为什么是U(1)×SU(2)×SU(3)？因为1DD、2DD、3DD是不同的几何
Why U(1)×SU(2)×SU(3)? Because 1DD, 2DD, 3DD are different geometries
标准模型的规范群是U(1)×SU(2)×SU(3)。这是粒子物理最核心的结构之一，描述了电磁力、弱力和强力的对称性。
但标准模型没有告诉我们：为什么是这三个群？为什么是1、2、3的组合，而不是别的？这三个群从哪里来？
SAE的核心主张：nDD ↝ SU(n)。每一个DD层对应一个特定的规范对称群，来源是这个DD层的几何结构。
论证分三步。
第一：如果某DD层的内部自由度以复振幅表示，且物理变换保持厄米范数，那么自然的对称群是U(n)（酉群）。这是建模公设：余项在时空中传播，传播是振荡性的，振荡自然编码为复振幅。
第二：对n≥2的DD层，"整体相位"不携带新的内部区分，只保留不同方向间的相对混合——因此有效对称群从U(n)收缩为SU(n)（特殊酉群）。
第三：三个DD层的几何各自不同。1DD是点，最小的区分，对应一个相位自由度。2DD是线，二元极性（两个端点），对应两种内部态。3DD是体，三个空间方向，对应三色结构。
结果：1DD → U(1)（电磁），2DD → SU(2)（弱力），3DD → SU(3)（强力）。
箭头是"结构对应"，不是演绎推导的每个细节都无误差。但对称群的阶数模式——1、2、3——有了先验几何解释。
4DD不是SU(4)。4DD是时空本身——不是内部对称空间，而是整个场的活动背景。4DD的对称是微分同胚不变性，不是Yang-Mills规范对称。
引力不是规范力的原因不是"我们还没有找到正确的量子化方法"，而是结构上的原因：4DD和1DD-3DD是不同类的东西。前三DD给出局域规范扇区（荷守恒），4DD给出跨dual-4DD的全局记账（E₁+E₂=0）。
Anti-GUT预言：没有精确的单一能标规范耦合统一，三种规范力在更高能量下不汇聚到同一点，质子不通过规范介导通道衰变。这与Super-K至今没有观测到质子衰变一致。
The Standard Model's gauge group is U(1)×SU(2)×SU(3). This is one of the most central structures in particle physics, describing the symmetries of electromagnetism, the weak force, and the strong force.
But the Standard Model does not tell us: why these three groups? Why 1, 2, 3 — and not something else? Where do these three groups come from?
SAE's core claim: nDD ↝ SU(n). Each DD layer corresponds to a specific gauge symmetry group, originating from the geometric structure of that DD layer.
The argument has three steps.
First: if a DD layer's internal degrees of freedom are represented as complex amplitudes, and physical transformations preserve the Hermitian norm, then the natural symmetry group is U(n) (the unitary group). This is a modeling postulate: remainders propagate through spacetime; propagation is oscillatory; oscillation is naturally encoded as a complex amplitude.
Second: for n≥2 DD layers, the "global phase" carries no new internal distinction, only preserving relative mixing between different directions — so the effective symmetry group contracts from U(n) to SU(n) (the special unitary group).
Third: the geometry of the three DD layers is each different. 1DD is a point — the minimal distinction — corresponding to one phase degree of freedom. 2DD is a line, binary polarity (two endpoints), corresponding to two internal states. 3DD is a volume, three spatial directions, corresponding to a three-color structure.
Result: 1DD → U(1) (electromagnetism), 2DD → SU(2) (weak force), 3DD → SU(3) (strong force).
The arrows represent "structural correspondence," not an error-free deductive derivation of every detail. But the pattern of gauge group orders — 1, 2, 3 — has an a priori geometric explanation.
4DD is not SU(4). 4DD is spacetime itself — not an internal symmetry space, but the background in which all fields operate. 4DD symmetry is diffeomorphism invariance, not Yang-Mills gauge symmetry.
The reason gravity is not a gauge force is not "we haven't found the right quantization method yet" — it is structural: 4DD and 1DD-3DD are different kinds of things. The first three DDs give local gauge sectors (charge conservation); 4DD gives global accounting across dual-4DD (E₁+E₂=0).
Anti-GUT predictions: no exact single-scale gauge coupling unification; the three gauge forces do not converge at a single point at higher energies; the proton does not decay through gauge-mediated channels. This is consistent with Super-K's continued non-observation of proton decay.