The remaining sharp construction problem

A successor seeking the original nonlinear observable must provide:

1. a product domain and topology not satisfying all incompatible requirements (Q1)–(Q4);

2. a complete binary product family, including its generated counterterm outputs;

3. reconstruction and classical-presentation descent;

4. the associativity and comparison identities (eq:associativity-equations) and (eq:comparison-equation);

5. mixed time-ordered products based on actual functional support;

6. a compatible quantum gauge differential and the relevant multiple-insertion Ward identities;

7. a normalization catalogue and a specified physical state.

One numerical finite part does not discharge any unproved entry in this list.