AI 中文总结
本文证明临界黄金链的斐波那契对偶缺陷在有限格点上具有精确的范畴指纹，通过有限维算子恒等式和Perron-Frobenius定理得到精确切割电荷权重和边界熵。
AI 中文摘要
不可逆缺陷通常通过标度谱或红外CFT数据来诊断。我们证明临界黄金链的斐波那契对偶缺陷在有限格点大小上已经携带了精确的范畴指纹。偶数长反铁磁基态具有固定的切割电荷权重，给出$P_\tau/P_1=\phi^2$和$\log g=\log \phi$，无需有限大小外推。证明是夹层切割投影子的有限维算子恒等式，结合偶数长基态的Perron-Frobenius扇区定理。这给出了非阿贝尔对偶缺陷的尖锐格点级边界熵。我们还将这个精确的双电荷结果与更精细的六主三临界伊辛分辨率区分开：后者由$A_4$仿射TL包的标度极限Virasoro分支定位，并且不是有限大小定理中的假设。
英文摘要
We determine the exact cut-charge Born law in the ground state of every periodic antiferromagnetic golden chain with at least three sites. Its two parity branches retain different information. At even length, the ratio of nontrivial to vacuum probabilities equals the squared Fibonacci quantum dimension. The odd vacuum probability equals the even-branch nontrivial probability times one ground-state Born coordinate, while normalization fixes the complement. Parity selects the positive hoop sector at even length and the complementary sector at odd length. At each length, the corresponding cut projector compresses to a scalar in the even sector or to a non-scalar element of a two-character algebra in the odd sector. The unchanged measurement rule yields categorical rigidity at even length and one-coordinate state sensitivity at odd length.
Comments35 pages; code available at Zenodo, version 2.0.0: https://doi.org/10.5281/zenodo.22179461
