AI 中文总结
本文构造三维概率元胞自动机等价于费米子QFT，其单粒子激发为Weyl费米子，并揭示各向同性锥与因子化输运的二分法障碍。
AI 中文摘要
Wetterich证明了某些1+1维概率元胞自动机等价于费米子QFT，并将三维构造作为开放问题提出。我们构造了一个：一种分层自动机（"coincube"），其转换块构成Cl(0,3)的实四元数表示，由二元环境场控制，其流送速度超过载体（"新鲜磁带"）——没有比特被重复使用，单粒子系综传播子在每个时刻等于退火Bloch算子。精确结果：步算子对于显式复结构是酉的；局部Grassmann作用被机械地提取；单载体激发是Weyl费米子，具有各向同性的前导锥（斜率比在误差内为1，因子化输运被>=10误差棒排除）；在有限动量下，节点携带奇宇称各向异性c(q)kx ky kz/|k|，在狄拉克分支上被抵消，其间隙为2 arctan[qm/(1-qm)]，而失谐旁观者保持无质量；介质介导相互作用满足Ug = (1-2gq^2) U。障碍：弹道输运仅允许有限速度集；阿贝尔符号规范保留因子化表面；穷举搜索未发现受保护的二分量节点。最后，四元数事件类存在二分法：各向同性锥强制过阻尼——Q = w_0/Gamma <= pi/(2 ln 2)在所有密度下，工作密度下为0.66——而态内酉性强制因子化输运。后选择双边界振幅规避了这一点，在新鲜磁带下所有时刻精确酉，诱导权重正性未决：这里的相对论对象是一种振幅，其概率解读尚未确定。
英文摘要
Wetterich showed that certain 1+1D probabilistic cellular automata are equivalent to fermionic QFTs and posed the 3D construction as an open problem. We construct one: a layered automaton ("coincube") whose conversion blocks form the real quaternion representation of Cl(0,3), controlled by binary environment fields whose streaming outruns the carrier ("fresh tape") -- no bit is consulted twice, and the single-particle ensemble propagator equals the annealed Bloch operator at every time. Exact results: the step operator is unitary for an explicit complex structure; the local Grassmann action is extracted mechanically; the single-carrier excitation is a Weyl fermion with an isotropic leading cone (slope ratios 1 within errors, factorized transport excluded by >=10 error bars); at finite momentum the node carries a parity-odd anisotropy c(q)kx ky kz/|k|, cancelled on the Dirac branch whose gap is 2 arctan[qm/(1-qm)], while off-resonant spectators stay massless; media-mediated interaction obeys Ug = (1-2gq^2) U. Obstructions: ballistic transport admits only finite velocity sets; Abelian sign gauges leave the factorized surface; no protected 2-component node survives an exhaustive search. Finally, a dichotomy for the quaternionic event class: an isotropic cone forces overdamping -- Q = w_0/Gamma <= pi/(2 ln 2) at all densities, 0.66 at working density -- while in-state unitarity forces factorized transport. Postselected two-boundary amplitudes evade this, exactly unitary at all times under the fresh tape, with induced weight positivity open: the relativistic object here is an amplitude whose probabilistic reading is unsettled.
