Declarations

scope. This manuscript continues XIV-C's J2 problem. Its new constructions are the complete smooth-slot derivative ledger, common-variable support comparison, retained-germ reduction, and branch-level fiber identity. It does not claim to solve the joint characteristic extension problem.

scope. ${{\Phi }^{(2)}}_{\mathrm{D}}$ retains its scalar-linear predecessor meaning. The full observable $\mathcal{O}$ contains the scalar-sourced slot once. No entry is changed after the retained test.

of zero statements. The branches proved zero on the chosen kernel germ remain in the global pair. The proofs use support and species, not undefined pointwise evaluations of distributions.

scope. ${\mathfrak{C}}_{\mathrm{part}}$ is unchanged. The conditional characteristic ambiguity proposition adds no member to it and selects no reference extension.

scope. XIV-C supplies the characteristic geometry and its retained monomial diagnostic. XIII-C supplies the inventory, partial contacts, and primitive extensions. XIII-B supplies the tree and retarded convention. XII-E supplies the classical completion and tree kernels. XII-C supplies the source representative. XIV-A and XIV-B are not analytic inputs.

. No successful pdflatex execution, proof-assistant verification, independently executed symbolic computation, independent referee review, or journal acceptance is asserted. All new algebraic calculations are displayed. No numerical residue has been computed.