Corollary: Scalar descent is unrestricted within the parent class

For this sector,

For every fixed real $c$, both calibrated scalar maps in Theorem thm:scalarfactor exist uniquely as algebraic maps on the actual degree-two intermediate blocks.

Proof. Both relation kernels vanish by Theorem thm:qinjective. The actual sharp argument has its unique observation test. Thus the parent pairing descends, and constants belong to ${\mathcal{P}}_{\Sigma }$.