Invariant Spectral Decomposition of the Record-Silent Sector in the Coupled Dirac–Lambda Dynamical System: A Structural Classification of Dark Matter, Light, and Computation

This paper proves a structural decomposition theorem within the Coupled Dirac–Lambda dynamical system (E1–E8). Working entirely at the Tier-1 operator level, it shows that the record-silent sector, defined by the vanishing of the nontrivial stationary projector induced by the dissipative record generator admits a canonical decomposition into exactly three minimal, mutually disjoint, KKT-invariant spectral faces. These three faces are: • A curvature-support face (geometric/Yukawa-decoupled modes that remain outside the effective record band at all KKT-active scales)• A null-coherence face (modes with vanishing dispersion and zero entropy production, corresponding to null propagation)• A recursive-traversal face (modes lying in invariant orbits of a budget-preserving recursion operator) Record-silence is not postulated. It is derived rigorously from the capacity inequality, the Fejér determinant structure of the Lambda budget, complementary slackness, and an explicitly defined effective record band. Mutual disjointness follows from spectral support separation and KKT invariance. Minimality is established under clearly stated irreducibility assumptions for each face. The identification of these three faces with dark matter, light, and computation-as-traversal is a corollary of the spectral structure, not an input assumption. No new particles, fields, or modifications of general relativity are proposed. The result is conditional only on the explicitly listed structural assumptions of the Coupled Dirac–Lambda framework. This work provides a rigorous internal taxonomy of the record-silent sector and demonstrates that, within the stated framework, the three-face decomposition is unavoidable