Enhanced Draft v1.8c Formal Definition of the Semantic Dissipation Operator within a Discrete Toroidal Manifold

Abstract This draft formalizes the Semantic Dissipation Operator (SDO) on discrete toroidal manifolds for DTBC, ensuring semantic stabilization via Laplacian decay. Rigorous derivations include the Lyapunov spectrum on tori for instability quantification and Riemannian dissipation metrics for energy bounds. Concise proofs establish exponential decay and stability. The framework enhances geometric-semantic coherence, with falsifiability via spectrum positivity. Explicit definitions of the semantic metric space and a formal statement linking the operator to CORE 3.3 invariant corridors are provided for reviewer clarity Eduardo Filho.