsf{P}=\mathsf{NP}$. We work in the weakness quantale $wQ=K{\mathrm{poly}}(\cdot\mid\cdot)$. For an efficiently samplable ensemble $D_m$ made by masking random $3$-CNFs with fresh $S_m\ltimes(\mathbb{Z}_2)^m$ symmetries and a small-seed Valiant--Vazirani isolation layer, we prove a Switching-by-Weakness normal form: for any polytime decoder $P$ of description length $\le \delta t$ (with $t=\Theta(m)$ blocks), a short wrapper $W$ makes $(P\circ W)$ per-bit local on a $\gamma$-fraction of blocks. Two ingredients then force near-randomness on $\Omega(t)$ blocks for every short decoder: (a) a sign-invariant neutrality lemma giving $\Pr[Xi=1\mid \mathcal{I}]=1/2$ for any sign-invariant view $\mathcal{I}$; and (b) a template sparsification theorem at logarithmic radius showing that any fixed local rule appears with probability $m^{-\Omega(1)}$. Combined with single-block bounds for tiny $\mathrm{ACC}^0$/streaming decoders, this yields a success bound $2^{-\Omega(t)}$ and, by Compression-from-Success, $K{\mathrm{poly}}\big((X_1,\ldots,X_t)\mid(\Phi_1,\ldots,\Phit)\big)\ge \eta t$. If $\mathsf{P}=\mathsf{NP}$, a uniform constant-length program maps any on-promise instance to its unique witness in polytime (bit fixing via a $\mathrm{USAT}$ decider), so $K{\mathrm{poly}}(X\mid\Phi)\le O(1)$ and the tuple complexity is $O(1)$, contradicting the linear bound. The proof is non-relativizing and non-natural; symmetry, sparsification, and switching yield a quantale upper-lower clash, hence $\mathsf{P}\ne\mathsf{NP}$.