Proposition: What no longer fails, and what still fails at F0

The following documentary gaps in XV-F's Proposition prop:F0 are removed:

1. the missing local amplitude generators and coefficient class;

2. the missing display of the canonical-domain target recipe;

3. the incomplete and disputed description of the grouped blocks;

4. the missing full list of joint-map clauses and the meaning of a compact test meeting $N$;

5. the factor ambiguity in the stress convention adopted by this patch.

The four patch ledgers are completed, including the explicit boundaries on residual-bundle and contact-role completion.

However, the stronger statement that every owned frozen-object gap now passes the original F0 is not established. In particular:

1. the actual residual output bundle is not identified;

2. the complete common presentation space, image topology, and reconstruction kernel are not recovered;

3. the actual graphwise correction parameters and the presentation-level space $\mathcal{A}$ are not supplied;

4. the remaining inherited coefficient definitions are not fully instantiated.

Consequently no preliminary lift for the actual frozen graph is defined by this patch, and no actual null-defect test is available. Gates F1–F4 are not entered.

Proof. Definition def:amodule reproduces the local coefficient class and generators, giving (i). Definition def:mcirc and (eq:target) give (ii). Equations (eq:blocks)–(eq:Cross) give (iii). Definitions def:mapclass and def:meeting give (iv). Definition def:polarization and Lemma lem:Hessian give (v).

Proposition prop:Gstatus states the residual-codomain boundary. The distinction between the local coefficient module and the complete graph presentation is recorded in Section sec:I, and its topology limitation is explicit in (eq:quotienttopology). Proposition prop:Cstatus proves that the contact templates do not recover their frozen parameters or determine $\mathcal{A}$. The copied response displays leave the coefficient ingredients listed in Table tab:assembled open.

A preliminary lift requires the actual presentation domain, the actual value codomain, and values assigned according to the frozen composition rule. Naming these dependencies and exposing missing parameters does not give those assignments. A null defect additionally requires the actual reconstruction kernel and correction map class. They are not supplied. The F0 stop rule therefore applies, without an analytic obstruction being asserted.