Requirement: C-I1–C-I9

The inherited free sector is subject to:

1. Admission of every output and required directional descendant.

2. Classical multiplication at order zero.

3. Exact agreement with fixed old products on declared overlaps.

4. Retention of the locked first-stage coefficients.

5. The one common calibrated scalar parent $U_c$, with its declared observation compatibility.

6. No subtraction changing a fixed old product.

7. No requirement that unchanged approximants converge sharply in ${\tau }_{\Sigma }$.

8. Respect for all finite actual-presentation relations.

9. Named continuity domains and proofs, without promoting test-family continuity to actual-stage continuity or hypocontinuity.