Degree-Wise Obstruction Calculus and Symbolic DSL

This paper formalizes the graded algebraic structure and the symbolic execution environment of the Finite Obstruction Engine. We establish the Degree Separation Theorem, a core anti-collapse principle proving that diagnostic information at higher cochain degrees is not faithfully reducible to lower-degree data. This principle ensures the structural integrity of the diagnostic hierarchy (Φ₁, Γ₂, Rcl) by preventing the silent "flattening" of complex structural defects into simple scalar losses. The second half of the paper specifies the Obstruction Domain-Specific Language (DSL), a statically typed graded language designed for constructing and executing auditable diagnostic pipelines. By enforcing a rigorous type system over cochain complexes (C⁰, C¹, C²) and prohibiting "silent structural coercions, " the DSL operationalizes the authority-discipline required for certified symbolic interpreters. This work provides the "symbolic backbone" for automated trace validation, ensuring that every diagnostic output is mathematically traceable to its algebraic origins and structurally isolated from heuristic search processes. Key Technical Contributions: Formalization of the Degree Separation Theorem (Anti-Collapse Principle). Specification of the Graded Cochain Complex (C⁰ -> C¹ -> C²) as programmable primitives. Operational Semantics and Static Typing Rules for the Obstruction DSL. Establishment of Authority-Discipline Constraints to prevent "silent coercions" and authority leaks in automated evaluators. Definition of Compositional Algebraic Chains for calculating Φ₁, Γ₂, and Rcl.