From the SU(3) Gauge Group to Local Relativistic Spacetime Features

Preliminary note: The mathematical structure presented below is independently derived from the algebraic properties of the SU(3) color gauge group. Whether this structure corresponds directly to real physical spacetime remains an entirely open question. This paper merely records the existence of this structure and suggests that it may offer a reference perspective for exploring the relationship between microscopic and macroscopic geometry. Starting from a color-singlet hadron, this paper introduces a mapping rule termed “perspective breaking,” which simultaneously retains three equivalent su(2) embedding schemes organized by the S₃ Weyl group. In the Cartan decomposition of su(3), the closed so(3) subalgebra is tentatively regarded as the skeleton of spatial rotations, the u(1) generator as the direction of causal evolution, and the coset as the geometric measure of spatial deviation — these physical interpretations are presupposed assumptions and may be replaced. From the information allocation table of the three coexisting schemes, a set of norm square identities is obtained, with the core constraint being 3S = 4 + τ² (where S is the total spatial deviation norm square and τ² is the causal advancement intensity). The constant 4 arises from the trace identity of the Gell-Mann matrices. The entire derivation presupposes no spacetime background, introduces no free parameters, and modifies no existing gauge field equations. This mathematical structure exhibits several properties formally analogous to local relativistic features, including: an algebraic signature structure of the metric, a formal association between inertial and gravitational mass scales, an algebraic expression of a light-cone, an intrinsic upper bound on inertial mass, and a geometric reinterpretation of quark confinement provided by the incomplete coset coverage of a single quark. The physical interpretation of this framework remains open to discussion, and quantitative predictions with physical dimensions are reserved for future work.