ᑕ. (TAA): Exact State Contraction — Definition, Trace Preservation, and Affine-Cost Composition

A proposed exact state contraction term and symbol, defined relative to an observation contract. The paper gives a trace-preservation theorem and an associative affine quadratic-cost composition law with complete state-dependent cross-terms. A companion exact-rational verifier checks the worked example and finite test families. This work names a contract and uses established quotient-state mathematics with attribution to prior work. Supporting paper: Affine Cycles: Exact Cut Defects and Minimal Retained State, DOI 10.5281/zenodo.23931722.