Half-Line Free Fermions: Local CAR and Modular Scaling with a Type-Forced Mass-Axis Obstruction半直线自由费米子:局域 CAR 与模流标度,及类型强制的质量轴障碍

Along the scaling axis: wavelet-embedded quasi-free states converge in norm on every finite-mode CAR subalgebra, upgraded to local modular-automorphism convergence on the analytic core. Along the mass axis: a type I∞ / III₁ incompatibility forces the global folium comparison to fail — the obstruction is proved, not conjectured.标度轴上:经小波嵌入的准自由态在每个有限模 CAR 子代数上范数收敛,并升级为解析核上的局域模自同构收敛;质量轴上:I∞ 与 III₁ 的类型不相容强制全局 folium 比较失败——障碍是被证明的,不是猜想。