Theorem: Scope-corrected definitional release

Using only the supplied XIV-G, XIII-C, XIV-I, and XIV-J texts, and the XV-F manifest as the record being patched:

1. the common local space, selected locus, and residual-testing interface are transcribed;

2. a residual-species codomain family is defined with its unidentified output-fiber parameter exposed;

3. collision coordinates and coherent contact-role formulas are displayed, without identifying their free parameters with the frozen graphwise data;

4. the local retarded-pole amplitude module, its chart-function coefficient class, reconstruction rule, and named coefficient seminorms are transcribed;

5. coefficientwise local reconstruction is $C^{\infty }$-linear, and the displayed chart-function relations are local null presentations;

6. the canonical-domain target, actual grouped block symbol, all five map clauses, and global descent criterion are transcribed;

7. the unique symmetric stress polarization is fixed from the displayed vertex, with its mixed-Hessian factor proved;

8. the canonical-domain complement equality remains refused;

9. the copied response formulas and retarded kernel support are recognized as available, while their remaining coefficient instantiation is left open;

10. no actual preliminary lift, complete null-defect test, characteristic prescription, new analytic estimate, or admitted quantum coefficient is constructed.

The four owned documentary ledgers are complete within these qualifications. The actual frozen graph remains Unresolved at F0. Gates F1–F4 remain unentered.

Proof. Input statement input:G and Proposition prop:Gstatus establish (i)–(ii). Definitions def:collisions, def:Cpart, and def:contacttemplate, together with Proposition prop:Cstatus, establish (iii).

Definition def:amodule, Lemma lem:linearity, Lemma lem:relations, and (eq:seminorms) establish (iv)–(v), with their local scope. Definitions def:mcirc, def:mapclass, and def:meeting, equations (eq:blocks)–(eq:Cross), and Proposition prop:descent establish (vi). Lemma lem:Hessian establishes (vii).

Section sec:domain records (viii). Equations (eq:Rsource), (eq:Rsupport), and (eq:Q)–(eq:K9), with Table tab:assembled, establish (ix). Proposition prop:F0patch establishes (x) and the unchanged F0 stop. No result in the proof assigns a characteristic value to the complete grouped target or supplies an admission line.