Ontology V8.3:Clifford Algebra Basis Reconstruction

Addressing four core problems that have long persisted in contemporary quantum field theory and spacetime ontology modeling --- the fixed-basis misconception, the inconsistency of scalar algebra, the conflation of symbolic systems, and the split between low-dimensional and high-dimensional spacetime algebras --- this paper, relying on the constrained field spectral geometry unified theory (Ontology 8.3), fully develops the underlying axiomatic derivation of Clifford algebra, the tensor-product matrix construction, the complete algebraic verification, and the grade-classification analysis. The paper first establishes, through a rigorous Hermitian-conjugation derivation, that a pure scalar complex field cannot self-consistently carry spacetime dynamical operators, and argues that the spacetime algebra must jump to a non-commutative matrix representation space. Then, based on tensor products of Pauli matrices, it explicitly constructs the 2+1 dimensional spacetime so(2,1) Lorentz subalgebra system, writes out all 4×4 explicit matrices, and item by item completes the full rigorous verification of Hermiticity, squared constraints, anticommutation relations, and Lie-algebra commutators. On this basis, it autonomously constructs a completely new 3+1 dimensional spacetime Dirac matrix basis, writes out all explicit γ^μ matrices, item by item verifies the core Cl(1,3) Minkowski Clifford axiom \γ^μ,γ^ν\=2ημνI₄, and fully carries out the step-by-step product derivation of γ⁵=iγ⁰γ¹γ²γ³. The paper introduces the Clifford algebra Grade classification system, decomposes and maps the 2+1 dimensional triple $i,j,k$ onto different algebraic grades, and clarifies the hierarchical relation between the low-dimensional subalgebra and the four-dimensional Clifford algebra. It clearly distinguishes the basis-dependent representation from the spacetime-invariant ontology, corrects the cognitive bias of treating a textbook standard basis as the unique spacetime structure, and, through dimensional analysis and algebraic computation, rigorously distinguishes the dimensionless imaginary unit i from the dimensional Planck constant , thereby disproving the erroneous assumption that the two are equivalent. The results show that the custom Dirac basis is mathematically fully self-consistent and Lorentz-covariantly legitimate, differing from the classical basis only by a similarity transformation. The paper retains all the original derivation steps, explicit matrices, grade tables, and item-by-item checks, providing a rigorous and complete algebraic basis and ontological paradigm for the spacetime geometric encoding, spinor-field dynamical reconstruction, and unified-field-equation upgrade of the constrained field ontology.