Manuscript XX-F@1 · XX-F.tex · theorem · de0bd24f
Theorem: XX-F release
Native prerequisite audit and mathematical release · lines 1676–1735 · proof included or linked
XX-F@1#thm:release
On the identical printed target, XX-F proves:
the coupled classical identity including the original rod contribution;
the explicit first-order Leibniz defect and a same-operator witness excluding the specified unfiltered central-second-jet derivation;
the correction that this centrality defect begins at total on the weighted regular jet algebra, while the free-equation quotient obstruction remains at order ;
weighted decreasing-source Newton existence, uniqueness, decay, and cutoff-error estimates;
the complete null test and exact Newton image for the displayed spatial contact module;
conditional native breaking and correction-image formulas, including changes of the Ward operation;
constrained simultaneous repair and the distinction between unrestricted linear solvability and actual admissibility.
Definition def:entry has not been discharged for the native quantum lapse. Its actual complete breaking, admissible quantum counterterm image, cancellation, interacting identity, and complete quantum remainder are not released.
Native Q3 remains open. Under the proposed entry rule, native Q4 and Q5 remain unentered and unclosed. The specified comparison obstruction is not a universal nonexistence theorem for native completion.
Proof. Item (i) is Lemma lem:classical. Item (ii) is Theorem thm:Leibniz, Lemma lem:witness, and Theorem thm:unfiltered. Item (iii) is Theorem thm:filtered and Proposition prop:quotient. Item (iv) is Theorem thm:weighted. Item (v) is Theorem thm:contactnormal. Item (vi) is Theorems thm:breaking and thm:image. Item (vii) is Theorem thm:repair and Proposition prop:positivity.
The regular comparison does not admit the native noncompact Hessian. The weighted criteria do not select or authenticate a covariance. The breaking formula assumes the missing quantum operation and inventory. The repair theorem assumes their actual maps and defects. None of these assumptions is among the conclusions, proving the stated release boundary.