Second Operator (Local Metric and Probabilistic Pruning Operator M_chi o E_local) Rigorous Mathematical Derivation and Specification (Standardized Edition)

This specification succeeds the formal parametric topology generated by the First Operator () and strictly adheres to the No-Dimension Principle. The framework completely eradicates any dependency on background coordinate metrics, embedding spaces, or artificial spatiotemporal metrics, computing discrete evolutionary steps purely via local topological invariants (causal depths and graph-walk statistics).