From Clifford Algebra through Spacetime Discrete Structures to the Standard Model

Starting from the non-self-consistency of the commutative scalar complex field, this paper establishes the noncommutative matrix algebraic structure of spacetime through Clifford algebra basis review, grade classification, dimensional upgrade, and dimensional reduction projection. On this basis, the paper systematically diagnoses the logical gaps from alge braic ontology to physical dynamics, and provides closure schemes one by one: through the emergence pathway and causal set discrete action, the G1 closure scheme (the tension between time quantization and Lorentz covariance) is given; through Connes’ noncommu tative geometry spectral triple framework, the G2 closure scheme (the derivation gap from Clifford algebra to quantization postulates) is given; through the spectral action principle and heat kernel expansion, the G6 closure scheme (the derivation gap from algebra to dy namical equations) is given; through the minimal dynamical dimension argument, the G3 closure scheme (the necessity of dimensional reduction projection) is given; through Wick rotation and Riemann–Lorentz bridging, the G4 closure scheme (the physical motivation of imaginary time coordinates) is given; through linearity-homogeneity constraints and spectral normalization, the G5 closure scheme (the uniqueness of dimensional upgrade) is given; through Lorentz invariance and the variational principle, the G2d closure scheme (the uniqueness proof of the core equation dx(v)) is given. The full text is divided into eleven parts, forming a complete framework from algebraic basis review to physical dy namics. The lower part implements algebraic ontology as a physical framework capable of carrying dynamics through stray-i contamination diagnosis and Path B correction, Dirac sea positive energy projection, and CP violation analysis. The core conclusions of this paper are limited to the proven scope; open questions are explicitly flagged where they arise (and collected in the final summary), not presented as established results, without extrapolation beyond the evidence.