Theorem: Release

For the model fixed in this paper:

1. all internal rows and positive-scale contractions exist, including the inner cone vertices;

2. the advanced root and local weight identities hold;

3. the response and seed adjoints are exact;

4. the first-correction master expansion has the stated mixed-derivative and direct scale-remainder control;

5. $P_2,P_3$, and $C_{5z}$ are explicitly calculated;

6. the complete seven-row leading expansion is (eq:main-expansion), with (eq:main-remainder);

7. the inner-tip cancellation is (eq:tip-cancellation);

8. the complete leading coefficient survives and the raw family fails to converge;

9. incidence-supported corrections fail, and the necessary larger-support condition of Theorem thm:necessary holds.

No complete lower-order singular expansion, subtracted finite part, profile-independent limit, physical identification, or admitted quantum coefficient is established.

Proof. The construction and exact adjoints prove (i)–(iii). Theorem thm:first-correction proves (iv). Proposition prop:vertex-jets and Theorem thm:5z prove (v). Theorems thm:seven and thm:tip-cancellation prove (vi)–(vii). The separated witness proves (viii), independently of the negative-placement asymptotics. Theorems thm:correction and thm:necessary prove (ix).