We present a conservative, representation-theoretic reconstruction of the Standard Model as the admissible low-energy realization of an SO(10) unification framework selected by determinant-closure criteria. Working without assumptions about symmetry-breaking dynamics, coupling unification, scalar sectors, or ultraviolet microphysics, we show that the Standard Model gauge group SU(3) × SU(2) × U(1), the chiral fermion content of one generation (including a right-handed neutrino), hypercharge quantization, and anomaly cancellation arise as inherited consequences of restricting a single SO(10) spinor representation. All four-dimensional anomaly conditions, local gauge anomalies, mixed gauge anomalies, mixed gauge–gravity anomalies, and the global SU(2) anomaly are satisfied automatically without introducing additional low-energy chiral exotics. The observed number of fermion generations is treated as an imported result and not re-derived here. The analysis is deliberately structural rather than dynamical: no claims are made regarding fermion masses, Yukawa couplings, flavor hierarchies, symmetry-breaking mechanisms, renormalization-group running, or ultraviolet completion. The result isolates the minimal and conventional representation-theoretic content needed to organize the observed Standard Model as a consistent descent of an admissible SO(10) unification carrier.