Preservation is recorded, not extended by fiat

The coefficient maps in the preceding propositions are the old contraction formulas wherever those formulas are defined. No finite-part choice has been introduced.

A future quantum multiplication is required to reproduce these coefficients on this common domain. The present propositions do not define how to multiply their outputs by every other admitted element.

In particular, they do not assign the value of

after either association. That belongs to the subsequent graph and coherence problem.