0.6 Seven-Layer Truncation: Representation-Theoretic Boundary

Abstract

This article proves that Seven-Layer Truncation () is not a mathematical approximation, but an **insurmountable representation-theoretic boundary**. This boundary is jointly sealed by Bott Periodicity and Interlock. The 128-dimensional anti-commuting residue subspace of Cl(8) is a zero map in Cl(7)-type physical representations; the constrained normal ideal of Cl(9) has no physical counterpart under projection; enters Bott periodic repetition, carrying no independent new geometric information. This article identifies geometric degrees of freedom beyond Seven-Layer Truncation as **Non-Computable Residue**——an irreducible byproduct of Consummate Reproduction (theorem propositions) in the Clifford reduction chain, not new physical entities, requiring no new axioms. **Keywords**: Seven-Layer Truncation; Bott Periodicity; Clifford Algebra; non-computability; representation-theoretic boundary; Interlock