Vacuums at the Planck scale

At the Planck scale, a generalized vacuum, as a quasi-Euclidean space with Planck length and symmetry, begins to present a series of new features, thereby defining a physical world with spontaneous particles and quantum constraints. Because of the Planck length, a vacuum is non-commutative with its corresponding Euclidean space, carrying uncertainty, UV cutoff, IR cutoff, and extremely small spaces named Planck units. Due to rotational symmetry, a Planck unit typically exists in two isolated states, the in situ state and the rotational/tangent state in low-dimensional spaces, until the 10D Planck unit connects these two states and the corresponding 10D vacuum becomes a non-trivial one. Further investigation has provided several results, including that the non-triviality lies in a (3+1)D subspace; two long-range interacting forces exist with constants of ~1/137.036 and ~1/1.628E+38; and the 10D Planck unit acts as a stationary electron and a Compton photon in its two allowed states, and it exhibits either an up quark or a down quark when it behaves in an anomalous state with broken dimensional structures. These results reveal the origin of the gravity-and-electromagnetism interaction, and also demonstrate that the entire first generation of Fermions stems from the quantum behavior of the 10D Planck unit. This exploration establishes a BSM approach to acquire the elemental particles of SM theoretically, aiming to lay the foundation for a new GUT.