Claim ledger

The named internal amplitude module is constructed at I2. & XIV-I@1, thm:I2, lines 1288–1378. & Finite fixed retarded-pole module; both placements; exact finite remainder. & Untested reconstruction with retained residual variables. & Internal frequency estimates; no asserted target transverse degree. & Copied input\ (source: constructed at I2). & A single-Lagrangian symbol theorem, a joint characteristic map, or quantum admission.

The fixed retarded pole is an exact presentation of an existing internal line. & XIV-I@1, prop:pole, lines 726–826. & $(\lambda -i0{)}^{-1}$ with its fixed delta contribution. & Nonzero characteristic-sheet charts. & Internal Fourier representation. & Copied input; elementary chart identity also checked in Section sec:pole. & A new graph regulator, adjustable characteristic counterterm, or characteristic prescription for the joint target.

The common precomposition sum exists, but the joint map is unresolved at I3. & XIV-I@1, thm:I3, lines 1459–1548; thm:release, lines 1729–1814. & $K_{47}+K_5+K_6+K_8+K_9$, with grouped cross-lines still to be composed. & Canonical admissible domain versus tests meeting $N$. & Required quantum target not admitted. & Copied input\ (source: unresolved at I3). & That internal estimates prove the final product, or that the canonical domain is automatically the entire complement of $N$.

A presentation-level map descends exactly when it annihilates the reconstruction kernel. & XIV-J@1, prop:descent, lines 813–846. & Linear reconstruction $\mathsf{Rec}$. & Presentations and their reconstructed image. & Order-independent linear algebra. & Proved here; source result recorded as predecessor input. & Uniqueness on a larger carrier than $\mathrm{im}\mathsf{Rec}$, or descent across $N$ from off-characteristic agreement alone.

$q{\delta }^{\prime }(q)+\delta (q)=0$ gives a nontrivial null presentation. & XIV-J@1, lem:null, lines 853–883. & Adapted internal amplitude chart. & Distributional reconstruction. & Presentation-frequency degree. & Proved here. & That the highest polynomial degree is an intrinsic reconstructed symbol, or that XIV-I's estimates are invalid.

The supported-sector reference is constructed away from the characteristic locus. & XIV-J@1, thm:reference, lines 1215–1299. & $K_{\mathrm{supp}}=K_6+K_8+K_9$ only. & $U\setminus N_U$. & Partial grouped quantum reference; no full admission. & Copied input\ (source: constructed on its stated domain). & The full six-branch map, either characteristic $K_5$ composition, or characteristic composition of $K_{47}$.

Supported normal-order-preserving extension has a conditional coefficient interface. & XIV-J@1, thm:conditionalextension, lines 1427–1470. & Finite response-normal jets. & Supported realizations of normal order at most three. & Conditional extension interface. & Copied input; support-explicit interface proved here. & Existence, selected finite part, uniform estimates, or characteristic normalization.